From 5815838049dac25202dd14ff632afebef38c3342 Mon Sep 17 00:00:00 2001 From: 202310715235 SYABRINA BENING PUTRI <202310715235@mhs.ubharajaya.ac.id> Date: Wed, 19 Nov 2025 13:34:04 +0700 Subject: [PATCH] Upload files to "Regression" First Commit Praktikum --- ...N-Reg-Mulitple-Linear-Regression-Co2.ipynb | 773 +++++++++ ...35_ML0101EN-Reg-NoneLinearRegression.ipynb | 897 ++++++++++ ...0101EN-Reg-Polynomial-Regression-Co2.ipynb | 899 ++++++++++ ...1EN-Reg-Simple-Linear-Regression-Co2.ipynb | 1467 +++++++++++++++++ 4 files changed, 4036 insertions(+) create mode 100644 Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb create mode 100644 Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-NoneLinearRegression.ipynb create mode 100644 Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb create mode 100644 Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb diff --git a/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb new file mode 100644 index 0000000..d12dec3 --- /dev/null +++ b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb @@ -0,0 +1,773 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

\n", + " \n", + " \"Skills\n", + " \n", + "

\n", + "\n", + "\n", + "# Multiple Linear Regression\n", + "\n", + "\n", + "Estimated time needed: **15** minutes\n", + " \n", + "\n", + "## Objectives\n", + "\n", + "After completing this lab you will be able to:\n", + "\n", + "* Use scikit-learn to implement Multiple Linear Regression\n", + "* Create a model, train it, test it and use the model\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Table of contents

\n", + "\n", + "
\n", + "
    \n", + "
  1. Understanding the Data
  2. \n", + "
  3. Reading the Data in
  4. \n", + "
  5. Multiple Regression Model
  6. \n", + "
  7. Prediction
  8. \n", + "
  9. Practice
  10. \n", + "
\n", + "
\n", + "
\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Importing Needed packages\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "import pylab as pl\n", + "import numpy as np\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Downloading Data\n", + "To download the data, we will use !wget to download it from IBM Object Storage.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--2025-10-20 07:43:50-- https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv\n", + "Resolving cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)... 169.63.118.104, 169.63.118.104\n", + "Connecting to cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)|169.63.118.104|:443... connected.\n", + "HTTP request sent, awaiting response... 200 OK\n", + "Length: 72629 (71K) [text/csv]\n", + "Saving to: ‘FuelConsumption.csv’\n", + "\n", + "FuelConsumption.csv 100%[===================>] 70.93K --.-KB/s in 0.002s \n", + "\n", + "2025-10-20 07:43:50 (45.5 MB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n", + "\n" + ] + } + ], + "source": [ + "!wget -O FuelConsumption.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

Understanding the Data

\n", + "\n", + "### `FuelConsumption.csv`:\n", + "We have downloaded a fuel consumption dataset, **`FuelConsumption.csv`**, which contains model-specific fuel consumption ratings and estimated carbon dioxide emissions for new light-duty vehicles for retail sale in Canada. [Dataset source](http://open.canada.ca/data/en/dataset/98f1a129-f628-4ce4-b24d-6f16bf24dd64)\n", + "\n", + "- **MODELYEAR** e.g. 2014\n", + "- **MAKE** e.g. Acura\n", + "- **MODEL** e.g. ILX\n", + "- **VEHICLE CLASS** e.g. SUV\n", + "- **ENGINE SIZE** e.g. 4.7\n", + "- **CYLINDERS** e.g 6\n", + "- **TRANSMISSION** e.g. A6\n", + "- **FUELTYPE** e.g. z\n", + "- **FUEL CONSUMPTION in CITY(L/100 km)** e.g. 9.9\n", + "- **FUEL CONSUMPTION in HWY (L/100 km)** e.g. 8.9\n", + "- **FUEL CONSUMPTION COMB (L/100 km)** e.g. 9.2\n", + "- **CO2 EMISSIONS (g/km)** e.g. 182 --> low --> 0\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Reading the data in

\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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MODELYEARMAKEMODELVEHICLECLASSENGINESIZECYLINDERSTRANSMISSIONFUELTYPEFUELCONSUMPTION_CITYFUELCONSUMPTION_HWYFUELCONSUMPTION_COMBFUELCONSUMPTION_COMB_MPGCO2EMISSIONS
02014ACURAILXCOMPACT2.04AS5Z9.96.78.533196
12014ACURAILXCOMPACT2.44M6Z11.27.79.629221
22014ACURAILX HYBRIDCOMPACT1.54AV7Z6.05.85.948136
32014ACURAMDX 4WDSUV - SMALL3.56AS6Z12.79.111.125255
42014ACURARDX AWDSUV - SMALL3.56AS6Z12.18.710.627244
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" + ], + "text/plain": [ + " MODELYEAR MAKE MODEL VEHICLECLASS ENGINESIZE CYLINDERS \\\n", + "0 2014 ACURA ILX COMPACT 2.0 4 \n", + "1 2014 ACURA ILX COMPACT 2.4 4 \n", + "2 2014 ACURA ILX HYBRID COMPACT 1.5 4 \n", + "3 2014 ACURA MDX 4WD SUV - SMALL 3.5 6 \n", + "4 2014 ACURA RDX AWD SUV - SMALL 3.5 6 \n", + "\n", + " TRANSMISSION FUELTYPE FUELCONSUMPTION_CITY FUELCONSUMPTION_HWY \\\n", + "0 AS5 Z 9.9 6.7 \n", + "1 M6 Z 11.2 7.7 \n", + "2 AV7 Z 6.0 5.8 \n", + "3 AS6 Z 12.7 9.1 \n", + "4 AS6 Z 12.1 8.7 \n", + "\n", + " FUELCONSUMPTION_COMB FUELCONSUMPTION_COMB_MPG CO2EMISSIONS \n", + "0 8.5 33 196 \n", + "1 9.6 29 221 \n", + "2 5.9 48 136 \n", + "3 11.1 25 255 \n", + "4 10.6 27 244 " + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_csv(\"FuelConsumption.csv\")\n", + "\n", + "# take a look at the dataset\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's select some features that we want to use for regression.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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ENGINESIZECYLINDERSFUELCONSUMPTION_CITYFUELCONSUMPTION_HWYFUELCONSUMPTION_COMBCO2EMISSIONS
02.049.96.78.5196
12.4411.27.79.6221
21.546.05.85.9136
33.5612.79.111.1255
43.5612.18.710.6244
53.5611.97.710.0230
63.5611.88.110.1232
73.7612.89.011.1255
83.7613.49.511.6267
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" + ], + "text/plain": [ + " ENGINESIZE CYLINDERS FUELCONSUMPTION_CITY FUELCONSUMPTION_HWY \\\n", + "0 2.0 4 9.9 6.7 \n", + "1 2.4 4 11.2 7.7 \n", + "2 1.5 4 6.0 5.8 \n", + "3 3.5 6 12.7 9.1 \n", + "4 3.5 6 12.1 8.7 \n", + "5 3.5 6 11.9 7.7 \n", + "6 3.5 6 11.8 8.1 \n", + "7 3.7 6 12.8 9.0 \n", + "8 3.7 6 13.4 9.5 \n", + "\n", + " FUELCONSUMPTION_COMB CO2EMISSIONS \n", + "0 8.5 196 \n", + "1 9.6 221 \n", + "2 5.9 136 \n", + "3 11.1 255 \n", + "4 10.6 244 \n", + "5 10.0 230 \n", + "6 10.1 232 \n", + "7 11.1 255 \n", + "8 11.6 267 " + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n", + "cdf.head(9)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot Emission values with respect to Engine size:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Creating train and test dataset\n", + "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set. \n", + "This will provide a more accurate evaluation on out-of-sample accuracy because the testing dataset is not part of the dataset that have been used to train the model. Therefore, it gives us a better understanding of how well our model generalizes on new data.\n", + "\n", + "We know the outcome of each data point in the testing dataset, making it great to test with! Since this data has not been used to train the model, the model has no knowledge of the outcome of these data points. So, in essence, it is truly an out-of-sample testing.\n", + "\n", + "Let's split our dataset into train and test sets. Around 80% of the entire dataset will be used for training and 20% for testing. We create a mask to select random rows using the __np.random.rand()__ function: \n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "msk = np.random.rand(len(df)) < 0.8\n", + "train = cdf[msk]\n", + "test = cdf[~msk]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Train data distribution\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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B4375S2D37sCP7d7NDk9ztWABMGeO/+ik0ymOR3o9FaexwGksIrJeUpIY3tdDrXVVUeH9pREog3J2NjB+vOjk+B5/8UV9mZXHjgXWr/c/npcnRm1Up0+LEZxQTp3ilFZzFS0ZlNnZATs7RGQtIx0dT9u2NSUQVEeCZP/lVmtmvf22XIcnWEdH5dnhue02786P1jnXrg0dR6QX1+wQEUWBI0fC6+gAYtEyIKakpk+X7+gATbEFBaGntOrqtDs6gHhcndL66iu5NsjGEVmFnR0iIgv17Bn+OTIzxf2OHf5re2QoClBZKZ6vZc4cufOpcampcvGycURWYWeHiMhCp04Zf67DIaqZDxggflZHeIwK9fyDB+XOo8ZNmiQXLxtHZBV2doiILCSzgDcQda3NkiVNi5PVER6jQj2/e3e586hx2dly8bJxRFZhZ4eIYp5Z262tUF4uF9epk/fP2dn+i4oHDBDH1Y6QLN8RomACVanWipN9bbJxRFZhZ4eIYlq0J+S75JLQW20TE4GjR8Wuq6IicV9R4b97yukU28gBfR0eRfEeIQomOVnsttKSlyfiANFGGbJxRFZhZ4eIYpbRhHyRVl8fvMOTmCgedzrF9vLx48V9sI5Jfr4Y8bnkEu/jaWnmtHXduuAdHt88O9FYA4koEObZAfPsEEUbmTpRLpcYwQm2OylYQj47HTkidmedOiXW8pSX+3daZHm+R506ARMnmvte1NWJXVcHD4o1OgsXNo3oqCJZA4koENnvb1Y9J6KoEiw7sG8W4FDbsD23W6sJ+ex2ySXAjz+acy51JAgQ65TMfi+Sk4GlS7Vj1BpIWmt9Il0DiSgQdnaIKGoEyw6sTkt5LtiV3YYd7nbtSAknrb6d74Va42jRIu8RHqdTdHTMrIEU65XhyT5cs0NEUUErO3CgLMCy27DD3a4dCYWFYjpoxgwxmjJjhvi5sFDu+Xa/FwsWiKmqxYtF0dDFi8XPZnZ0on0hOkU3dnaIKCromZYCxF/1oRblpqWF3m4dSQ0NYlfUtGnivqFBdGgWLvRf9+JyieMyHZ5QW9Jlt56Hw+kEfv5zoH9/cW/miEusLESn6MXODhFFhXiblvIVaPSmVSvgT3/Sft6iRaFra2ltSQ+UnNBsVo666B3xIwqEnR0iigp6p2J27ACOH9eOPX48dD2oSAg2eqMooYt6ulxiLU8owbakB0pOaCarR130jvgRBcIFykQUFdSpmCNHAncA1O3TeutE2T0S1NAgRmfCsX07kJ4eelFufr7IhROpRbyhRl0cDjHqkpcXOHWATDtj5XOm6MaRHSKKCnqnYuxelCtr2bLwp1jWrZOfHpJNTmgGo6Mueqa9YuVzpujGzg4RRQ09UzHRsChXxqFD5p4vmhblGhl10TvtFSufM0U3dnaIKKrk5wOHD4dXJyoSi3K1eBYmNTtHfTQtypUdTfn+e/FebN2qf7FxNH/OFDtYLgIsF0EUywJlXM7JEV+AVi3K1dseGS1aAI2N+p6zbZu92aFDlewARCdEb6cs0OuKts+ZogPLRRBRs6C1KDfSGXeDZYCW0akTUFWl7zlbt4b/2sLJ3Ox0Ar17a3d2jIw+BZoey88HRo0y3lZq3jiyA47sEMUj2RpbZpEZ5bCSkddWWBhemQeZQqBGyI7sWPl5UmyQ/f7mmh0iijt2ZNwNtTPJanpfmxmZm83YaeYp2GJjZlCmcHEai4jiSji5X8Jhd54X9bVNnw6kpgLV1cGnt2Ry//zpT2Jq7Ztvgk8ZmbnTLNhiY7s+T4ovHNkhorhiV8bdaMjzoijitQ8dqp2/RmZERlGAOXO0C5N262Ze24NlemYGZTIDOztEFFesyLgbqICnr1D5YOwSaKrHyIhMoOmtyZONjaao2bC3bNFOLwAwgzKZg50dIoorZmfcDVTAM9Aoh5oPRu+Wj1atrO0gqfW3PPPXhDMi41mYNDFRLGbWQ32tL74IDBkSOtMzMyiTGdjZIaK4MmAA0LatdkxKilzGXb2LeD/+WPt806cDU6YAw4eL+7Nngb/9TTxm9YiQ51SP0REZwL8w6fXXa8enpXn/rLcwKTMokxm49Rzcek4UTxoagORk7QR9LVoAdXXaOVpktlU7naLDkpioP96T0USEeq1aBdx7r/hvtSNnxNSpwEsvyW23z84GVqzQXjAdirobC/AeOVM7QFZWdafoxq3nRNRseJZnmDkzdCbixkbv0YlAZBbxeo5y6I335FsiY/Fi7fMY9cMPTf+9YIFYgGxkhEedBpPZbv/dd+Ia4RQm1VMzjSgQWzs7L7/8Mnr16oV27dqhXbt26NevH9577z334xMnToTD4fC6Xe8zZlpfX49p06ahY8eOaNOmDcaMGYPv7Ex2QUQR5VtB+89/lnvewYPaj8su4lXj9Mb78qxWPm1a6KkbzwW+Tzwhd+2LL/b+ecECMdK0eLEYrVm4UIx6aXE6xTQYIBY/y5CN0yJbM40oEFvz7GRnZ+P555/H5ZdfDgB48803kZeXh88++wxXX301AOCWW27B8uXL3c9J9Bn/LSgowMaNG1FcXIy0tDTMmjULo0aNQllZGZxMukAU18IpzxBqjYzsIl41Tm+8FnWx87hxop2Bpm7UBb6AGNV67rnQ5/UdGQHElFpBQdPP1dXa01szZzZNw3mOFGmRjQtF7RAS6aZEmfbt2yuvv/66oiiKMmHCBCUvLy9o7MmTJ5WEhASluLjYfezIkSNKixYtlPfff1/6mjU1NQoApaamxnC7iUi/+npFWbxYUaZOFff19fLPvXBBUbKz1b1G+m8rVoRum9OpfQ6ns6nNeuNlrFnj/xpzcsRxve9FTo6IkzFnjv9rcTrFcU+rVsm916tWyb9mIj1kv7+jZs2Oy+VCcXExzpw5g379+rmPl5aWolOnTujRowd++9vforq62v1YWVkZzp8/j+HDh7uPZWVlITc3F7t27Qp6rfr6etTW1nrdiCiyZLd0BxNueYYTJ7Qfl9lW7TnKoTfeV6BcPrJTN+pIkNa0l29mYi2+01uLF4uffetlBRopCkQ2jsgyEep8BfX5558rbdq0UZxOp5Kamqq8++677seKi4uVd955RykvL1c2bNigXHPNNcrVV1+tnDt3TlEURfnb3/6mJCYm+p1z2LBhyoMPPhj0mk8//bQCwO/GkR2iyJgzR3skwHcEIZCiIuOjOrKjDWvWaJ/Dd4RFfW0yoyLhPidYe2VGgsxy4YKipKVpv0dpafIjSkR6yY7s2L71vKGhAd9++y1OnjyJNWvW4PXXX8f27dtx1VVX+cUeO3YMnTt3RnFxMfLz81FUVIQHHngA9fX1XnHDhg1Dt27d8MorrwS8Zn19vddzamtrkZOTw63nRBEQzhZtT6WlYlGyUYEqa3sKta1aXSRcURG49tSyZWIxsmddqdOngfvvbzq+ciXwxz9qr5GZM0euArlnu3fsEBmFjW711nOt9HTg+PHgMWlpwPffs24VWUN267nthUATExPdC5T79OmD3bt348UXX8Srr77qF5uZmYnOnTvj4E/bKDIyMtDQ0IATJ06gffv27rjq6mr0798/6DWTkpKQlJRk8ishIhl6tmh7Lpz1pSabO3JE/wJlmSR0emoy+XaafBf9AsAvfwns3t30c3m5SG4YyqJFwLx52h0/T5FcxLtjh3ZHBxCPB3qPiCIpatbsqBRF8RupUR0/fhyVlZXI/CkveO/evZGQkIDNmze7Y44dO4Z9+/ZpdnaIyD7hbtFWqetUAPnsww6H/PoVM2sy+XZ09AiWmycasG4VxQpbOztPPPEEduzYgcOHD6O8vBxPPvkkSktLce+99+L06dOYPXs2PvroIxw+fBilpaUYPXo0OnbsiNtuuw0AkJqaikmTJmHWrFnYunUrPvvsM9x3333o2bMnhg4daudLI6IgzNyiHSzZXE6OmP7JzvY+ricJnVk1mU6fNt7RURkp3BkJrFtFscLWNTuTJk3C1q1bcezYMaSmpqJXr1547LHHMGzYMNTV1WHs2LH47LPPcPLkSWRmZmLw4MH4z//8T+Tk5LjPce7cOcyZMwdFRUWoq6vDkCFDsGzZMq+YUFgugihyzFqz4ynYOpVw1q80NIginVr/QjocwLlz2u287TZg3Tq5awazeLH2lJ6nSK/Z6dIl+FSi1romIjPIfn/bvkA5GrCzQxRZoeoy6V2Ua4VNm4ARI0LHffCBKOwZTK9eYn2OUXo6foFqbGVni+k+qzINl5QAt98e/PE1a5jlmKzD2lhEFLWC1WVyOsXxZ54R+V1GjBD3dXXGruNZM6u0NPTCaE8rV5oTJzttF4xWbh5PajZp30XVR46I4yUl4bUjmOefD+9xokjgyA44skNkl0BbtO+8E1i/3j82L0/fdFC4oxxjxwZuh952nT4tt+uqRQvvAqZOp+joyIxwhbNNPhyyr+3UKaBtW/OuS6SKma3nRBTfguWcAfy3aGt1MNavF4/LdHiC1cxSRzlkFimbtfi2bVugb1/tRcp9+wI7dwZ/n0IJZ5t8OO6/Xz5u7VrzrkukF6exiMgyekpC1NWFHklZvz70lJbLJUZ0Ao1Zq8cKCkJPaV1/vfbjeuI++UR0aALp21c8rnb8XnpJ3Mt2dAD7toB/9ZW5cURWYWeHKAzhrAmJFla9BnURsu/5XC5x3LfDM2eO3HlDxekZ5dASqnaW3rhPPhEJ9nJzgQ4dxP3x4+J4uOzaAp6aam4ckVXY2SEyqKRErJMYPBi45x5x36WLdQtBrWDVa2hoEJl/tSxaJOJUPyVGDylUnFmjHB5J2U2JKywEOnUC9u0DfvxR3HfqJF/4VIuaTVqrEKhM1mi9Jk0yN47IKuzsEBlg184XM1n5GvSUhFB17y537lBxZo1yyCYClInTO8qll1Y2afVnPVXPZXXtam4ckVXY2SHSyaw1IXay+jUYKQmhlXfHU6g4s0Y5ZPephoozMsplRLBs0pdcIp81Wi/1vdZixYgSkV7s7BDpZNaaEDtZ/RqMlIRIThbbuLXk5Yk4LWaNcpg10mRklCscvp0vK5OLqO+1WnPMk546ZERWY2eHSKd4KH5o9WuYPDn0F5zTKeI8rVsXvMOjlc/Gd5F1Xl7gUQ49tbEmTxa5b7S0aOH/GnyZVfg0FHVa8sgR7+NHj1o7taqOKGVleR+3ckSJSC92doh0iofih1a/hsREkRBPS7DMwOvWifIIU6aIMgxTpoifg3V0gi2yBoDDh4Ft24CiInFfUSH/5et0im3yWtq0Cd2pM7PwaTB2T61+/LF/x/joUXGcKBowgzKYQZn0iYfih+G8Bj2FJgsLxXoUzy9ZPZmBQwmWPFCdUvnv/wY6djRWFLO0VHScQtm2TTtRnxWFT32Z1VZPsp9zLNQ5o/gl/f2tkFJTU6MAUGpqauxuCsWINWsUxeEQN/FVK27qsTVr7G5haEZew5o1ipKd7R2fna39euvrFWXxYkWZOlXc19eb0/4LF/zb4ntzOvW11VNRkfa51VtRUehzzZmjfY45c8J7L8xsq6LIf8719f7vcaDPwKzPnMiX7Pc3OzsKOztkTKAvhJyc2OjoqPS8BrVz5PtlZlcHb9s2uS94o22VPf+2bXLtnTPHv2PgdIbf0TG7rXo+58WL5a67eHH4r5EoENnvb05jgdNYZJyeKZ1oJfMa7Co0qWX1arFGRy/ZtloxXalVJywcZrVV7+c8bZooAxLK1KmiDAaR2VgIlCgCnE5zCyvaQeY12FVoUovRxdOybVW3VY8bJ77kPTsRRhP1+RY+NYva1ttvD/y4osi1Ve/nHInF10Rm4G4somZOpjZWNG63D5U8MBSZtgZL1KdnC3ss0fs5T54c+v13OEJvzyeyGjs7RM2YbG2saNxur5U8UIZsW/Pzw9vCHgnq1vNgHA65refR+DkTmYGdHaJmSk9trAEDgLQ07fOlpZlXFkC2EnuwkRet6Rp13YnLFdvV6j2ZlRFbb6mNZcsCrxHyvXag7NCynzGRGdjZIWqG7E5Cp0VvJfZAIy+rVwcvYaAoQF0dMHSo3Pljobq9WdOMekttHDggd13fuFh4TynORGRvWJTj1nNqbvRuVTZ7G3YwZm5vD7StPi1N35b0YO1RnxMtaQbM/nxkUxKMHSt33bFjvc8dTSkMKLbJfn9zZIeoGdI7ElBZKRcvGxeI2aNNviM+W7YELyIa6Pxa7VGfo3f068cfgZ49xZRfz57iZzOYVeldJbtOSe8an2geUaT4xs4OUTOk90vqn/+Ui5eNC8SKSuzqtvrx48V/6zl/qPYA+tqTkSE6Ofv2iU7Ovn3i54wMuedrMavSu+851fdu0KDAz+3RQ+5capwVnzGRDHZ2iJohvSMBsqlHw0lRavX2dr3n960eHoxMXEYG8P33gR/7/ntzOjx2bJPXW90+GlMYUPPAzg5RM6R3JKB7d7nzysYFctFF5sb50jua9cMPcvGh4n78MXhHR/X99+ZMaUV6m7ze6vZWf8ZEwbCzQ9RM6RkJ0PsXvBGvvmpunC91NEuL52jWxRfLnTdU3MCBcueRjQtFZvrJTAsWiMrmvtdxOv0rnm/YIHdO2TgiWSwXQRRn9NTrys8H8vJCxycmAr/4BbB7d/Dr/uIX4dV5+vprc+N8OZ2iA7BwYfCYu+9ueu2+ncBgQsUdPSp3Htm4UOyo17ZgATBvXui6X1Z/xkTBsLNDFEdKSsRuF89FoNnZYsoq2FSGTG2shgZgzx7tmD17RJzRDk+3bkB5uVycEWoSQS3FxcD8+eI96dNH7ryh4rKy5KaosrLkrqfFyOdvFpm6X927A5s2hT5XONOhRIFwGosoTujJiKzXsmWhtwO7XIEz5cpaudLcOF96d1f97ndy5w0Vt3273Hlk44Kx8vM3i9aompE4Ilns7BDFAavzlxw6ZG5cIG3bAn37asf07SvijNC7E+jgQbn4UHEdOgDp6dox6ekiLpCGBrFYfNo0cd/Q4B8TK/lrkpPFtKmWvLzg+ZCIjGJnhygOWJ2/RHbqyOgUk+qTT4J3ePr2FY8bpXc3lpk70Kqqgnd40tPF44EUFgKtWwMzZgBLl4r71q3FcU+xlL9m3brgHZ68PPE4kdkcihJOZoz4UFtbi9TUVNTU1KBdu3Z2N4dISkND04LQmhq56Z377wdSU4MvINW6VuvW2iMDTidw9qz/OY0smD19WrRVXey6cqXxER3PdnTpIqZ1Av2rpxYIragQ7aurE685lLNn5UcifvxR7Lo6elSs0dm+PfiITmGh9nSO506n1atFjalQiorEIu1oUFcnXsPBg6LDuHAhR3RIP+nv74gUr4hyrI1FsWbOHEVxOuXqEgW7OZ3iPHquqXW+QOcKVGMpO9u++kdqXSbf2kyB6jLV18u9j/X15rezvj705+t0Nl07UrXLiKINa2MRxSn1L/5w11+4XOI8vlMiwaj5VFr4/KvRooV/PhUgOhfM6sktJLvYOpxF2Vrn1LMgfMCA0CNfKSnytbGI4g07O0QxpKEBWLTI3HMuWhR40Wsg11/vv/YlM1Mc9xRqwayRIppmkc0yHIlF2cHoXRztconpNC1nzti/QJnILuzsEIXB5QJKS8WaidJS679MZP7i10t2y7g6UuNbC+roUf+RGrOLaBoV7PORyTIcqUXZgQSrWRYsbtkyoLFRO7ax0ZpRKKJYwM4OkUElJWLB6+DBYnHo4MHiZyunZ6wYRZA5r96tzWYW0TQq3M/n3nvNjdPjuuv0xdk5CkUUC9jZITLArvUoVowiyJxX79Zms4poGmXG53PbbXLXko3TIydHX5ydo1BEsYCdHSKd7EzgJlOQUy+ZAp56E/KZVUTTCLM+n2++kbuebJwe/fvLFV7t31/8dyQKtRLFMnZ2iHSyM4FbYiIwc6a555w5M3S+Hb0J+cwqommEWZ/PRRfJXU82To9du+R2Y+3aJf5b5vdC5nMmile2dnZefvll9OrVC+3atUO7du3Qr18/vPfee+7HFUXB3LlzkZWVheTkZAwaNAj79+/3Okd9fT2mTZuGjh07ok2bNhgzZgy+C7UykigMekc5zKZuAff9S97pFBlos7O9j+fkiOOB4gNtGQ9E79bmAQP82+ErJ8eardCy7/vWrdoLy0MVtdQbB8iVfgCM/Y757ojzFepxorgWmbQ/gW3YsEF59913lQMHDigHDhxQnnjiCSUhIUHZt2+foiiK8vzzzyspKSnKmjVrlPLycuWuu+5SMjMzldraWvc5Hn74YeWSSy5RNm/erOzZs0cZPHiwcs011ygXLlyQbgeTCpIeW7bIJXDbssW6NqxZoyhZWd7Xy8oSxy9cEMnjiorEvfq/Qn29oixerChTp4p7Pcnw6usVpUUL7dfbooX3OdUEfoFifRP4mUk2wV6oRIdmf86BEkEGS+yo99oXLvgnb/R9v3Nymn4XiOKF7Pe3rZ2dQNq3b6+8/vrrSmNjo5KRkaE8//zz7sfOnTunpKamKq+88oqiKIpy8uRJJSEhQSkuLnbHHDlyRGnRooXy/vvvS1+TnR3Sw+7OTrBOhJoF+L//O3BnJ5hgnSNPixfLvebFi/3b6vslnJNjfkfH8zVs2SKuGayjFawz4NsBM/Nz1pt9Wu+1mUGZmquYy6DscrlQXFyMM2fOoF+/fqioqEBVVRWGDx/ujklKSsLAgQOx66eJ6rKyMpw/f94rJisrC7m5ue6YQOrr61FbW+t1I5JVXW1unB4yyfrGj5ffbi27Pdvo1mbZBH7h8H0NQ4eKukuKIp+vRn0/PRcum/U5yySC9E3sqPfadk+tEkU72zs75eXlaNu2LZKSkvDwww9j7dq1uOqqq1D1UxngdJ9Swenp6e7HqqqqkJiYiPbt2weNCWT+/PlITU1133Jk93kSQf9iXTPJJOvzXX8SbLu1nu3Z4WxtlkngZ1Sw1/Djj+I+WJHNQBTFe+GyWZ+z3tIPRq5t5+8kUSywvbNzxRVXYO/evfj444/xyCOPYMKECfjiiy/cjzt8/jRTFMXvmK9QMY8//jhqamrct8rKyvBeBDUr6uLbYL9iDof24ttwsi4b+ctcHbWYPr1pUe7Wrfq2Z9uZYC+YUKNcDoeoor1lixhVeuopufOq73G4n7PKyKiYbFLBujrxebpcYmdbuG0lilctjT7x5MmT+OSTT1BdXY1Gnzzlv/71r6XPk5iYiMsvvxwA0KdPH+zevRsvvvgiHnvsMQBi9CbT48+R6upq92hPRkYGGhoacOLECa/RnerqavRXE1AEkJSUhKSkJOk2EnlyOoEXXwRuvz3w44oidtoEGsEoKRFf0J4jEdnZ4nwyUztG/zJXFHHNoUPl49VRjkGD9CXY27nTWBv1ktli/t134nMYP150LOfNC31e9T0O53P2ZGRU7NVX5Z7zq181/XdaWuCOHyDfVqJ4ZWhkZ+PGjbj00ksxcuRITJ06FdOnT3ffCvTswwxAURTU19eja9euyMjIwObNm92PNTQ0YPv27e6OTO/evZGQkOAVc+zYMezbt0+zs0NkBzOy+g4YALRqZU37AlFHOb79Vi5eNi6UmhrgxhuBSy8V9zU1wdsWiudITVqadmxamvmjH7KJ/DzjjJR1OH5c+/GPP9Z/Tj0iXSeOSBcjq5+7d++uTJ8+XTlz5oyRp7s9/vjjyocffqhUVFQon3/+ufLEE08oLVq0UDZt2qQoith6npqaqpSUlCjl5eXK+PHjA249z87OVrZs2aLs2bNHufnmm7n1nCwVapuvuuPI81fQrK3BZ8/K7zAy46bu3rnhBrn4G24I//3t1i3wubt1847TuwPpwgVFSUvTjk1La/oMzPrMjh+Xa+fx403Pkd39pufmdOpLN6BHoF13gbbzE5nN0q3nrVu3Vg4dOmSoYZ5+85vfKJ07d1YSExOViy++WBkyZIi7o6MoitLY2Kg8/fTTSkZGhpKUlKTcdNNNSnl5udc56urqlKlTpyodOnRQkpOTlVGjRinffvutrnaws0N6GNnma9bW4ClTItPJ8f0iP3lS7nknT+p7L31z/3Ttqn1+zw6P2hnRyuXj+Rr0fgZmfWa5uXLnyc31fl9C5TUycvNNDWCGUKkQ2OEhK8l+fxtaszNixAh8+umnuOyyy8IaVXrjjTc0H3c4HJg7dy7mzp0bNKZVq1Z46aWX8NJLL4XVFiJZsuvZPePM2hr85Zdy5wmHusjVc41HaqpYU6I1vdKtm4iTVVgotlzrme44dEhMaaWmNq2pGTdOtFlRtF+D3krsZn1mR4/KncczzukEWrcGTp+We64ss6ueyywSLygInMGbKJIMdXZuvfVWzJkzB1988QV69uyJhIQEr8fHjBljSuMotrhcYtHosWNikeeAAZH7B66hQWzdPXRIfOlOnmxdHaB//lM+7v77xX+btTW4TRu584QjO1t0EnwXTC9YEHyxrvq4rMJCYOFCQ83Drbc2LYLOzwfefjvwom/f16C3ErtZn1m7dk1b4UPFqXbsML+jA5hf9VxPHbJBg8y9NpEuRoaNHA5H0FuLFi0MDUXZidNY4bNzzl5PGn4zTJ4sN2UweXLTc/ROuQSzYoX5UxstWijKpk3aGZSNrFMKpr7e//PSc8vJCdy+UFmgV62SO/+qVSL+1Cm5+FOntF/va6/Jnee115qeU1Rk/udsxZod2XYWFZl7XSKVpRmUGxsbg95cXILf7Jixy8godYTA99fO5RLHCwvNv2b37vrj1CkXwD8XSqApl2A6d5a7th6NjUBCgnbSP5lkhrKV3mWS7Gm59FL/YzKJC/VWYv/d7+TiQ8UZ+X2xIvmfFVXPmcyQYoXtSQUptoWaswe8k9OZyUgafjNMnhy6U+J0+m85VqdcfL90s7PFcZk8OzLVxI0ItQ5J73oXLeGuG3n3XWPP01uJ/eBBufOGijNSAT5UQkPA/3fQjOr2epmVeJHIaoY7O9u3b8fo0aNx+eWXo3v37hgzZgx2yPxZR3FFz5y92Yyk4TdDYiIwapR2zKhRgf+KDrdWlOcIkZlCrUPSu95FSzjrRvQugvakvndaX8yeo2tGRmTMuK7nc9THfeMdDqC42P/3aN064OxZYPFiYOpUcX/2rDUdHZl2AkxmSNHBUGdn1apVGDp0KFq3bo1HH30UU6dORXJyMoYMGYKioiKz20hRzM4ChEaLU4bL5QI2btSO2bgxeEfMylpRRgUamfN08cVy55GJmzxZvkCnp27dgK++CvyYbEI7dXTNd6QlJ8d/dE12AbVMnJ7r+j4n2EhgsKzWiYliNPWll8S9VQv1ZdtpZtFXIsOMLAi68sorlUWLFvkd/6//+i/lyiuvNHJKW3GBsnFm5SIxQjbxmtm5Rdavl7vu+vXmXldR5BYKG7mFeo/M/Jzr64Mv1FZvDoei9OsnFiPfcIN2/h4ji+NlFjQriqLk5Wm3My8v9Os1ct1Qz4nGJH5GXhtRuGS/vx2KEupvOn9JSUnYv3+/u6aV6quvvkJubi7OnTtnUlcsMmpra5Gamoqamhq089z/SSG5XEB6unaq+rQ04PvvzR/BaGgQuUi0prKcTjGMb+Zftzk5oRfrAuIvW7NrzJaWAoMHm3tOhwM4d077PXK5gC5dtF93To6YSgn1OS9ZAsyYEbpdY8eK91ArlYC6ON73XzF15MiMkYWxY4H16/2P5+WJaaNIi8RrJooVst/fhqaxcnJysHXrVr/jW7duRU5OjpFTEumWmCh2mGixYgfKyZPmxulhxXSgDJm1QrJrM2SnFdetA5YuFR2j1q39d9ZFanH8unXAqVOi09Ozp7g/dcqejo6dGwKIYpmhzs6sWbPw6KOP4pFHHsHKlSuxatUqPPzww5g+fTpmz55tdhspiu3YEboA4fHj1ixQBsTCyzlzIrsDJVQxSb1xelixhVdR5BZxhyokKVto0sgC5UCpBCK1OL6kBPjZz0Tnprxc3P/sZ9amVAjGzg0BRLHMUGfnkUceQXFxMcrLy1FQUIDp06dj3759eOutt/DQQw+Z3UaKYnYuUFYtWBDZHShz5pgbp4fMlmQj/vd/tR83c5u/zNZ9mWvI/k5t3Wq8EredOaQCiYb/34hikeGt57fddht27tyJ48eP4/jx49i5cyfy8vLMbBvFgGhJKhbJHShbtpgbp4c6naR/pZ22/fu1Hzdzm7/M9KPMNWR/p+bNA+65R6x16tJFvoNixZRRQ4OY7ps2TdzrzQEVLf+/EcUaJhWksDTHpGJnzpgbp5fsdJEeycnaj5u9zT/Y9KOeaxgZ5fruO/kRGbOnjAoLxdqjGTO01yJpieb/32S3/xPZQbqz06FDB/z73/8GALRv3x4dOnQIeqPmozkmFZMt2WBFaQeZ6SQjrrhC+3HZdTZ61uP4Tj+OHavvGlq/e1oURW5ExswpI7PKmkTr/28lJWLUbPBgY6NoRFaT3nr+5ptv4u6770ZSUhJWrFgBh8a/LhMmTDCtgZHArefhKynxrzydkxO4enY0CKdC++jRwDvvhI4bNSp08kG9ZLdt6/XggyKzc/fu4svXd6QnEtv8jV4j0O+ejG3btCtxy27zD3UeK967aPr/jVvhyU7S398RyPkT9ZhU0ByxklQs3IRsPXvKJdjr2dP8tj/yiPkJBWWT5c2Zo/0cM6rMG72G5+/eE0/IvUa1unkwZlWqtyr5ZTT8/xYqyaXse0RklKVVz/fs2YPy8nL3z+vXr8fYsWPxxBNPoMHsqosUM6KxDIIvM3bXXHaZ3LVk4/SI1C6b9ev9p5Uisc3f6DU8f/dkS1uEquNl1pSRVWVNouH/N26Fp1hhqLPz0EMP4csvvwQAfP3117jrrrvQunVr/N//+39RqGe1HVEEmbW75j/+Q+56snF6pKeH9/zUVGD4cOC3vw0du349UFfnfczsbf6BdieFew0z63iZUffJivVO0YJb4SlmGBk2ateunfLVV18piqIozz//vDJ8+HBFURRl586dSnZ2tpFT2orTWM2DWfWdnnpK7jxPPWX+a5gyJbzpqRtu0HeeKVPMfw2qOXMUxen0vp7TGf50mBX12sKZMqqv93+dvjenU8TFGjtr4xEpisXTWIqioLGxEQCwZcsW/OpXvwIgykioO7aIok08/BV63XXhPT87W4yiyOYAOngwvOsFY9bupEDU7dla9G7PDmfKyK6yJpEQzVvhiTwZ6uz06dMH8+bNw8qVK7F9+3bceuutAICKigqkhzvOTmSRTp3MiZP9h9uKf+A7dgzv+W+9JXK8HDggF9+9e3jXC8TMbMyBqGttHI7Aa20cjshvz77++vAej1bRuhWeyJehzs6SJUuwZ88eTJ06FU8++aS7+vnbb7+N/v37m9pAomgj+w+3Ff/Ab9hg/jm1LFxo/jnNzMYcjBlrbcyirhULxuGI7eKd0fReEwXT0siTevXq5bUbS7Vw4UI42YVvthoaxBfUoUNiseXkydE1NF9dbU5cuOcJluNHJvfP11/LXdsMeXmhMysbITuqJBsXTH6+yHVk9++knh1LWvl6oll+vvh9MZq7ishqhjo7lZWVcDgcyP5pYvyTTz5BUVERrrrqKjz44IOmNpBiQ2GhmHrw/Ot09myxFsGqgpx6mVVXKJzzBEoGl50t1oKsXu1//MUXvf8y7t4d2LRJ7vrhyMsT1b2tUFVlblwwgd7r//ov//fUavGwVkyGuq6JKCoZWf184403Kn/9618VRVGUY8eOKe3atVP69eunpKWlKc8884yRU9qKu7HCE4lkc2YwK0nchQuKkpam/ZrT0vzPs2ZN8GsHa4/D4Z3s8OzZ8HZjBbvl5irK8OFi99XZs+a/955kEyM+8ojxawR7rwO9p1bjjiUi61i6G2vfvn345S9/CQD47//+b+Tm5mLXrl0oKirCihUrzOuJUdSzerGpmexcTKmV4ycYNdZzPUdiItCqlenNw333AR98IBYvWzF15alHD3PjfFlRrTwc3LFEZD9DnZ3z588jKSkJgNh6PmbMGADAlVdeiWOxPhZLukRisamZzFhMuWMHcPy4dszx495ZY0Ot2wjGcz2Hep5z5/SfJ5RIrgWaPDl0h9LpFHFGRFtWX+5YIrKfoc7O1VdfjVdeeQU7duzA5s2bccsttwAAjh49irS0NFMbSNHNqlT4VsrPF0Uvt20DiorEfUWF/DoOI2swwv0bQH3+kSPhnSeYigprzhuI1XlnonGNDHcsEdnL0ALlF154AbfddhsWLlyICRMm4JprrgEAbNiwwT29Rc1Dly7mxkVKOIspL7pIf5xsjp9g1MXOR4+Gd55gfhqojRh10brvonanM/xF7WblUzIbdywR2cdQZ2fQoEH497//jdraWrRv3959/MEHH0Tr1q1NaxxFv549zY0LJZxt22aRzXWzYQMwcmT410tLa1rP8a9/hX++QM6ckY81671esACYN8/+reGRxB1LRPYw1NkBAKfT6dXRAYAu0fbnO1kuVOVovXFawt22bZavvtIfJ5ubJxQ9nRI9amvl4oJ9Bkbf68REsVjYTJHa2k5EsUO6s/OLX/wCW7duRfv27XHttdfCEWxrAYA9e/aY0jiKfpHq7JSUAOPG+e+w+e67wFl+v/tOxFuxHsK3ErhMnGxunkDUxc6DBgE33mhN/pukJNFh1BqpCfYZHDli3XttRCQ74EQUG6Q7O3l5ee4dWGPHjrWqPRRjLr7Y3LhAjGzbBkR8QYFYJ2HmlNYVVwD/8z9ycar+/Zum24xQF9P+x3+IZI1m27VL3IDAIzWhtnOrJQ/Mfq+NiMTvJBHFFunOztNPPx3wv6l5891dEm5cIEa3bQPWpOH/8Uf9cbt2hZfXRR0ZevJJ4+eQFWikJpZKHkTid5KIYouhreeeTp8+jdraWq8bNR9qwjQt4SZMC3eLcGVleM/3JVt53DMunNfgdIqRIQA4eND4eWQFSrwXjdu5g4nE7yQRxRZDnZ2KigrceuutaNOmDVJTU9G+fXu0b98eF110kd+iZYpvasI0hyNwwjSHI/yEaeGsdwGAf/4zvOf7+vhj/XHhvAaXq2mKqXt34+fRwzfxnll1xSIhEr+TRBRbDO3GuvfeewEA/+f//B+kp6drLlam+KcmTAu0S2fJkvAXrQ4YACQkAOfPG3u+3rU+Zp3PM04dbThyxFh71BGT558H/vxn/c83Sr1uqPY7HOLxaBktsfp3kohii6HOzueff46ysjJc4bkCk5o1KxOm1dUZ7+gA5o+GXH45sH+/XJxKHW0YN050DPR2eNQRE3WEJ1LUxHta7Y/WkgdM4kdEKkPTWH379kWl2QshKOapCdPGjxf3Zn2p3H9/eG0KVGPJ5QJKS8V269JSfYuHH3rIWFywkgFa75Nvkci//lW+nWaLxZIHVv1OElFsMTSy8/rrr+Phhx/GkSNHkJubi4SEBK/He/XqZUrjiAD5JH6BBKqxFG5iPNkEgYHiAo02/PADcOedgc+hKN4jJuG8F0b4lqfgaAkRxSJDIzs//PADDh06hAceeAB9+/bFz3/+c1x77bXue1nz589H3759kZKSgk6dOmHs2LE4cOCAV8zEiRPhcDi8btdff71XTH19PaZNm4aOHTuiTZs2GDNmDL4zuleZok5qqv7nOJ3AnDn+NZbUxHi+vx7qduuSktDnlk3qFywunNGGSHd2Ai3u5mgJEcUaQyM7v/nNb3Dttddi9erVYS1Q3r59O6ZMmYK+ffviwoULePLJJzF8+HB88cUXaNOmjTvulltuwfLly90/J/r8qV5QUICNGzeiuLgYaWlpmDVrFkaNGoWysjI4+S9xzHvgAbkkfnfeKdaYBKuxZFZivFOn5NodLM6ztlSnTqJNwdidrC+c3EBERNHCUGfnm2++wYYNG3C55wpMA95//32vn5cvX45OnTqhrKwMN910k/t4UlISMjIyAp6jpqYGb7zxBlauXImhQ4cCAFatWoWcnBxs2bIFI0aMCKuNZD/ZzkW/ftp1lsxKjHfunFx7AsUFmkLT4tumtm1F+YhI4d8KRBQPDE1j3XzzzfiXBeWXa2pqAAAdOnTwOl5aWopOnTqhR48e+O1vf4tqj8UQZWVlOH/+PIYPH+4+lpWVhdzcXOwKsnWlvr6eiRAtUFcHTJ0KjBgh7mVrSIViVvp/sxLjGa30HmwKTcazz4r3NTlZ/3PDcd11kb0e+QtnMT0RCYZGdkaPHo0ZM2agvLwcPXv29FugPGbMGN3nVBQFM2fOxI033ojc3Fz38ZEjR+KOO+5A586dUVFRgd///ve4+eabUVZWhqSkJFRVVSExMdEvmWF6ejqqgpQ1nj9/Pp555hndbaTgxo4F1q9v+nnTJpEPJi8v/MKVZqX/NysxnmzGBc84o/W9VFu2GHteuIIMqFKEmF1lnqjZUgxwOBxBby1atDBySmXy5MlK586dlcrKSs24o0ePKgkJCcqaNWsURVGUv/3tb0piYqJf3NChQ5WHHnoo4DnOnTun1NTUuG+VlZUKAKWmpsZQ25u7vDxFEV/jgW95eeGd/8IFRWnbVvsabduKuFDnyc5WFIcj8DkcDkXJyQl9nvr64OfwPFd9fdNztm3Tjo/W23/9V3ifHRm3Zk3g3zOHQ9x++ieQqFmrqamR+v42NI3V2NgY9OYyMMY6bdo0bNiwAdu2bUN2iKI2mZmZ6Ny5Mw7+VCQoIyMDDQ0NOHHihFdcdXU10tPTA54jKSkJ7dq187qRMXV13iM6gaxfH96UlssFnD2rHXP2bOjhfTUxHhC4jABgXWK8aKgZZcShQ3a3oHkKtZge8K5dRkTadHV2fvWrX7nX1QDAs88+i5MnT7p/Pn78OK666irp8ymKgqlTp6KkpAT/+Mc/0LVr15DPOX78OCorK5H501xD7969kZCQgM2bN7tjjh07hn379qG/Wj2RLDNnjrlxgSxbBjQ2asc0Noq4UMxIjLdsWejpKEXxbk801IwygpVg7KFnMT0Rhaars/PBBx+gvr7e/fMLL7yAH3/80f3zhQsX/PLkaJkyZQpWrVqFoqIipKSkoKqqClVVVaj7aRjg9OnTmD17Nj766CMcPnwYpaWlGD16NDp27IjbbrsNAJCamopJkyZh1qxZ2Lp1Kz777DPcd9996Nmzp3t3FllHtgp3ONW6v/zS3Lj8fODwYWDbNqCoSNxXVMivgZAd7fCMk6nEnZ0t1uYUFQF9+shdw2pcoGyPWKoyTxQLdC1QVnz+nPX9Wa+XX34ZADDIZ5/v8uXLMXHiRDidTpSXl+Ovf/0rTp48iczMTAwePBhvvfUWUlJS3PGLFy9Gy5Ytceedd6Kurg5DhgzBihUrmGMnArp3F4uRZeKMsuIffjUxnhHduumPczpFEr6FC4PHjx8PDBki/vt//gf49FNj7TNTTo7dLWieYqnKPFEscCg6eiwtWrRAVVUVOv1UHTAlJQX/+te/cNlllwEAvv/+e2RlZRlat2On2tpapKamoqamhut3dPrxRyAtLXTc8eOAT0YBaY88ArzySui4/v2BX/wieFJBszQ0AK1ba6+XcDrFOiK1DS4X0KWL9tRETo4YYXI6gdOnAY/+vC0820ORpf6+hKoyz8+HmjvZ729d01hquQbfY9R8/eEP5sYFIrvVe9cuYOlSYMYM0RkpLDR+TS2JiaLmlhbfmlyh1mAA3msw7BzVcTjELdqqmDcndi6mJ4pHuqexJk6ciKSkJADAuXPn8PDDD7tLO3iu56HmIRJrdiZPBmbP1rfzxOVqmjLyrY+lPh5OMUv1nH/6k/df3i1aALNm+V9T71ScnWsxsrPFFynzuNhLXUwfKM8OPx8ifXR1diZMmOD183333ecX8+tf/zq8FlFM+WkG07S4QNSRFK31LsEsWgTMm+c9ymJWorYvv/SfYmhsDLxQWu8aDJmpQbPMmgWMGsUq5tGIVeaJzKGrs+NZjJMIAMaMkVtPYyCptilcLrEFXK2ZpZZs8O2kfPedOC67/dw3Y7Sn9evF456Zo9XdWKHWYAwYIH4uLw/dhnAFG4Wi6BLOYnoiEgwlFSRS/fvf5sYF0tAgRmiMUreAhyrZoChyidqMJFJU12BoXdtzDcbXX2ufn4iI5LGzQ2H55z/NjQtk2bLwMsWqW8D1LhIOJhKJFCOx7r+xUUwNWrWQm4goWrCz04xYUT1ZtgxEOOUidOSp9ON0igXOgJhCkhEqzsiibHVUKRiHw3tUKZLJ/BYtEqNnRETxip2dZqKkROTtGDwYuOcecd+lizgejk8+MTcukHDWr3huAf/hB7nnhIqTTZDoGac3/X8kk/mp65qIiOIVOzvNgLoo1/fL9sgRcTzcDo+M06eNjyglJ5vThosvNidOdleYZ5zerecDBkR2RxYLfhJRPGNnJ85ZXT25c2e5uMOHjY8oXX65kZYJnlM0vsU/gwkVJ7vt1zMu2tP/y5bAICKKRezsxDmrqydnZOh/jt4RpXC2rXtO0ciMlqSlNW3/DkZ2ysczTt16HmzhscMhpq7Ua+/YIUpsRILnuiYionjEzk6cs7p68uHD+p+jd0Tp6FH91/Bk9hSNkQXKetP/RzKDsm9pCyKieMPOTpyzevrk+++NPU/PiNKSJcauofLceh5qtOT48dBtkt0W7hunpv/3nSbLzvZPZhiJ6SynU2yPZ1JBIop3ujIoU+zRm7lXr3AX0cqMYPz4Y3jX+I//EPdmbT3v3VvuPIHiZNP/h/rcjMrNFdl4ra4MT0QUTTiyE+f0Zu7V65tvDDcNgNwIRrhfyK+/Lu7N2noe7nZ7Nf3/+PHiPtB7H+pzM+rnPwdeeklMIbKjQ0TNBTs7FJafCt7r5rsgV8uwYcauoVLX7Ji19dzqdVCqjz8O7/mB3H+/+eckIop27OzEuVCZe4Hwtp4bSX4XaEGulnC3RWdliXuztp6npMidRzYukHDrgQXSti0wZIi55yQiigXs7MQ5s+pBBXPihP7nBFqQq2XXLv3X8PTRR+JeXQejRWa06Z575K4rGxdIuPXAAnnzTePTlUREsYydnThn1qLccJ/XsSNQVARs2wZUVMh3dAARH46vvhL36joYrVw3MqNNsmtdwlkTY0VGYyumxYiIYgE7O3HOrEW5wVx0kVxcRob2glwt4U5jVVU1/be6/dt3hCcnR360qbpa7rqycYFYkdGYBT+JqLliZyfOmbUoN5iCAnPjAlm50vhzAaB1a++f8/NFMsRt24yNNkWi9MPkyeZPObHgJxE1V8yzE+dkyzkYKfsAiOkpM+MCSU4GEhKA8+eNPT9Q/S51+7cR111nblwgiYkis7Fs0VFZLPhJRM0RR3YoLE8+aW5cIDt2GO/oAMDvfmf8uYG8+qq5ccEsWCAyHJs5wsOCn0TUHLGzE+fCWV/S0CAW7E6bJu4DrfeIRM6ZcPPVnD4d3vN9yY6OmDGKsmABcPYssHgxMHUq0KOH8XOx4CcRNVecxopznToZiyssFAtaPbc/z54tplY8ayllZcmVc1Bz3RgRbkmKcJ/vS3Z0xKxRlMTEpjVPU6cCX35p7Dws+ElEzRVHdshPYaFYK+Kb58XlEscLC5uOzZsnd07ZuEDKy40/14zn+5JZPGzVKIqRNTws+ElEzR07O3HOc9u1TJxM5l7PLcwnT8qdXzYuEKMjGaqDB8N7vi918bAWq0ZRkpNFIVEto0c3TXstXiymwdjRIaLmjNNYMczlCl09W2+eHZnMveoW5oICYN06ufOvWwdMmCAX62v/fmPPU+3b539M5r3TsmCB6IStX+//WF6etZ2LX/868HVVEyfqS9pIRBTvOLITo0pKgC5dgMGDRVmCwYPFzyUl3nGy61XUOL2LbyMxspOcbPy5ANCqlffPsu+dlpKS4B2O9ev1nUuPULXOHI7wap0REcUjdnZiUEkJMG6cf82rI0fEcc8v2uPH5c6pxuldfPu//ysXLxsXyBVXGH8uAFx5ZdN/63nvgnG5gAcf1I558EFrOhyhap0pSni1zoiI4hE7OzFG/cteUfwfU495/mWvN4OynYtvg3n22fCery7q1fveBVNaGroTefy4iDNbJLb6ExHFG3Z2Yozev+wvuUTuvGqc3sW3Z87InV82LpDly40/Ny+vaRrMrFER2U6MFZ2dSJSqICKKN+zsxBi9f9kPGBB63U5amohTqZl7W/j8drRo4b+FuV07ufbIxgViNDlfXp73Aup4GBUx8nkSETV37OzEmEj9ZX/99f7nyMwUxz1ZXXsL8K9QLiMrS+xa8mTWeydbU8to7S0iIjIXOzsxRu9f9jt2yK0v8Zy6URfxHjniHXf0qP8iXtmEfeEk9quo0P+cQG0dMEB0nByOwM9xOICcnNCjIoMGyX0GVnR2jHyeRETNHTs7ce6bb/TF6V3EK1ugM5xCnkY6O4Bor2dbnU7gxRfFf/t2eNSflyyRW6D92mvaMa+9Zm4BT1U8TMUREUUaOzsxRu9f9nqS/qnn17OIN9goiS/ZuEC6dzf+XN8Fx/n5wNtv+y/czs4Wx2WT8eXnA2vW+E+xZWeL41Yl9eMCZSIi/ZhBOcbo/ctetuK3Gqf3/N27y5VzCKfDsnAh8Oc/G3++7+hWfr5YvBxOBmUzz6OHOhV35Ejg0TeHQzzOBcpERE3Y2Ykxev+yb9tWLl6N03v+iy+W6+zI5vsJRK0HpVUiQUugUhVOpzlrasw6j57rvfgicPvtgR9XFLmpOCKi5oTTWDFG7yLbsWPlzqvG6V0APWmS3Pll44Lp0cP4c8PJ8UNERLHP1s7O/Pnz0bdvX6SkpKBTp04YO3YsDhw44BWjKArmzp2LrKwsJCcnY9CgQdjvUxmyvr4e06ZNQ8eOHdGmTRuMGTMG32ktPIlh6l/2gaYwAP+/7GW3bRvZ3g0AHTuaGxeITCV2LZdfbvy50Ya1sYiI9LO1s7N9+3ZMmTIFH3/8MTZv3owLFy5g+PDhOOPxp/iCBQuwaNEiLF26FLt370ZGRgaGDRuGU6dOuWMKCgqwdu1aFBcXY+fOnTh9+jRGjRoFF//F103vAujnn5c7r2xcIDKV2LWMGWP8udGGtbGIiPSzdc3O+++/7/Xz8uXL0alTJ5SVleGmm26CoihYsmQJnnzySeT/tL3lzTffRHp6OoqKivDQQw+hpqYGb7zxBlauXImhQ4cCAFatWoWcnBxs2bIFI0aMiPjrspLsX/Z5eWJ0R3aAS43zza0TjBp3+LBcvGxcIOEUEQWAEyfCe3404dZzIiL9omrNTk1NDQCgQ4cOAICKigpUVVVh+PDh7pikpCQMHDgQu3btAgCUlZXh/PnzXjFZWVnIzc11x/iqr69HbW2t1y1WyP5l/9JLwOrVwF/+Indedev5Dz/IxatxdXVy8bJxgfjMWuoWT9uwufWciEi/qNmNpSgKZs6ciRtvvBG5ubkAgKqqKgBAenq6V2x6ejq++Wk/cVVVFRITE9G+fXu/GPX5vubPn49nnnnG7JcQEbJ/sc+Yoe+86syhz9sYlBqXni43cuLzEeqSlGT8uQBw3XXhPT+acOs5EZF+UTOyM3XqVHz++edYvXq132MOn61HiqL4HfOlFfP444+jpqbGfausrDTe8Aiz6i92dbfT7t1y8Wrc2bNy8bJxgdTXG38uALz6anjPjyZmZYEmImpOoqKzM23aNGzYsAHbtm1Dtse2oIyfqkf6jtBUV1e7R3syMjLQ0NCAEz7DC54xvpKSktCuXTuvW6wItfXcqKefFvfBdnn5UuNkv1TD+fK9+mrjzwWAgwfDe360MSsLNBFRc2FrZ0dRFEydOhUlJSX4xz/+ga5du3o93rVrV2RkZGDz5s3uYw0NDdi+fTv69+8PAOjduzcSEhK8Yo4dO4Z9+/a5Y+JJqK3nRj34oLiXzXSsxh09KhcvGxdIQoLx5wLmdwyjQX6+WPS9bRtQVCTuKyrY0SEiCsTWzs6UKVOwatUqFBUVISUlBVVVVaiqqkLdT6tZHQ4HCgoK8Nxzz2Ht2rXYt28fJk6ciNatW+Oee+4BAKSmpmLSpEmYNWsWtm7dis8++wz33Xcfevbs6d6dFW8+/tj8cx46JO4nT5YrhDl5svjvSNTGCnfNjZVrdlwuoLRULAYvLWV+GyKiqKTYCEDA2/Lly90xjY2NytNPP61kZGQoSUlJyk033aSUl5d7naeurk6ZOnWq0qFDByU5OVkZNWqU8u2330q3o6amRgGg1NTUmPXSLFNfryhOp6KIsR3zbmPHNl1jzhzt2DlzmmIvuUTu/JdcYvw1b9sW3mvbts34tbWsWaMo2dne18rOFsetZue1iYiihez3t0NRzJ4QiT21tbVITU1FTU1N1K/fWbJE/04rGadONdXHGjtWuw5VXl7TVvWMDOD770OfPz0dCLI5LiSXC+jSRT5nkKe0NNE+sxfslpQA48b5TyeqI1hWrp0Jdm31+ly3Q0TNhez3d1QsUCZ5MkU3jWhoEPd1daELbq5f35Q3RzZhXziJ/Tx3IEUDNbFjoM6Gesyqkg1a11avz3IRRETe2NmJMVZlxh04UNzPmSMXr8YlJsrFy8YFY3SdkmdpC7PYWbIh1LUBlosgIvLFzk6M+Wk3fkj9+gFTpwKtW8vFq7ul/t//k4tX44YNk4uXjQsk3EKgZncQ7SzZ8FMuTdPiiIiaA3Z2YswVV8jFffQRsHSpfDK/rCxxL7P+xjPu4ovl4mXjAgm3EKjZiRjtLNmgrpUyK46IqDlgZyfGTJ4MtLDgU9u+XdzLlnVQ41pKFhyRjQtE3Ravl8MB5OSYXzohVGJHq64LNJX1MCuOiKg5YGcnxjid8lNTeqg7sa68Ui5ejfNIeK1JNi6Qbt2MPU9RrCmdYGfJBrWsh1lxRETNATs7MWbHDuD0afPPu2yZuF+4UC5ejfvoI7l42bhAZBIdRppdJRv0fj5ERMTOTsyxqmbpvn3iPjERaNVKO7ZVq6bdVbJTTEanotQ2zZyp/3kOh7XbsO0o2ZCcLPIcacnLE3FERCSwsxNj/vlPa85bUiLud+wAzp3Tjj13rmlr8/HjcueXjQvm+uv1P8fKLeAqpxMYNAgYP17cR2IEat264B0ez4SPREQkhLFslOxw/rw1562vF/eyI0dqnJqhOJS0NGPtApoS6RllVW4iO61bJxI7zpkjqrp37y6mrjiiQ0Tkj52dGFNdbc15O3US97IjR//8J3D//WLx8BdfhI43usgYkEukp8WKLeDRIDlZpBcgIiJtnMaKMVZ9cX/yibiXrZSmxvXvLxcvGxeI0ZEZK7eAExFR7GBnJ8b47v4xi7rgWHYERo2rqJCLl40LxGgHz6qt50REFFvY2Ykx77xjzXlvvVXc9+wpF6/G7d8vFy8bF0ioJH7NVUOD6MxNmybu1WKuRETkjZ2dGBPO2hUthw+L+3//Wy5ejQu1TV0lGxeIVhK/UOK1AnhhoUguOWOGWLczY4b4ubDQ7pYREUUfdnZizEUXWXNetYaW3rpPKSly8bJxwQRL4hdKPFYALywUO698O3EulzjODg8RkTd2dmJMQYE151W3hvfvH3qNi9PZtOB47Fi588vGafFN4vfEE3LPO3Ik/GtHC5kK8IsWcUqLiMgTOzsxJpwt3FrUpH+7doWe9nG5RBwAdO4sd37ZuFA8k/jJVlL/4Qdzrh0NZCrAu1xN5T+IiIidnZgzYEB4CfqCUYuLym7zVuPUxcNarNr+LdvZkY2LBZEoz0FEFG/Y2SEAQJcu4l7vmh118bDDEbgCuMNh3fZv2fU7Vm3Xt4Pe1ABERAQ4FEU2jVz8qq2tRWpqKmpqatCuXTu7m6OptBQYPNj88548CaSmiimQLl20d33l5Ii8OZ4dmMJCsVbEc4rF6RQFPBcsML+9gPG2xrK6uqZROC1nz7J0BBHFP9nvb47sxBgr6jx16yY6OoDoFIwfrx1/993enYeSEuBPfwq8O+hPf2oqMmo2I22NdXrKeRARkcDOTowxu1xEejrw1VdNP7tcwOrV2s8pLm7q2KhFOrXGB63KdaO3rfFA75oqIiJiZyfmDBgAtG1rzrkcDlFY1HPkRabopmfumlDximJdrhu9bY0HetdUEREROzsxx+VqSgAYLnU0xnPkRTYnjRpn50jDN9+YGxcLQpXOYPFTIiJ/7OzEmGXLgMZG887nO/Iim5NGjbNzpGHdOnPjYoFW6Qz1ZxY/JSLyxs5OjDl40JrzqiMvsjl8PDMutwjxW9SiRVPGZTOdOWNuXKwIVjojO1scz8+3p11ERNGKnZ0YY1Xlb3XkRc2kHIoat2NH6JGmxkZr1s306GFuXCzxLZ2xbZvYYs+ODhGRP3Z2Ysx115l7Pt81HnqzEpeWysXLxumxcKG5cbHGs3TGoEGcuiIiCoadnRiTlWXu+RTFe41HRobc82TjrJScDOTlacfk5TG5HhFRc8fOThRpaBAdj2nTxH0sVK4eNMjcOL3WrQve4cnLi6/FyUREZAw7O1GisFCUAZgxA1i6VNy3bi2Oe6quNve6Dof31vOqKrnnqXGyC4+tWKCsWrdObMefMgUYPlzcnz3Ljg4REQkt7W4AiQ5NoHUlLlfTcbW+lNlbuD23ng8apH/r+auvysW/+qroVFklOVl0EomIiHxxZMdmDQ2igKaWRYuaprRCJZUzyujWc9mt8FZtmSciIgqFnR2bLVsWunaTyyXigKakcmbXqje69Vy202XVlnkiIqJQ2Nmx2aFD5sYB/qMzWluSw916LrsV3uwt80RERLK4Zsdm3brpi1OrjAfjcIj1K1u2iMXMmZlifc1dd4nHPUeEApUX8M3KG4wal5MjFy8bR0REZDaHopg9IRJ7amtrkZqaipqaGrRr1y6i125oELuutKaynE6xuygxUSTnGzw49Hm3bfPe7l1SAjz6qHehz+xsMSXmmXXX5QK6dNGuJp6TI7L1Op3644mIiMwi+/3NaSybJSYCM2dqx8ycKeKA8KqMy6ybUdcEORyBC006HN4jQZ7xgfjGExERRRo7O1FgwQJgzhz/DoHTKY6r284BY1XGS0qAceP8R1+OHBHHS0q8j+stNKnGZ2d7H8/JYWFKIiKyn63TWB9++CEWLlyIsrIyHDt2DGvXrsXYsWPdj0+cOBFvvvmm13Ouu+46fPzxx+6f6+vrMXv2bKxevRp1dXUYMmQIli1bhmzfb14Ndk5jeWpoELuuDh0Sa3QmT24a0VGp00ZHjgTekeVwiE6H7DSTb7zvtXbsEKNEmZliEbPWCI3eeCIionDIfn/bukD5zJkzuOaaa/DAAw/g9ttvDxhzyy23YPny5e6fE32+/QsKCrBx40YUFxcjLS0Ns2bNwqhRo1BWVgZnjH3TJiaGTrynThuNGyc6KqEWHO/Yob2exjepoO+19JR50BtPREQUCbZ2dkaOHImRI0dqxiQlJSEjSNXJmpoavPHGG1i5ciWGDh0KAFi1ahVycnKwZcsWjBgxwvQ2y5IZpTFKnTaaPt27I5OdLTo6ntNG4azxISIiigdRv2antLQUnTp1Qo8ePfDb3/4W1R7FocrKynD+/HkMHz7cfSwrKwu5ubnYtWtX0HPW19ejtrbW62Ym2TpX4cjPBw4fFruuiorEfUWF//oYI2t8iIiI4klU59kZOXIk7rjjDnTu3BkVFRX4/e9/j5tvvhllZWVISkpCVVUVEhMT0b59e6/npaeno0qjouX8+fPxzDPPWNJmPXWuwiUzbaSWlwi1xkdNKhiOSKzZ4bogIiLSK6pHdu666y7ceuutyM3NxejRo/Hee+/hyy+/xLvvvqv5PEVR4NDYZ/3444+jpqbGfausrDSlvXrrXEWCusYHCLyVHDBna3hJiVgIPXgwcM894r5LF/+dXtF+DSIiij9R3dnxlZmZic6dO+PgT1UlMzIy0NDQgBMnTnjFVVdXIz09Peh5kpKS0K5dO6+bGfTWuZLlcolkgqtXi/tQ1/Cldyu5Xnq3tkfrNYiIKD7FVGfn+PHjqKysROZPC0x69+6NhIQEbN682R1z7Ngx7Nu3D/379494+6yoc2XWaIbsGh+91PIVgabI1GMFBfo7aHquoSjhX4OIiOKXrWt2Tp8+ja+++sr9c0VFBfbu3YsOHTqgQ4cOmDt3Lm6//XZkZmbi8OHDeOKJJ9CxY0fcdtttAIDU1FRMmjQJs2bNQlpaGjp06IDZs2ejZ8+e7t1ZkaS3zlUo6miG75e8Opqhd1TGiq3h4WxtN+saQPjXICKi+GXryM6nn36Ka6+9Ftdeey0AYObMmbj22mvxhz/8AU6nE+Xl5cjLy0OPHj0wYcIE9OjRAx999BFSUlLc51i8eDHGjh2LO++8EzfccANat26NjRs32pJjZ/Lk0GtfnE4RF0okRkzMEImt7Z71vMyIIyKi5sXWkZ1BgwZBK4HzBx98EPIcrVq1wksvvYSXXnrJzKYZota5CrQbS+VZ50pLJEZMzBCJre0//GBuHBERNS9RvfU8Fqnbyhct8h51cTpFR0dr27nntuovvpC7nt3JACOxtf3ii+XiPv0UmDbN/CSOREQU22ytjRUtrKiNpTeDckmJf0ZkGdu22b9ORV1bBAQuXxHujq/SUrEwWw+ZziUREcU22e9vdnZgfyHQYAuRtZhZwNMMgTprOTn+5SuMCFXMVItv1XgiIoof7OzoYGdnx8gXudaISaBOR3a2SCwYbqcjFCs7WUY6hIC4/tmznNIiIopHst/fMZVnJx7JbKv2FSwZoN2J99St7ePHi3szR5PUxIjZ2fqeZySJIxERxRd2dmwmu8D4qae0kwHGylb1cPgmRhw7Vu55epI4EhFR/OFuLJvJbskeMkR7IXKsbFUPl2dixO+/B9atC/0c2SSOREQUnziyYzN163awuqUOh1joG2rrdiSS+0UbM5M4EhFR/GJnx2ZmVSWPRHK/aKMmcdQim8SRiIjiFzs7UcCMquRmjRB5CrfaeiRcf314jxMRUfzj1nPYn2dHFe7WbTOT+9m5hV1WqG37WrmIiIgo9nHreQwKd+u2GSNEgP1b2GXpWZRNRETNF3djxZn8fCAvz/gIUagt7A6H2MKel2f/aElzXJRNRET6sbMThzy3Z+sVS1vYm+OibCIi0o/TWOQllkZLrFiUTURE8YednRhmxW6pWBotMWvbPhERxTd2dmJUSYnYiTR4MHDPPeK+S5fwFw/37y+XqK9///CuYxazFmUTEVH84tZzRM/Wc1nBKoAb2WLuq7RUdJxC2bbN/jU7nqysuE5ERNFJ9vubC5RjjNW7pWJpzY6ncBZlExFRfOM0VoyxOrdMLK3ZISIiksHOToyxeuSFO5yIiCjesLMTY6weeeEOJyIiijfs7MSYSIy8cIcTERHFEy5QjjHqyMu4caJjE6jgpxkjL+GWnSAiIooW7OzEIHXkJVBV8iVLzBt54Q4nIiKKB+zsxCiOvBAREclhZyeGceSFiIgoNC5QJiIiorjGzg4RERHFNU5jUVB6602xPhUREUUjdnYooJKSwLu9Xnwx8G4vvfFERESRwmmsOORyierlq1eLe5dL3/PVquq+NbiOHBHHS0rCiyciIookh6IEqp/dvMiWiI8F4Y6wuFxAly7Bi406HOJ8FRViikpvPBERkVlkv785shNHzBhh0VtV3eoq7EREROFiZydOuFxiRCfQOJ16rKAg9JSW3qrqVldhJyIiChc7O3HCrBEWvVXVra7CTkREFC52duKEWSMsequqR6IKOxERUTjY2YkTZo2wqFXVAf8OTKCq6nrjiYiIIo2dnThh5giLWlX9kku8j2dni+O+u7r0xhMREUUSt54jfraeq7uxAO+FymoHSG/HgxmUiYgomsXE1vMPP/wQo0ePRlZWFhwOB9atW+f1uKIomDt3LrKyspCcnIxBgwZh//79XjH19fWYNm0aOnbsiDZt2mDMmDH4Tmulbhwze4RFrao+fry4D9Vx0RtPREQUCbZ2ds6cOYNrrrkGS5cuDfj4ggULsGjRIixduhS7d+9GRkYGhg0bhlOnTrljCgoKsHbtWhQXF2Pnzp04ffo0Ro0aBZfetMFxIj8fOHwY2LYNKCoS9xUVnEoiIqLmK2qmsRwOB9auXYuxY8cCEKM6WVlZKCgowGOPPQZAjOKkp6fjhRdewEMPPYSamhpcfPHFWLlyJe666y4AwNGjR5GTk4O///3vGDFihNS142Uai4iIqDmJiWksLRUVFaiqqsLw4cPdx5KSkjBw4EDs2rULAFBWVobz5897xWRlZSE3N9cdE0h9fT1qa2u9bkRERBSforazU1VVBQBIT0/3Op6enu5+rKqqComJiWjfvn3QmEDmz5+P1NRU9y0nJ8fk1hMREVG0iNrOjsrhs5daURS/Y75CxTz++OOoqalx3yorK01pKxEREUWfqO3sZGRkAIDfCE11dbV7tCcjIwMNDQ04ceJE0JhAkpKS0K5dO68bERERxaeo7ex07doVGRkZ2Lx5s/tYQ0MDtm/fjv79+wMAevfujYSEBK+YY8eOYd++fe4YIiIiat5a2nnx06dP46uvvnL/XFFRgb1796JDhw649NJLUVBQgOeeew7du3dH9+7d8dxzz6F169a45557AACpqamYNGkSZs2ahbS0NHTo0AGzZ89Gz549MXToULteFhEREUURWzs7n376KQYPHuz+eebMmQCACRMmYMWKFSgsLERdXR0mT56MEydO4LrrrsOmTZuQkpLifs7ixYvRsmVL3Hnnnairq8OQIUOwYsUKOJnRjoiIiBBFeXbsxDw7REREsSfm8+wQERERmcHWaaxooQ5uMbkgERFR7FC/t0NNUrGzA7hrbTG5IBERUew5deoUUlNTgz7ONTsAGhsbcfToUaSkpIRMWKhHbW0tcnJyUFlZ2WzWAvE18zXHK75mvuZ4FcuvWVEUnDp1CllZWWjRIvjKHI7sAGjRogWys7MtO39zTFzI19w88DU3D3zNzUOsvmatER0VFygTERFRXGNnh4iIiOIaOzsWSkpKwtNPP42kpCS7mxIxfM3NA19z88DX3Dw0h9fMBcpEREQU1ziyQ0RERHGNnR0iIiKKa+zsEBERUVxjZ4eIiIjiGjs7Fvnwww8xevRoZGVlweFwYN26dXY3yVLz589H3759kZKSgk6dOmHs2LE4cOCA3c2y1Msvv4xevXq5E3H169cP7733nt3Nipj58+fD4XCgoKDA7qZYau7cuXA4HF63jIwMu5tluSNHjuC+++5DWloaWrdujZ///OcoKyuzu1mW6dKli9/n7HA4MGXKFLubZpkLFy7gqaeeQteuXZGcnIzLLrsMf/zjH9HY2Gh300zHDMoWOXPmDK655ho88MADuP322+1ujuW2b9+OKVOmoG/fvrhw4QKefPJJDB8+HF988QXatGljd/MskZ2djeeffx6XX345AODNN99EXl4ePvvsM1x99dU2t85au3fvxmuvvYZevXrZ3ZSIuPrqq7Flyxb3z06n08bWWO/EiRO44YYbMHjwYLz33nvo1KkTDh06hIsuusjupllm9+7dcLlc7p/37duHYcOG4Y477rCxVdZ64YUX8Morr+DNN9/E1VdfjU8//RQPPPAAUlNTMX36dLubZyp2diwycuRIjBw50u5mRMz777/v9fPy5cvRqVMnlJWV4aabbrKpVdYaPXq018/PPvssXn75ZXz88cdx3dk5ffo07r33XvzlL3/BvHnz7G5ORLRs2bJZjOaoXnjhBeTk5GD58uXuY126dLGvQRFw8cUXe/38/PPPo1u3bhg4cKBNLbLeRx99hLy8PNx6660AxGe8evVqfPrppza3zHycxiJL1NTUAAA6dOhgc0siw+Vyobi4GGfOnEG/fv3sbo6lpkyZgltvvRVDhw61uykRc/DgQWRlZaFr1664++678fXXX9vdJEtt2LABffr0wR133IFOnTrh2muvxV/+8he7mxUxDQ0NWLVqFX7zm9+YWhw62tx4443YunUrvvzySwDAv/71L+zcuRO/+tWvbG6Z+TiyQ6ZTFAUzZ87EjTfeiNzcXLubY6ny8nL069cP586dQ9u2bbF27VpcddVVdjfLMsXFxdizZw92795td1Mi5rrrrsNf//pX9OjRA99//z3mzZuH/v37Y//+/UhLS7O7eZb4+uuv8fLLL2PmzJl44okn8Mknn+DRRx9FUlISfv3rX9vdPMutW7cOJ0+exMSJE+1uiqUee+wx1NTU4Morr4TT6YTL5cKzzz6L8ePH290007GzQ6abOnUqPv/8c+zcudPupljuiiuuwN69e3Hy5EmsWbMGEyZMwPbt2+Oyw1NZWYnp06dj06ZNaNWqld3NiRjP6eiePXuiX79+6NatG958803MnDnTxpZZp7GxEX369MFzzz0HALj22muxf/9+vPzyy82is/PGG29g5MiRyMrKsrsplnrrrbewatUqFBUV4eqrr8bevXtRUFCArKwsTJgwwe7mmYqdHTLVtGnTsGHDBnz44YfIzs62uzmWS0xMdC9Q7tOnD3bv3o0XX3wRr776qs0tM19ZWRmqq6vRu3dv9zGXy4UPP/wQS5cuRX19fdwv3AWANm3aoGfPnjh48KDdTbFMZmamX4f9Zz/7GdasWWNTiyLnm2++wZYtW1BSUmJ3Uyw3Z84c/O53v8Pdd98NQHTmv/nmG8yfP5+dHaJAFEXBtGnTsHbtWpSWlqJr1652N8kWiqKgvr7e7mZYYsiQISgvL/c69sADD+DKK6/EY4891iw6OgBQX1+P//3f/8WAAQPsboplbrjhBr/UEV9++SU6d+5sU4siR91coS7ajWdnz55FixbeS3edTie3npO806dP46uvvnL/XFFRgb1796JDhw649NJLbWyZNaZMmYKioiKsX78eKSkpqKqqAgCkpqYiOTnZ5tZZ44knnsDIkSORk5ODU6dOobi4GKWlpX470+JFSkqK3xqsNm3aIC0tLa7XZs2ePRujR4/GpZdeiurqasybNw+1tbVx95evpxkzZqB///547rnncOedd+KTTz7Ba6+9htdee83uplmqsbERy5cvx4QJE9CyZfx/PY4ePRrPPvssLr30Ulx99dX47LPPsGjRIvzmN7+xu2nmU8gS27ZtUwD43SZMmGB30ywR6LUCUJYvX2530yzzm9/8RuncubOSmJioXHzxxcqQIUOUTZs22d2siBo4cKAyffp0u5thqbvuukvJzMxUEhISlKysLCU/P1/Zv3+/3c2y3MaNG5Xc3FwlKSlJufLKK5XXXnvN7iZZ7oMPPlAAKAcOHLC7KRFRW1urTJ8+Xbn00kuVVq1aKZdddpny5JNPKvX19XY3zXQORVEUe7pZRERERNZjnh0iIiKKa+zsEBERUVxjZ4eIiIjiGjs7REREFNfY2SEiIqK4xs4OERERxTV2doiIiCiusbNDREREcY2dHSKKOStWrMBFF11kaxsGDRqEgoICW9tARHKYQZmITDNx4kS8+eabfsdHjBhhas2wuro6nDp1Cp06dTLtnHr9+OOPSEhIQEpKim1tICI58V/pjIgi6pZbbsHy5cu9jiUlJZl6jeTkZNsLzHbo0MHW6xORPE5jEZGpkpKSkJGR4XVr3769+3GHw4HXX38dt912G1q3bo3u3btjw4YNXufYsGEDunfvjuTkZAwePBhvvvkmHA4HTp48CcB/Gmvu3Ln4+c9/jpUrV6JLly5ITU3F3XffjVOnTrljFEXBggULcNlllyE5ORnXXHMN3n77bc3XsmzZMnTv3h2tWrVCeno6xo0b537McxqrtLQUDofD7zZx4kR3/MaNG9G7d2+0atUKl112GZ555hlcuHBB57tLREaws0NEEffMM8/gzjvvxOeff45f/epXuPfee/Hjjz8CAA4fPoxx48Zh7Nix2Lt3Lx566CE8+eSTIc956NAhrFu3Du+88w7eeecdbN++Hc8//7z78aeeegrLly/Hyy+/jP3792PGjBm47777sH379oDn+/TTT/Hoo4/ij3/8Iw4cOID3338fN910U8DY/v3749ixY+7bP/7xD7Rq1cod/8EHH+C+++7Do48+ii+++AKvvvoqVqxYgWeffVbvW0dERthac52I4sqECRMUp9OptGnTxuv2xz/+0R0DQHnqqafcP58+fVpxOBzKe++9pyiKojz22GNKbm6u13mffPJJBYBy4sQJRVEUZfny5Upqaqr78aefflpp3bq1Ultb6z42Z84c5brrrnNfo1WrVsquXbu8zjtp0iRl/PjxAV/LmjVrlHbt2nmd09PAgQOV6dOn+x3/97//rXTr1k2ZPHmy+9iAAQOU5557zitu5cqVSmZmZsBzE5G5uGaHiEw1ePBgvPzyy17HfNe39OrVy/3fbdq0QUpKCqqrqwEABw4cQN++fb3if/nLX4a8bpcuXbwWC2dmZrrP+cUXX+DcuXMYNmyY13MaGhpw7bXXBjzfsGHD0LlzZ1x22WW45ZZbcMstt7in3oI5f/48br/9dlx66aV48cUX3cfLysqwe/dur5Ecl8uFc+fO4ezZs5rnJKLwsbNDRKZq06YNLr/8cs2YhIQEr58dDgcaGxsBiLU1DofD63FFYtOo1jnV+3fffReXXHKJV1ywxdMpKSnYs2cPSktLsWnTJvzhD3/A3LlzsXv37qDb3h955BF8++232L17N1q2bPrntbGxEc888wzy8/P9ntOqVauQr42IwsPODhFFlSuvvBJ///vfvY59+umnYZ3zqquuQlJSEr799lsMHDhQ+nktW7bE0KFDMXToUDz99NO46KKL8I9//CNgp2XRokV466238NFHHyEtLc3rsV/84hc4cOBAyE4gEVmDnR0iMlV9fT2qqqq8jrVs2RIdO3aUev5DDz2ERYsW4bHHHsOkSZOwd+9erFixAgD8RnxkpaSkYPbs2ZgxYwYaGxtx4403ora2Frt27ULbtm0xYcIEv+e88847+Prrr3HTTTehffv2+Pvf/47GxkZcccUVfrFbtmxBYWEh/vznP6Njx47u15+cnIzU1FT84Q9/wKhRo5CTk4M77rgDLVq0wOeff47y8nLMmzfP0GsiInncjUVEpnr//feRmZnpdbvxxhuln9+1a1e8/fbbKCkpQa9evfDyyy+7d2OFk6/nP//zP/GHP/wB8+fPx89+9jOMGDECGzduRNeuXQPGX3TRRSgpKcHNN9+Mn/3sZ3jllVewevVqXH311X6xO3fuhMvlwsMPP+z1uqdPnw5AJFV85513sHnzZvTt2xfXX389Fi1ahM6dOxt+PUQkjxmUiSjqPfvss3jllVdQWVlpd1OIKAZxGouIos6yZcvQt29fpKWl4X/+53+wcOFCTJ061e5mEVGMYmeHiKLOwYMHMW/ePPz444+49NJLMWvWLDz++ON2N4uIYhSnsYiIiCiucYEyERERxTV2doiIiCiusbNDREREcY2dHSIiIopr7OwQERFRXGNnh4iIiOIaOztEREQU19jZISIiorj2/wFUsoYf9HJDVgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Multiple Regression Model

\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In reality, there are multiple variables that impact the co2emission. When more than one independent variable is present, the process is called multiple linear regression. An example of multiple linear regression is predicting co2emission using the features FUELCONSUMPTION_COMB, EngineSize and Cylinders of cars. The good thing here is that multiple linear regression model is the extension of the simple linear regression model.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[11.0479666 7.14624226 9.58182024]]\n" + ] + } + ], + "source": [ + "from sklearn import linear_model\n", + "regr = linear_model.LinearRegression()\n", + "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n", + "y = np.asanyarray(train[['CO2EMISSIONS']])\n", + "regr.fit (x, y)\n", + "# The coefficients\n", + "print ('Coefficients: ', regr.coef_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As mentioned before, __Coefficient__ and __Intercept__ are the parameters of the fitted line. \n", + "Given that it is a multiple linear regression model with 3 parameters and that the parameters are the intercept and coefficients of the hyperplane, sklearn can estimate them from our data. Scikit-learn uses plain Ordinary Least Squares method to solve this problem.\n", + "\n", + "#### Ordinary Least Squares (OLS)\n", + "OLS is a method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters of a linear function of a set of explanatory variables by minimizing the sum of the squares of the differences between the target dependent variable and those predicted by the linear function. In other words, it tries to minimizes the sum of squared errors (SSE) or mean squared error (MSE) between the target variable (y) and our predicted output ($\\hat{y}$) over all samples in the dataset.\n", + "\n", + "OLS can find the best parameters using of the following methods:\n", + "* Solving the model parameters analytically using closed-form equations\n", + "* Using an optimization algorithm (Gradient Descent, Stochastic Gradient Descent, Newton’s Method, etc.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Prediction

\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean Squared Error (MSE) : 599.96\n", + "Variance score: 0.86\n" + ] + } + ], + "source": [ + "y_hat= regr.predict(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n", + "x = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n", + "y = np.asanyarray(test[['CO2EMISSIONS']])\n", + "print(\"Mean Squared Error (MSE) : %.2f\"\n", + " % np.mean((y_hat - y) ** 2))\n", + "\n", + "# Explained variance score: 1 is perfect prediction\n", + "print('Variance score: %.2f' % regr.score(x, y))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Explained variance regression score:__ \n", + "Let $\\hat{y}$ be the estimated target output, y the corresponding (correct) target output, and Var be the Variance (the square of the standard deviation). Then the explained variance is estimated as follows:\n", + "\n", + "$\\texttt{explainedVariance}(y, \\hat{y}) = 1 - \\frac{Var\\{ y - \\hat{y}\\}}{Var\\{y\\}}$ \n", + "The best possible score is 1.0, the lower values are worse.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Practice

\n", + "Try to use a multiple linear regression with the same dataset, but this time use FUELCONSUMPTION_CITY and FUELCONSUMPTION_HWY instead of FUELCONSUMPTION_COMB. Does it result in better accuracy?\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[11.23160902 6.45598471 6.94570618 2.0883399 ]]\n", + "Residual sum of squares (MSE): 610.81\n", + "Variance score (R^2): 0.86\n" + ] + } + ], + "source": [ + "from sklearn import linear_model\n", + "import numpy as np\n", + "\n", + "# Membuat model regresi linear\n", + "regr = linear_model.LinearRegression()\n", + "\n", + "# Menentukan fitur dan target\n", + "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n", + "y = np.asanyarray(train[['CO2EMISSIONS']])\n", + "\n", + "# Melatih model\n", + "regr.fit(x, y)\n", + "\n", + "# Menampilkan koefisien\n", + "print('Coefficients: ', regr.coef_)\n", + "\n", + "# Memprediksi nilai CO2EMISSIONS pada data test\n", + "y_ = regr.predict(np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']]))\n", + "\n", + "# Menghitung residual sum of squares dan variance score\n", + "x_test = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n", + "y_test = np.asanyarray(test[['CO2EMISSIONS']])\n", + "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_ - y_test) ** 2))\n", + "print('Variance score (R^2): %.2f' % regr.score(x_test, y_test))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python\n", + "regr = linear_model.LinearRegression()\n", + "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n", + "y = np.asanyarray(train[['CO2EMISSIONS']])\n", + "regr.fit (x, y)\n", + "print ('Coefficients: ', regr.coef_)\n", + "y_= regr.predict(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n", + "x = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n", + "y = np.asanyarray(test[['CO2EMISSIONS']])\n", + "print(\"Residual sum of squares: %.2f\"% np.mean((y_ - y) ** 2))\n", + "print('Variance score: %.2f' % regr.score(x, y))\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thank you for completing this lab!\n", + "\n", + "\n", + "## Author\n", + "\n", + "Saeed Aghabozorgi\n", + "\n", + "\n", + "### Other Contributors\n", + "\n", + "Joseph Santarcangelo\n", + "\n", + "##

© IBM Corporation 2020. All rights reserved.

\n", + " \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python", + "language": "python", + "name": "conda-env-python-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.12" + }, + "prev_pub_hash": "c1170d4cb1c9bbce7dbbef74b645fc6b265a5aaf4ce89c4ac861feed8769ed99" + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-NoneLinearRegression.ipynb b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-NoneLinearRegression.ipynb new file mode 100644 index 0000000..56803ad --- /dev/null +++ b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-NoneLinearRegression.ipynb @@ -0,0 +1,897 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

\n", + " \n", + " \"Skills\n", + " \n", + "

\n", + "\n", + "\n", + "# Non Linear Regression Analysis\n", + "\n", + "\n", + "Estimated time needed: **20** minutes\n", + " \n", + "\n", + "## Objectives\n", + "\n", + "After completing this lab you will be able to:\n", + "\n", + "* Differentiate between linear and non-linear regression\n", + "* Use non-linear regression model in Python\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression since linear regression presumes that the data is linear. \n", + "Let's learn about non linear regressions and apply an example in python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Importing required libraries

\n" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Although linear regression can do a great job at modeling some datasets, it cannot be used for all datasets. First recall how linear regression, models a dataset. It models the linear relationship between a dependent variable y and the independent variables x. It has a simple equation, of degree 1, for example y = $2x$ + 3.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(-5.0, 5.0, 0.1)\n", + "\n", + "##You can adjust the slope and intercept to verify the changes in the graph\n", + "y = 2*(x) + 3\n", + "y_noise = 2 * np.random.normal(size=x.size)\n", + "ydata = y + y_noise\n", + "#plt.figure(figsize=(8,6))\n", + "plt.plot(x, ydata, 'bo')\n", + "plt.plot(x,y, 'r') \n", + "plt.ylabel('Dependent Variable')\n", + "plt.xlabel('Independent Variable')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Non-linear regression is a method to model the non-linear relationship between the independent variables $x$ and the dependent variable $y$. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). For example:\n", + "\n", + "$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n", + "\n", + "Non-linear functions can have elements like exponentials, logarithms, fractions, and so on. For example: $$ y = \\log(x)$$\n", + " \n", + "We can have a function that's even more complicated such as :\n", + "$$ y = \\log(a x^3 + b x^2 + c x + d)$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's take a look at a cubic function's graph.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(-5.0, 5.0, 0.1)\n", + "\n", + "##You can adjust the slope and intercept to verify the changes in the graph\n", + "y = 1*(x**3) + 1*(x**2) + 1*x + 3\n", + "y_noise = 20 * np.random.normal(size=x.size)\n", + "ydata = y + y_noise\n", + "plt.plot(x, ydata, 'bo')\n", + "plt.plot(x,y, 'r') \n", + "plt.ylabel('Dependent Variable')\n", + "plt.xlabel('Independent Variable')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some other types of non-linear functions are:\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Quadratic\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$ Y = X^2 $$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(-5.0, 5.0, 0.1)\n", + "\n", + "##You can adjust the slope and intercept to verify the changes in the graph\n", + "\n", + "y = np.power(x,2)\n", + "y_noise = 2 * np.random.normal(size=x.size)\n", + "ydata = y + y_noise\n", + "plt.plot(x, ydata, 'bo')\n", + "plt.plot(x,y, 'r') \n", + "plt.ylabel('Dependent Variable')\n", + "plt.xlabel('Independent Variable')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exponential\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = np.arange(-5.0, 5.0, 0.1)\n", + "\n", + "##You can adjust the slope and intercept to verify the changes in the graph\n", + "\n", + "Y= np.exp(X)\n", + "\n", + "plt.plot(X,Y) \n", + "plt.ylabel('Dependent Variable')\n", + "plt.xlabel('Independent Variable')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Logarithmic\n", + "\n", + "The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n", + "\n", + "Please consider that instead of $x$, we can use $X$, which can be a polynomial representation of the $x$ values. In general form it would be written as \n", + "\\begin{equation}\n", + "y = \\log(X)\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n", + " This is separate from the ipykernel package so we can avoid doing imports until\n" + ] + }, + { + "data": { + "image/png": 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Zrq6uCAwMxMKFC5GTk4MNGzYAAObMmYOVK1di/vz5mD17No4ePYp169bh66+/lupHIKJ2qqpGg72p1/DdqRwc+O06NNr6U+qWFjIM6eKOCX19cW+4Fxxt+T9SRB2NSZWhpKQkjBw5Uve8YW7PjBkzEB8fj7y8PGRlZeleDwkJwc6dO/H888/jk08+ga+vLz766CNeVk9EAOpvh5F4qQjbTuVg17l8lKv/uBKsj78CE/v6YXyELzwceeqcqCOTiYYZxdQslUoFhUIBpVIJJycnqeMQkQFcul6OLSevYuvJnEb3A/NztsOD/fwwsZ8vung6SpiQiO6UPt/fJjUyRETUWqrqWuw4k4dvT1zFiSsluu1Otla4r48vHuznx7WAiMwUyxARdVgarcCRjEJ8e+Iqdp3Lh7pOCwCwkAHDu3ng4cgA3B3GidBE5o5liIg6nCtFFfhPUnaT02BdPR3wcKQ/HuznB08nWwkTElF7wjJERB1Cda0Gu1Pysfl4No5kFOm2O9laYUJfPzwc6Y8+/oqbLrhKROaLZYiITNqFfBW+OZaNbadyoKyqBQDIZMCwrh54JMof94R58TQYEd0SyxARmZxydR22n87FN8ezcfqGRRF9FbZ4dEAAHokKgJ+znXQBiciksAwRkck4e1WJTb9ewfenc1FZowEAWFnIMLqnFyYPCMSQLu68LxgR6Y1liIjataoaDbafycWmxCs4fVWp2x7q0QlTBgRgUn9/uDtwUUQiaj2WISJql9ILyrDp1yxsOXEVqur6laFtLC0Q29sbUwcGYmCIKydDE5FBsAwRUbtRU6fFnvP52Jh4BYmXinXbA1zt8Fh0EB6J9IcbR4GIyMBYhohIcgWqamz8NQtf/ZqFwnI1gPqFEe8O88Jj0YEY1tWDK0MTkdGwDBGRJIQQOJVdivjDl7HzbB7qfr9LvKejHFMGBmLKgAD48oowImoDLENE1KbUdRrsOJOH+COXceaGCdFRQS6YeVcwxvT0hrWlhYQJicjcsAwRUZu4pqrGpsQr+OpYFgrLawAANlYWeCDCFzMHB6OXn0LihERkrliGiMiozuUosfbQJfxw5o9TYT4KW/x1UBCmDAjghGgikhzLEBEZnFYrsO9CAdb+cqnRVWEDg10x865gjA73ghVPhRFRO8EyREQGU12rwZaTV7Hul0xcul4BoH6F6Pv7+ODJoaE8FUZE7RLLEBHdsetlanx59DI2/pqF4or6+UCOtlaYOjAQM+8Kho+CV4URUfvFMkRErXbpejnWHLyEradyUFOnBQD4u9jhibtC8OiAADjI+VcMEbV//JuKiPR2LkeJ1QkZ2HkuD6J+TjT6BTpj9tBQzgciIpPDMkRELSKEQOKlYqxKSMehi4W67Xf38MTfRnRGVLCrhOmIiFqPZYiIbkmrFfgp9RpWH8jAqaxSAIClhQzj+/hgzojO6OHtJG1AIqI7xDJERM2q02jx/elc/PtABn67Vg6gfpHEyVEB+L9hoQhwtZc4IRGRYbAMEVEjtRottp3KwSf703GlqBIA4Ci3wl9jgvDEXSHwcOQiiUTUsbAMERGA30vQyRys3J+OrOL6EuTayQazhoRgWkwQnGytJU5IRGQcLENEZq6mToutJ6/ik4R0ZBdXAQDcHWzwf8NC8ddBQbC34V8TRNSx8W85IjNVU6fFtyeu4pP96cgp/aMEPTWsMx4bFMgSRERmg3/bEZmZWk19CVq578YSJMec4aF4LDoIdjaWEickImpbLENEZkKrFfjhbB7+tfc3ZBbW3zfMw1GOOcM7Y+rAQJYgIjJbLENEHZwQAvvTCvDu7t+QmqcCUD8x+ukRnfHXQUGwtWYJIiLzxjJE1IH9eqkI7+5OQ9KVEgD1l8jPHhaKJ4aE8L5hRES/49+GRB3QuRwl3t2dhgO/XQcAyK0sMHNwMOYM7wyXTjYSpyMial9M7m6Kq1atQkhICGxtbREZGYlDhw7ddN+EhATIZLImjwsXLrRhYqK2c6WoAs9sOon7P/4FB367DisLGR6LDsTBF0di4bgwFiEiomaY1MjQ5s2bMW/ePKxatQp33XUXPv30U8TGxuL8+fMIDAy86XFpaWlwcvrj/kkeHh5tEZeozZRW1uDjfenYcPQyajUCMhkwIcIXz9/bDUFunaSOR0TUrsmEEELqEC0VHR2N/v37Y/Xq1bptYWFhmDhxIuLi4prsn5CQgJEjR6KkpATOzs6t+kyVSgWFQgGlUtmoUBG1BzV1Wmw4ehkf70uHsqoWADCsmwcWxvZAmA//fSUi86XP97fJjAzV1NTgxIkT+Oc//9lo++jRo3HkyJFbHtuvXz9UV1cjPDwcr776KkaOHHnTfdVqNdRqte65SqW6s+BERiCEwK5z+Vi264Lu/mE9vB2xcFwYhnfjyCcRkT5MpgwVFhZCo9HAy8ur0XYvLy/k5+c3e4yPjw/WrFmDyMhIqNVqfPnll7j77ruRkJCAYcOGNXtMXFwcli5davD8RIZyKqsEb+1I1V0h5uEox4LR3fBwZAAsLWQSpyMiMj0mU4YayGSN/7IXQjTZ1qB79+7o3r277nlMTAyys7Px3nvv3bQMLVy4EPPnz9c9V6lUCAgIMEByojuTU1qFuJ2p+OFMHgDAztoS/zcsFP83LBSdeJk8EVGrmczfoO7u7rC0tGwyClRQUNBktOhWBg0ahI0bN970dblcDrlc3uqcRIZWXavBZwcv4ZOEdFTXaiGTAQ/398c/RneHt8JW6nhERCbPZMqQjY0NIiMjsXfvXjz44IO67Xv37sWECRNa/D6nTp2Cj4+PMSISGZQQAj+nFuD1H84jq7h+XlB0iCsWjQ9HT1+FxOmIiDoOkylDADB//nxMmzYNUVFRiImJwZo1a5CVlYU5c+YAqD/FlZOTgw0bNgAAVqxYgeDgYPTs2RM1NTXYuHEjtmzZgi1btkj5YxDdVmZhBV7fnoL9afWLJno72eKV+8Jwfx+fm54WJiKi1jGpMjR58mQUFRXh9ddfR15eHnr16oWdO3ciKCgIAJCXl4esrCzd/jU1NViwYAFycnJgZ2eHnj17YseOHRg3bpxUPwLRLVXW1GHlvnSsPZSJGo0W1pYyPDk0FHNHduG8ICIiIzGpdYakwHWGqC0IIbDjbB7e2pGKPGU1AGB4Nw8sHh+OUA8HidMREZmeNllnqKamBpmZmejcuTOsrPh/rEStlVlYgVe/O4vD6UUAAH8XOyy6Pxz3hnvxlBgRURvQ+95klZWVmDVrFuzt7dGzZ0/daalnn30Wy5YtM3hAoo6qVqPFJ/vTMWbFQRxOL4LcygLz7umKn+YPx+ie3ixCRERtRO8ytHDhQpw+fRoJCQmwtf3jst577rkHmzdvNmg4oo7qVFYJ7v/oF7y7Ow01dVoM7eqOPc8Pw7x7usHW2lLqeEREZkXv81vfffcdNm/ejEGDBjX6P9fw8HBkZGQYNBxRR1OursN7u9Ow/uhlCAG4drLBa/eHYWJfP44EERFJRO8ydP36dXh6ejbZXlFRwb/MiW5h7/lrWPS/c7oJ0pP6++HV+8Lh2slG4mREROZN79NkAwYMwI4dO3TPGwrQZ599hpiYGMMlI+ogClTV+NvGE5i9IQl5ymoEutpj46xofPBoXxYhIqJ2QO+Robi4OIwdOxbnz59HXV0dPvzwQ6SkpODo0aM4cOCAMTISmSQhBLaczMHS7Skoq66DpYUMs4eG4rm7u8LOhvOCiIjaC71HhgYPHozDhw+jsrISnTt3xp49e+Dl5YWjR48iMjLSGBmJTE5BWTVmbziBBf89jbLqOkT4K7B97hD8M7YHixARUTvDRRdvg4sukr52ns3DK9vOoqSyFtaWMjx/bzc8NawzLC04p46IqK0YfNFFlUrV4g9nYSBzVVpZg0X/S8H3p3MBAGE+Tvjg0QiE+fC/CSKi9qxFZcjZ2fm2V4oJISCTyaDRaAwSjMiU7L9QgJe2nEFBmRqWFjI8PaIz/j6qK2ys9D4TTUREbaxFZWj//v3GzkFkksrVdXhrx3l8fSwbANDZoxPef7Qv+gY4SxuMiIharEVlaPjw4cbOQWRyjmUWY/5/knG1pAoA8MRdIXhxbHeuIE1EZGJadYfVkpISrFu3DqmpqZDJZAgLC8Pjjz8OV1dXQ+cjanc0WoGV+9Lx4c+/QSvqb6z67sMRiOnsJnU0IiJqBb0nNBw4cADBwcH46KOPUFJSguLiYnz00UcICQnhOkPU4eUrqzH1s0T866f6IvRQf3/smjeMRYiIyITpfWl9r169MHjwYKxevRqWlvWnAzQaDZ5++mkcPnwY586dM0pQqfDSemqw78I1LPjvGRRX1MDexhJvPdgLD/bzlzoWERE1Q5/vb73LkJ2dHZKTk9G9e/dG29PS0tC3b19UVVXpn7gdYxmimjotlu+6gLW/ZAIAevo64eO/9EOoh4PEyYiI6GYMvs7Qjfr374/U1NQmZSg1NRV9+/bV9+2I2rUrRRX4+9encOaqEgDw+F3B+GdsD8itOEmaiKijaFEZOnPmjO7Pzz77LJ577jmkp6dj0KBBAIDExER88sknWLZsmXFSEkng+9O5eHnrWZSr6+Bsb413H47AveFeUsciIiIDa9FpMgsLC8hkMtxu14646CJPk5mf6loNlnyfgm+O168dNDDYFR/+pS98FHYSJyMiopYy+GmyzMxMgwQjau9yS6swZ+MJnLmqhEwG/H1UVzw7qgusLLmSNBFRR9WiMhQUFGTsHESSS7xUhGc2nURRRQ1c7K3x8V/6Y0hXd6ljERGRkbVq0UUAOH/+PLKyslBTU9No+wMPPHDHoYjakhAC649cxps7UlGnFQj3ccKn0yIR4GovdTQiImoDepehS5cu4cEHH8TZs2cbzSNquJFrR5szRB1bda0Gr2w7hy0nrwIAJvT1xbJJfWBnw6vFiIjMhd4TIZ577jmEhITg2rVrsLe3R0pKCg4ePIioqCgkJCQYISKRceSWVuHRT49iy8mrsJABr94XhhWT+7IIERGZGb1Hho4ePYp9+/bBw8MDFhYWsLCwwJAhQxAXF4dnn30Wp06dMkZOIoP68/ygT6b2x+AunB9ERGSO9B4Z0mg0cHCoX3nX3d0dubm5AOonWaelpRk2HZGBCSHwxeFMPLb2VxRV1CDcxwnfzx3CIkREZMb0Hhnq1asXzpw5g9DQUERHR2P58uWwsbHBmjVrEBoaaoyMRAZRp9Hitf+dw9fH6tcPmtjXF3GcH0REZPb0LkOvvvoqKioqAABvvvkm7r//fgwdOhRubm7YvHmzwQMSGUKFug7PfHUSCWnXYSEDXh4XhllDQnQT/4mIyHzpfaPW5hQXF8PFxaVDfrFwBWrTV6CqxhPrj+Ncjgq21hb4+C/9eVsNIqIOzqg3am2Oq6urId6GyOAuXivDzC+OI6e0Cm6dbLBu5gD0DXCWOhYREbUjLSpDkyZNQnx8PJycnDBp0qRb7rt161aDBCO6U0czivB/XyahrLoOoe6dEP/4QAS6cSFFIiJqrEVlSKFQ6E6BKRQKowYiMoT/Jefghf+eQY1Gi8ggF6ydHgWXTjZSxyIionZIrzlDQghkZWXBw8MD9vbS/B/2qlWr8O677yIvLw89e/bEihUrMHTo0Jvuf+DAAcyfPx8pKSnw9fXFiy++iDlz5rT48zhnyLQIIbD6QAaW76pf5mFcb2988Ghf2FrzijEiInOiz/e3XusMCSHQtWtX5OTk3FHA1tq8eTPmzZuHV155BadOncLQoUMRGxuLrKysZvfPzMzEuHHjMHToUJw6dQovv/wynn32WWzZsqWNk1NbqNNo8ep353RFaPbQEKz8S38WISIiuiW9rybr2bMn1q1bh0GDBhkr001FR0ejf//+WL16tW5bWFgYJk6ciLi4uCb7v/TSS/j++++Rmpqq2zZnzhycPn0aR48ebfYz1Go11Gq17rlKpUJAQABHhtq56loN5n51Ej+lFkAmAxbfH46Zd4VIHYuIiCRitJEhAFi+fDleeOEFnDt3rtUBW6OmpgYnTpzA6NGjG20fPXo0jhw50uwxR48ebbL/mDFjkJSUhNra2maPiYuLg0Kh0D0CAgIM8wOQ0VTVaDB7QxJ+Si2A3MoC//5rJIsQERG1mN5l6K9//SuOHTuGiIgI2NnZwdXVtdHDWAoLC6HRaODl1Xh9GC8vL+Tn5zd7TH5+frP719XVobCwsNljFi5cCKVSqXtkZ2cb5gcgoyhX12HmF8dw6GIh7G0ssf6JgRjT01vqWEREZEL0XmdoxYoVRojRcn9e2FEIccvFHpvbv7ntDeRyOeRy+R2mpLagqq7FzM+P4WRWKRzlVoh/YgAig7jmFRER6UfvMjRjxgxj5Lgtd3d3WFpaNhkFKigoaDL608Db27vZ/a2srODm5ma0rGR8pZU1mP75MZy5qoTCzhpfzhqIPv7OUsciIiITpPdpshtVVVVBpVI1ehiLjY0NIiMjsXfv3kbb9+7di8GDBzd7TExMTJP99+zZg6ioKFhbWxstKxlXUbkaU9Yk4sxVJVw72eDr2YNYhIiIqNX0LkMVFRWYO3cuPD094eDgABcXl0YPY5o/fz7Wrl2Lzz//HKmpqXj++eeRlZWlWzdo4cKFmD59um7/OXPm4MqVK5g/fz5SU1Px+eefY926dViwYIFRc5LxFKiqMWVNIi7kl8HDUY7N/zcI4b68yo+IiFpP79NkL774Ivbv349Vq1Zh+vTp+OSTT5CTk4NPP/0Uy5YtM0ZGncmTJ6OoqAivv/468vLy0KtXL+zcuRNBQUEAgLy8vEZrDoWEhGDnzp14/vnn8cknn8DX1xcfffQRHnroIaPmJOPILa3CY2t/RWZhBXwUttj0ZDRCPRykjkVERCZO73WGAgMDsWHDBowYMQJOTk44efIkunTpgi+//BJff/01du7caayskuAK1O1DdnEl/vJZIq6WVMHfxQ5fzx6EAFfeZ4yIiJpn1HWGiouLERJSv4aLk5MTiouLAQBDhgzBwYMHWxGX6Nayiysx+dOjuFpShWA3e/znqRgWISIiMhi9y1BoaCguX74MAAgPD8d//vMfAMD27dvh7OxsyGxEKCirxl/X/YpcZTU6e3TCf56Kga+zndSxiIioA9G7DD3++OM4ffo0gPoJy6tWrYJcLsfzzz+PF154weAByXwpq2ox4/PjuFJUiQDX+lNjnk62UsciIqIOpsVzhubNm4cnn3wSvXr1arQ9KysLSUlJ6Ny5MyIiIowSUkqcMySNqhoNpn/+K45fLoG7gxxb/haDILdOUsciIiITYZQ5Q7t27UJERAQGDhyINWvW6NYUCgwMxKRJkzpkESJp1Gq0eOarkzh+uQSOtlb4ctZAFiEiIjKaFpehCxcu4ODBg+jduzcWLFgAX19fTJ8+nZOmyaC0WoEX/nsa+y4UwNbaAp/PHIAwH47IERGR8eg1Z+iuu+7CunXrkJ+fj48//hiXL1/GiBEj0LVrVyxbtgy5ubnGyklmQAiB1384j++Sc2FlIcPqxyIxIJj3GiMiIuPSe52hP8vIyMDnn3+O1atXo7y8HDU1NYbK1i5wzlDb+fCni/jXT7/V/3lKX0zo6ydxIiIiMlVGXWfoRhUVFThw4AAOHDiA0tJSdO7c+U7ejszY+iOXdUVo6QM9WYSIiKjNtKoMHTx4EI8//ji8vb3x3HPPoVu3bjh06BBSU1MNnY/MwP+Sc7D4+xQAwLx7umLG4GBpAxERkVlp8b3Jrl69ivXr1yM+Ph4ZGRmIjo7Gv/71L0yZMgUODrw/FLVOQloB/vGf+nWrZsQE4bm7u0qciIiIzE2Ly1BwcDDc3Nwwbdo0zJo1C2FhYcbMRWYgvaAMc786hTqtwIS+vlg8vidkMpnUsYiIyMy0uAz95z//wQMPPAArK71vdE/UhLKyFk+uT0K5ug4DQ1zx7sMRsLBgESIiorbX4mYzadIkY+YgM1Kn0WLu1ydxuagSfs52WP1Yf9hY3dFcfiIiolbjNxC1uXd2XcChi4Wws7bEmumRcHOQSx2JiIjMGMsQtaktJ67is0OZAID3HolAT1+FxImIiMjcsQxRm0nOLsXCbWcBAH8f1QX39fGROBEREVErytATTzyBsrKyJtsrKirwxBNPGCQUdTwFqmo89WUSauq0uCfMC8/f003qSERERABaUYbWr1+PqqqqJturqqqwYcMGg4SijqW6VoP/+/IErqnU6OrpgH9N5pVjRETUfrT4ajKVSgUhBIQQKCsrg62tre41jUaDnTt3wtPT0yghyXQJIfDKtnNIzi6Fws4aa2dEwdHWWupYREREOi0uQ87OzpDJZJDJZOjWrekpDplMhqVLlxo0HJm+zw9fxpaTV2EhAz6Z2h9Bbp2kjkRERNRIi8vQ/v37IYTAqFGjsGXLFri6uupes7GxQVBQEHx9fY0SkkzTLxcL8daO8wCAV+4Lx5Cu7hInIiIiaqrFZWj48OEAgMzMTAQEBMDCghei0c3lllbhma9OQiuAhyP98cRdwVJHIiIiapbe99YICgpCaWkpjh07hoKCAmi12kavT58+3WDhyDRptQL/+M9pKKtqEeGvwFsP9uI9x4iIqN3Suwxt374djz32GCoqKuDo6NjoS04mk7EMET47dAlHLxXB3sYSK6b0g9zKUupIREREN6X3ua5//OMfurWGSktLUVJSonsUFxcbIyOZkJRcJd7bkwYAWHR/OELcOWGaiIjaN73LUE5ODp599lnY29sbIw+ZsOpaDZ77Jhm1GoHR4V6YPCBA6khERES3pXcZGjNmDJKSkoyRhUxc3M5UpBeUw8NRjmUP9eE8ISIiMgl6zxm677778MILL+D8+fPo3bs3rK0bL6D3wAMPGCwcmY79aQVYf/QKgPobsLp2spE4ERERUcvIhBBCnwNudUm9TCaDRqO541DtiUqlgkKhgFKphJOTk9Rx2qWicjXGrDiEwnI1Zg4OxpIHekodiYiIzJw+3996jwz9+VJ6Mm9CCLy05SwKy9Xo5uWAf8b2kDoSERGRXu5o5cTq6mpD5SAT9c3xbPyUeg02lhZYMbkfbK15GT0REZkWvcuQRqPBG2+8AT8/Pzg4OODSpUsAgNdeew3r1q0zeMAGJSUlmDZtGhQKBRQKBaZNm4bS0tJbHjNz5kzd/dQaHoMGDTJaRnNz6Xo5Xt9ef7uNBWO6IdyXpxGJiMj06F2G3nrrLcTHx2P58uWwsfljkmzv3r2xdu1ag4a70dSpU5GcnIxdu3Zh165dSE5OxrRp02573NixY5GXl6d77Ny502gZzUmtRovnNyejqlaDwZ3d8OSQUKkjERERtYrec4Y2bNiANWvW4O6778acOXN02/v06YMLFy4YNFyD1NRU7Nq1C4mJiYiOjgYAfPbZZ4iJiUFaWhq6d+9+02Plcjm8vb1b/FlqtRpqtVr3XKVStT54B/bhTxdx+qoSTrZWeP/RCFhY8DJ6IiIyTa1adLFLly5Ntmu1WtTW1hok1J8dPXoUCoVCV4QAYNCgQVAoFDhy5Mgtj01ISICnpye6deuG2bNno6Cg4Jb7x8XF6U7FKRQKBARw4cA/O3GlGKsS0gEAb0/qDR+FncSJiIiIWk/vMtSzZ08cOnSoyfb//ve/6Nevn0FC/Vl+fj48PT2bbPf09ER+fv5Nj4uNjcWmTZuwb98+vP/++zh+/DhGjRrVaOTnzxYuXAilUql7ZGdnG+Rn6CjqNFq8su0ctAKY1M8P9/fxlToSERHRHdH7NNnixYsxbdo05OTkQKvVYuvWrUhLS8OGDRvwww8/6PVeS5YswdKlS2+5z/HjxwGg2dWMhRC3XOV48uTJuj/36tULUVFRCAoKwo4dOzBp0qRmj5HL5ZDL5S2Jb5a+TLyCC/llcLa3xmv3h0sdh4iI6I7pXYbGjx+PzZs34+2334ZMJsOiRYvQv39/bN++Hffee69e7zV37lxMmTLllvsEBwfjzJkzuHbtWpPXrl+/Di8vrxZ/no+PD4KCgnDx4kW9clK962VqfLDnNwDAC2O6w4WrTBMRUQegdxkC6u9PNmbMmDv+cHd3d7i7u992v5iYGCiVShw7dgwDBw4EAPz6669QKpUYPHhwiz+vqKgI2dnZ8PHxaXVmc7bsxwsoU9eht58CUwYESh2HiIjIIO5o0cW2EhYWhrFjx2L27NlITExEYmIiZs+ejfvvv7/RlWQ9evTAtm3bAADl5eVYsGABjh49isuXLyMhIQHjx4+Hu7s7HnzwQal+FJN14koxtpy8CgBYOqEnLHn1GBERdRAtGhlycXFp8R3Ii4uL7yjQzWzatAnPPvssRo8eDaD+hrArV65stE9aWhqUSiUAwNLSEmfPnsWGDRtQWloKHx8fjBw5Eps3b4ajo6NRMnZUGq3Aa9+lAAAejfJH/0AXiRMREREZTovK0IoVK3R/LioqwptvvokxY8YgJiYGQP2l77t378Zrr71mlJAA4Orqio0bN95ynxvvOWtnZ4fdu3cbLY85+erXKzifp4KTrRVeGst7jxERUcei913rH3roIYwcORJz585ttH3lypX46aef8N133xkyn+TM/a71ReVqjHwvAarqOrw+oSemxwRLHYmIiOi29Pn+1nvO0O7duzF27Ngm28eMGYOffvpJ37ejdm75rjSoqusQ7uOEx6KDpI5DRERkcHqXITc3N90k5Rt99913cHNzM0goah9OZZVgc1L9opOvc9I0ERF1UHpfWr906VLMmjULCQkJujlDiYmJ2LVrl1Fv1EptS6MVWPS/+knTk/r7ISrYVeJERERExqF3GZo5cybCwsLw0UcfYevWrRBCIDw8HIcPH2507zAybZuPZ+NsjhKOcissjA2TOg4REZHRtGrRxejoaGzatMnQWaidKKmowfLdFwAAz9/bDR6OvD0JERF1XK0qQ1qtFunp6SgoKIBWq2302rBhwwwSjKTz7p40lFbWoruXI6bHcNI0ERF1bHqXocTEREydOhVXrlzBn6/Kl8lk0Gg0BgtHbe/M1VJ8fSwLQP2kaStLk1iknIiIqNX0LkNz5sxBVFQUduzYAR8fnxavTE3tnxACS75PgRDAhL6+iA7l1YFERNTx6V2GLl68iG+//RZdunQxRh6S0KGLhTiZVQq5lQVeHsdJ00REZB70PgcSHR2N9PR0Y2Qhia3cV//PdWp0ILycbCVOQ0RE1Db0Hhn6+9//jn/84x/Iz89H7969YW1t3ej1Pn36GCwctZ3ES0U4drkYNpYWeGpYZ6njEBERtRm9y9BDDz0EAHjiiSd022QyGYQQnEBtwj7edxEA8OgAf3grOCpERETmQ+8ylJmZaYwcJKETV0pwOL0IVhYyzBnOUSEiIjIvepehoCCuO9PRNIwKTervB38Xe4nTEBERta1WLSLz5Zdf4q677oKvry+uXLkCAFixYgX+97//GTQcGd/Zq0okpF2HhQx4egSvECQiIvOjdxlavXo15s+fj3HjxqG0tFQ3R8jZ2RkrVqwwdD4ysoZRoQl9/RDs3kniNERERG1P7zL08ccf47PPPsMrr7wCS0tL3faoqCicPXvWoOHIuFLzVNhz/hpkMuCZkRwVIiIi86R3GcrMzES/fv2abJfL5aioqDBIKGobK/fXrys0rrcPung6SJyGiIhIGnqXoZCQECQnJzfZ/uOPPyI8PNwQmagNpBeUY+fZPADA30dxVIiIiMyX3leTvfDCC3jmmWdQXV0NIQSOHTuGr7/+GnFxcVi7dq0xMpIRrNqfDiGA0eFe6OHtJHUcIiIiyehdhh5//HHU1dXhxRdfRGVlJaZOnQo/Pz98+OGHmDJlijEykoFdKarA/07nAgD+PqqrxGmIiIikpXcZAoDZs2dj9uzZKCwshFarhaenp6FzkRGt2p8BjVZgRHcP9PZXSB2HiIhIUq0qQwBQUFCAtLQ0yGQyyGQyeHh4GDIXGcnVkkpsOXkVAEeFiIiIgFZMoFapVJg2bRp8fX0xfPhwDBs2DL6+vvjrX/8KpVJpjIxkQJ8euIQ6rcBdXdwQGeQidRwiIiLJ6V2GnnzySfz666/YsWMHSktLoVQq8cMPPyApKQmzZ882RkYykGuqamxOygbAUSEiIqIGep8m27FjB3bv3o0hQ4boto0ZMwafffYZxo4da9BwZFifHriEmjotBga7YlCom9RxiIiI2gW9R4bc3NygUDSddKtQKODiwtMu7VVhuRpfHau/j9zf7+a6QkRERA30LkOvvvoq5s+fj7y8PN22/Px8vPDCC3jttdcMGo4M59sTV1Fdq0WEvwJDurhLHYeIiKjd0Ps02erVq5Geno6goCAEBgYCALKysiCXy3H9+nV8+umnun1PnjxpuKTUakII/Pf3uUJTowMhk8kkTkRERNR+6F2GJk6caIQYZEynskuRcb0CttYWGNfbR+o4RERE7YreZWjx4sXGyEFG9N+k+nWFxvXygaOttcRpiIiI2he95wwBQGlpKdauXYuFCxeiuLgYQP0psZycHIOGu9Fbb72FwYMHw97eHs7Ozi06RgiBJUuWwNfXF3Z2dhgxYgRSUlKMlrE9qq7V4Iffb73xcJS/xGmIiIjaH73L0JkzZ9CtWze88847eO+991BaWgoA2LZtGxYuXGjofDo1NTV45JFH8Le//a3FxyxfvhwffPABVq5ciePHj8Pb2xv33nsvysrKjJazvdmdko8ydR38XewwKISX0xMREf2Z3mVo/vz5mDlzJi5evAhbW1vd9tjYWBw8eNCg4W60dOlSPP/88+jdu3eL9hdCYMWKFXjllVcwadIk9OrVC+vXr0dlZSW++uqrmx6nVquhUqkaPUxZwymyh/r7w8KCE6eJiIj+TO8ydPz4cTz11FNNtvv5+SE/P98goQwhMzMT+fn5GD16tG6bXC7H8OHDceTIkZseFxcXB4VCoXsEBAS0RVyjyCmtwuGMQgDAw5E8RUZERNQcvcuQra1ts6MlaWlp7epmrQ3FzMvLq9F2Ly+vW5a2hQsXQqlU6h7Z2dlGzWlMW05chRBATKgbAlztpY5DRETULuldhiZMmIDXX38dtbW1AACZTIasrCz885//xEMPPaTXey1ZskR31/ubPZKSkvSN2Mif19QRQtxynR25XA4nJ6dGD1Ok1Qp8e6L+FNkjnDhNRER0U3pfWv/ee+9h3Lhx8PT0RFVVFYYPH478/HzExMTgrbfe0uu95s6diylTptxyn+DgYH0jAgC8vb0B1I8Q+fj8sbZOQUFBk9Gijuj45WJkFVfCQW6Fsb28pY5DRETUbuldhpycnPDLL79g3759OHnyJLRaLfr374977rlH7w93d3eHu7txbg0REhICb29v7N27F/369QNQf0XagQMH8M477xjlM9uT//4+KnRfbx/Y2+j9j5mIiMhstPpbctSoURg1apQhs9xSVlYWiouLkZWVBY1Gg+TkZABAly5d4ODgAADo0aMH4uLi8OCDD0Imk2HevHl4++230bVrV3Tt2hVvv/027O3tMXXq1DbLLYUKdR12nq2/dxxPkREREd2aXmVIq9UiPj4eW7duxeXLlyGTyRASEoKHH34Y06ZNM+o9rxYtWoT169frnjeM9uzfvx8jRowAUD+JW6lU6vZ58cUXUVVVhaeffholJSWIjo7Gnj174OjoaLSc7cGOs3morNEg1L0TIoNcpI5DRETUrsmEEKIlOwohMH78eOzcuRMRERHo0aMHhBBITU3F2bNn8cADD+C7774zcty2p1KpoFAooFQqTWYy9aP/Popjl4vxwpjueGZkF6njEBERtTl9vr9bPDIUHx+PgwcP4ueff8bIkSMbvbZv3z5MnDgRGzZswPTp01uXmgzicmEFjl0uhoUMmNTfT+o4RERE7V6LL63/+uuv8fLLLzcpQkD9/KF//vOf2LRpk0HDkf62nKyfOD2kqwd8FHYSpyEiImr/WlyGzpw5g7Fjx9709djYWJw+fdogoah1NFqBLQ1rC3HFaSIiohZpcRkqLi6+5fo8Xl5eKCkpMUgoap0jGYXIVVbDydYK94Z3/LWUiIiIDKHFZUij0cDK6uZTjCwtLVFXV2eQUNQ6DTdlndDXD7bWlhKnISIiMg0tnkAthMDMmTMhl8ubfV2tVhssFOlPWVWL3Sn191zjTVmJiIharsVlaMaMGbfdh1eSSeeHM7lQ12nRzcsBffwVUschIiIyGS0uQ1988YUxc9AdajhF9khkgFEXvyQiIupo9L5rPbU/6QVlSM4uhaWFDBP7cW0hIiIifbAMdQANN2Ud2d0THo7Nz+kiIiKi5rEMdQA/pxYAACb285U4CRERkelhGTJx+cpqpBeUQyYDhnRxlzoOERGRyWEZMnG/pBcCAPr4KeBsbyNxGiIiItPDMmTifrl4HQAwpCtHhYiIiFqDZciECSHwS3oRAOAuniIjIiJqFZYhE5Z2rQyF5WrYWVsiMshF6jhEREQmiWXIhP1ysX6+0MAQV8iteC8yIiKi1mAZMmGHfi9DvIqMiIio9ViGTJS6ToNjmcUAOHmaiIjoTrAMmaiTV0pRVauBu4MNeng7Sh2HiIjIZLEMmahf0usvqb+riztvzEpERHQHWIZMVMMl9ZwvREREdGdYhkyQsrIWZ6+WAgCGdvWQNgwREZGJYxkyQUcyCqEVQBdPB3grbKWOQ0REZNJYhkzQoXReUk9ERGQoLEMm6DDLEBERkcGwDJmY7OJKXCmqhKWFDIM6u0kdh4iIyOSxDJmYhlWn+wU4w0FuJXEaIiIi08cyZGJ0p8i46jQREZFBsAyZEI1W4HBGfRkayjJERERkECxDJiQlV4nSylo4yK0Q4e8sdRwiIqIOgWXIhPzy+ymyQaFusLLkPzoiIiJDMJlv1LfeeguDBw+Gvb09nJ2dW3TMzJkzIZPJGj0GDRpk3KBG9MtFniIjIiIyNJMpQzU1NXjkkUfwt7/9Ta/jxo4di7y8PN1j586dRkpoXFU1GiRdLgHAydNERESGZDLXZi9duhQAEB8fr9dxcrkc3t7eRkjUto5dLkaNRgsfhS1C3TtJHYeIiKjDMJmRodZKSEiAp6cnunXrhtmzZ6OgoOCW+6vVaqhUqkaP9uDGVadlMpnEaYiIiDqODl2GYmNjsWnTJuzbtw/vv/8+jh8/jlGjRkGtVt/0mLi4OCgUCt0jICCgDRPfXMNiizxFRkREZFiSlqElS5Y0meD850dSUlKr33/y5Mm477770KtXL4wfPx4//vgjfvvtN+zYseOmxyxcuBBKpVL3yM7ObvXnG8r1MjVS8+pHqO7i/ciIiIgMStI5Q3PnzsWUKVNuuU9wcLDBPs/HxwdBQUG4ePHiTfeRy+WQy+UG+0xDOPL7QothPk5wd2hf2YiIiEydpGXI3d0d7u5tN9JRVFSE7Oxs+Pj4tNlnGgIvqSciIjIek5kzlJWVheTkZGRlZUGj0SA5ORnJyckoLy/X7dOjRw9s27YNAFBeXo4FCxbg6NGjuHz5MhISEjB+/Hi4u7vjwQcflOrH0JsQQrfY4hCeIiMiIjI4k7m0ftGiRVi/fr3ueb9+/QAA+/fvx4gRIwAAaWlpUCqVAABLS0ucPXsWGzZsQGlpKXx8fDBy5Ehs3rwZjo6ObZ6/tTKuVyBPWQ0bSwsMCHaVOg4REVGHYzJlKD4+/rZrDAkhdH+2s7PD7t27jZzK+BouqY8KdoGdjaXEaYiIiDoekzlNZq54ST0REZFxsQy1Y3UaLRIvFQHgfCEiIiJjYRlqxy4XVaJcXQd7G0v09FVIHYeIiKhDYhlqxzKu118p19nDAZYWvAUHERGRMbAMtWN/lCHemJWIiMhYWIbasfSCP0aGiIiIyDhYhtqxjOsVAIDOnixDRERExsIy1E4JIXDp95GhLixDRERERsMy1E5dL1OjTF0HCxkQ5GYvdRwiIqIOi2WonUr/ffJ0oKs95FZceZqIiMhYWIbaKd18IU6eJiIiMiqWoXYqo+FKMs4XIiIiMiqWoXaKawwRERG1DZahdiqDV5IRERG1CZahdqhCXYdcZTUAINSdZYiIiMiYWIbaoczC+snTbp1s4NLJRuI0REREHRvLUDvE23AQERG1HZahdkg3edqTk6eJiIiMjWWoHfrjSjKODBERERkby1A7lFHAG7QSERG1FZahdkajFboJ1F04MkRERGR0LEPtzNWSStRotJBbWcDX2U7qOERERB0ey1A703AlWYh7J1hayCROQ0RE1PGxDLUzf1xJxlNkREREbYFlqJ1pmDzN+UJERERtg2WoneHIEBERUdtiGWpneLd6IiKitsUy1I4UlatRUlkLgDdoJSIiaissQ+1IxvX6+UJ+znaws7GUOA0REZF5YBlqRxpOkXXhfCEiIqI2wzLUjmTwbvVERERtjmWoHeHd6omIiNqeSZShy5cvY9asWQgJCYGdnR06d+6MxYsXo6am5pbHCSGwZMkS+Pr6ws7ODiNGjEBKSkobpdZfw5whjgwRERG1HZMoQxcuXIBWq8Wnn36KlJQU/Otf/8K///1vvPzyy7c8bvny5fjggw+wcuVKHD9+HN7e3rj33ntRVlbWRslbrrpWg+ySSgAsQ0RERG1JJoQQUodojXfffRerV6/GpUuXmn1dCAFfX1/MmzcPL730EgBArVbDy8sL77zzDp566qkWfY5KpYJCoYBSqYSTk5PB8v9Zap4KsR8egsLOGsmL7oVMxvuSERERtZY+398mMTLUHKVSCVdX15u+npmZifz8fIwePVq3TS6XY/jw4Thy5MhNj1Or1VCpVI0ebeHGxRZZhIiIiNqOSZahjIwMfPzxx5gzZ85N98nPzwcAeHl5Ndru5eWle605cXFxUCgUukdAQIBhQt9Gwz3JeIqMiIiobUlahpYsWQKZTHbLR1JSUqNjcnNzMXbsWDzyyCN48sknb/sZfx5lEULccuRl4cKFUCqVukd2dnbrfjg98Z5kRERE0rCS8sPnzp2LKVOm3HKf4OBg3Z9zc3MxcuRIxMTEYM2aNbc8ztvbG0D9CJGPj49ue0FBQZPRohvJ5XLI5fIWpDesdK4xREREJAlJy5C7uzvc3d1btG9OTg5GjhyJyMhIfPHFF7CwuPWgVkhICLy9vbF3717069cPAFBTU4MDBw7gnXfeuePshqTVClwq5A1aiYiIpGASc4Zyc3MxYsQIBAQE4L333sP169eRn5/fZO5Pjx49sG3bNgD1p8fmzZuHt99+G9u2bcO5c+cwc+ZM2NvbY+rUqVL8GDeVq6xCda0W1pYyBLraSx2HiIjIrEg6MtRSe/bsQXp6OtLT0+Hv79/otRtXBkhLS4NSqdQ9f/HFF1FVVYWnn34aJSUliI6Oxp49e+Do6Nhm2VuiYbHFYLdOsLI0iX5KRETUYZjsOkNtpS3WGfr8l0y8/sN5jO3pjX9PizTKZxAREZkTs1hnqCPhPcmIiIikwzLUDvBKMiIiIumwDLUDDXOGunCNISIiojbHMiQxZWUtCsvVAIBQjgwRERG1OZYhiWX8vr6Qt5MtHOQmcXEfERFRh8IyJLGMAk6eJiIikhLLkMTSr3PyNBERkZRYhiTWcLd6Tp4mIiKSBsuQxC5xZIiIiEhSLEMSqqnT4kpxJQCWISIiIqmwDEkoq7gCGq1AJxtLeDnJpY5DRERklliGJKRbedrTATKZTOI0RERE5ollSEINK0/zFBkREZF0WIYk1LDGEK8kIyIikg7LkIR0d6v34IKLREREUmEZkogQgqfJiIiI2gGWIYkUlKlRrq6DpYUMgW72UschIiIyWyxDEmm4kizQ1R5yK0uJ0xAREZkvliGJZHDlaSIionaBZUgi5eo62Fpb8G71REREEpMJIYTUIdozlUoFhUIBpVIJJycng763ViugrtPCzoanyYiIiAxJn+9vjgxJyMJCxiJEREQkMZYhIiIiMmssQ0RERGTWWIaIiIjIrLEMERERkVljGSIiIiKzxjJEREREZo1liIiIiMwayxARERGZNZYhIiIiMmssQ0RERGTWWIaIiIjIrLEMERERkVljGSIiIiKzZiV1gPZOCAEAUKlUEichIiKilmr43m74Hr8VlqHbKCsrAwAEBARInISIiIj0VVZWBoVCcct9ZKIllcmMabVa5ObmwtHRETKZrEXHqFQqBAQEIDs7G05OTkZOSA34e5cGf+/S4O9dGvy9S6M1v3chBMrKyuDr6wsLi1vPCuLI0G1YWFjA39+/Vcc6OTnxPxYJ8PcuDf7epcHfuzT4e5eGvr/3240INeAEaiIiIjJrLENERERk1liGjEAul2Px4sWQy+VSRzEr/L1Lg793afD3Lg3+3qVh7N87J1ATERGRWePIEBEREZk1liEiIiIyayxDREREZNZYhoiIiMissQwZwapVqxASEgJbW1tERkbi0KFDUkfq0A4ePIjx48fD19cXMpkM3333ndSRzEJcXBwGDBgAR0dHeHp6YuLEiUhLS5M6Voe3evVq9OnTR7f4XExMDH788UepY5mVuLg4yGQyzJs3T+ooHd6SJUsgk8kaPby9vQ3+OSxDBrZ582bMmzcPr7zyCk6dOoWhQ4ciNjYWWVlZUkfrsCoqKhAREYGVK1dKHcWsHDhwAM888wwSExOxd+9e1NXVYfTo0aioqJA6Wofm7++PZcuWISkpCUlJSRg1ahQmTJiAlJQUqaOZhePHj2PNmjXo06eP1FHMRs+ePZGXl6d7nD171uCfwUvrDSw6Ohr9+/fH6tWrddvCwsIwceJExMXFSZjMPMhkMmzbtg0TJ06UOorZuX79Ojw9PXHgwAEMGzZM6jhmxdXVFe+++y5mzZoldZQOrby8HP3798eqVavw5ptvom/fvlixYoXUsTq0JUuW4LvvvkNycrJRP4cjQwZUU1ODEydOYPTo0Y22jx49GkeOHJEoFVHbUCqVAOq/mKltaDQafPPNN6ioqEBMTIzUcTq8Z555Bvfddx/uueceqaOYlYsXL8LX1xchISGYMmUKLl26ZPDP4I1aDaiwsBAajQZeXl6Ntnt5eSE/P1+iVETGJ4TA/PnzMWTIEPTq1UvqOB3e2bNnERMTg+rqajg4OGDbtm0IDw+XOlaH9s033+DkyZM4fvy41FHMSnR0NDZs2IBu3brh2rVrePPNNzF48GCkpKTAzc3NYJ/DMmQEMpms0XMhRJNtRB3J3LlzcebMGfzyyy9SRzEL3bt3R3JyMkpLS7FlyxbMmDEDBw4cYCEykuzsbDz33HPYs2cPbG1tpY5jVmJjY3V/7t27N2JiYtC5c2esX78e8+fPN9jnsAwZkLu7OywtLZuMAhUUFDQZLSLqKP7+97/j+++/x8GDB+Hv7y91HLNgY2ODLl26AACioqJw/PhxfPjhh/j0008lTtYxnThxAgUFBYiMjNRt02g0OHjwIFauXAm1Wg1LS0sJE5qPTp06oXfv3rh48aJB35dzhgzIxsYGkZGR2Lt3b6Pte/fuxeDBgyVKRWQcQgjMnTsXW7duxb59+xASEiJ1JLMlhIBarZY6Rod199134+zZs0hOTtY9oqKi8NhjjyE5OZlFqA2p1WqkpqbCx8fHoO/LkSEDmz9/PqZNm4aoqCjExMRgzZo1yMrKwpw5c6SO1mGVl5cjPT1d9zwzMxPJyclwdXVFYGCghMk6tmeeeQZfffUV/ve//8HR0VE3IqpQKGBnZydxuo7r5ZdfRmxsLAICAlBWVoZvvvkGCQkJ2LVrl9TROixHR8cmc+E6deoENzc3zpEzsgULFmD8+PEIDAxEQUEB3nzzTahUKsyYMcOgn8MyZGCTJ09GUVERXn/9deTl5aFXr17YuXMngoKCpI7WYSUlJWHkyJG65w3nkWfMmIH4+HiJUnV8DctHjBgxotH2L774AjNnzmz7QGbi2rVrmDZtGvLy8qBQKNCnTx/s2rUL9957r9TRiAzu6tWr+Mtf/oLCwkJ4eHhg0KBBSExMNPh3KtcZIiIiIrPGOUNERERk1liGiIiIyKyxDBEREZFZYxkiIiIis8YyRERERGaNZYiIiIjMGssQERERmTWWISIiIjJrLENEdFsymQzfffed1DFaZMmSJejbt6/UMQxuxIgRmDdvXov3T0hIgEwmQ2lp6U33iY+Ph7Oz8x1nIzJ1LENEHdjMmTMxceJEqWOYvJaUhvfffx8KhQKVlZVNXquuroazszM++OCDVmfYunUr3njjjVYfT0Q3xzJERGQA06dPR1VVFbZs2dLktS1btqCyshLTpk3T+31ra2sBAK6urnB0dLzjnETUFMsQkRkZMWIEnn32Wbz44otwdXWFt7c3lixZ0mifixcvYtiwYbC1tUV4eDj27t3b5H1ycnIwefJkuLi4wM3NDRMmTMDly5d1rzeMSC1duhSenp5wcnLCU089hZqaGt0+QggsX74coaGhsLOzQ0REBL799lvd6w2neX7++WdERUXB3t4egwcPRlpaWqMsy5Ytg5eXFxwdHTFr1ixUV1c3yfvFF18gLCwMtra26NGjB1atWqV77fLly5DJZNi6dStGjhwJe3t7RERE4OjRo7ocjz/+OJRKJWQyGWQyWZPfGQB4eHhg/Pjx+Pzzz5u89vnnn+OBBx6Ah4cHXnrpJXTr1g329vYIDQ3Fa6+9pis8wB+n+T7//HOEhoZCLpdDCNHkNNnGjRsRFRUFR0dHeHt7Y+rUqSgoKGjy2YcPH0ZERARsbW0RHR2Ns2fPNtnnRtu3b0dkZCRsbW0RGhqKpUuXoq6u7pbHEJk8QUQd1owZM8SECRN0z4cPHy6cnJzEkiVLxG+//SbWr18vZDKZ2LNnjxBCCI1GI3r16iVGjBghTp06JQ4cOCD69esnAIht27YJIYSoqKgQXbt2FU888YQ4c+aMOH/+vJg6daro3r27UKvVus91cHAQkydPFufOnRM//PCD8PDwEC+//LIuy8svvyx69Oghdu3aJTIyMsQXX3wh5HK5SEhIEEIIsX//fgFAREdHi4SEBJGSkiKGDh0qBg8erHuPzZs3CxsbG/HZZ5+JCxcuiFdeeUU4OjqKiIgI3T5r1qwRPj4+YsuWLeLSpUtiy5YtwtXVVcTHxwshhMjMzBQARI8ePcQPP/wg0tLSxMMPPyyCgoJEbW2tUKvVYsWKFcLJyUnk5eWJvLw8UVZW1uzve8eOHUImk4lLly7ptmVmZgqZTCZ27twphBDijTfeEIcPHxaZmZni+++/F15eXuKdd97R7b948WLRqVMnMWbMGHHy5Elx+vRpodVqxfDhw8Vzzz2n22/dunVi586dIiMjQxw9elQMGjRIxMbG6l5v+P2FhYWJPXv2iDNnzoj7779fBAcHi5qaGiGEEF988YVQKBS6Y3bt2iWcnJxEfHy8yMjIEHv27BHBwcFiyZIlzf8LRtRBsAwRdWDNlaEhQ4Y02mfAgAHipZdeEkIIsXv3bmFpaSmys7N1r//444+NytC6detE9+7dhVar1e2jVquFnZ2d2L17t+5zXV1dRUVFhW6f1atXCwcHB6HRaER5ebmwtbUVR44caZRl1qxZ4i9/+YsQ4o8v859++kn3+o4dOwQAUVVVJYQQIiYmRsyZM6fRe0RHRzcqQwEBAeKrr75qtM8bb7whYmJihBB/lKG1a9fqXk9JSREARGpqqhCiaWm4mbq6OuHn5ycWLVqk27Zo0SLh5+cn6urqmj1m+fLlIjIyUvd88eLFwtraWhQUFDTa789l6M+OHTsmAOiKWsPv75tvvtHtU1RUJOzs7MTmzZub/bmGDh0q3n777Ubv++WXXwofH59b/+BEJs5KogEpIpJInz59Gj338fHRnV5JTU1FYGAg/P39da/HxMQ02v/EiRNIT09vMn+luroaGRkZuucRERGwt7dv9D7l5eXIzs5GQUEBqqurce+99zZ6j5qaGvTr1++meX18fAAABQUFCAwMRGpqKubMmdNo/5iYGOzfvx8AcP36dWRnZ2PWrFmYPXu2bp+6ujooFIoWfU6PHj3QUpaWlpgxYwbi4+OxePFiyGQyrF+/HjNnzoSlpSUA4Ntvv8WKFSuQnp6O8vJy1NXVwcnJqdH7BAUFwcPD45afderUKSxZsgTJyckoLi6GVqsFAGRlZSE8PLzR76OBq6srunfvjtTU1Gbf88SJEzh+/Djeeust3TaNRoPq6mpUVlY2+udJ1JGwDBGZGWtr60bPZTKZ7otUCNFkf5lM1ui5VqtFZGQkNm3a1GTf232B//nzduzYAT8/v0avy+Xym+ZtyNJw/O007PfZZ58hOjq60WsN5cQQn3OjJ554AnFxcdi3bx+A+nLy+OOPAwASExMxZcoULF26FGPGjIFCocA333yD999/v9F7dOrU6ZafUVFRgdGjR2P06NHYuHEjPDw8kJWVhTFjxjSal3Uzf/5n2kCr1WLp0qWYNGlSk9dsbW1v+75EpopliIh0wsPDkZWVhdzcXPj6+gKAbiJxg/79+2Pz5s26idE3c/r0aVRVVcHOzg5AfRFwcHCAv78/XFxcIJfLkZWVheHDh7c6b1hYGBITEzF9+nTdtsTERN2fvby84Ofnh0uXLuGxxx5r9efY2NhAo9G0aN/OnTtj+PDh+OKLL3QTnzt37gygfjJzUFAQXnnlFd3+V65c0TvPhQsXUFhYiGXLliEgIAAAkJSU1Oy+iYmJCAwMBACUlJTgt99+u+loV//+/ZGWloYuXbronYnIlLEMEZHOPffcg+7du2P69Ol4//33oVKpGn1xA8Bjjz2Gd999FxMmTMDrr78Of39/ZGVlYevWrXjhhRd0p9hqamowa9YsvPrqq7hy5QoWL16MuXPnwsLCAo6OjliwYAGef/55aLVaDBkyBCqVCkeOHIGDgwNmzJjRorzPPfccZsyYgaioKAwZMgSbNm1CSkoKQkNDdfssWbIEzz77LJycnBAbGwu1Wo2kpCSUlJRg/vz5Lfqc4OBglJeX4+eff9ad/rvVKaMbT8utXbtWt71Lly7IysrCN998gwEDBmDHjh3Ytm1bizLcKDAwEDY2Nvj4448xZ84cnDt37qZrEL3++utwc3ODl5cXXnnlFbi7u9907alFixbh/vvvR0BAAB555BFYWFjgzJkzOHv2LN588029cxKZCl5aT0Q6FhYW2LZtG9RqNQYOHIgnn3yy0fwRALC3t8fBgwcRGBiISZMmISwsDE888QSqqqoajRTdfffd6Nq1K4YNG4ZHH30U48ePb3RJ+htvvIFFixYhLi4OYWFhGDNmDLZv346QkJAW5508eTIWLVqEl156CZGRkbhy5Qr+9re/NdrnySefxNq1axEfH4/evXtj+PDhiI+P1+tzBg8ejDlz5mDy5Mnw8PDA8uXLb7n/Qw89BLlcDrlc3uiU04QJE/D8889j7ty56Nu3L44cOYLXXnutxTkaeHh4ID4+Hv/9738RHh6OZcuW4b333mt232XLluG5555DZGQk8vLy8P3338PGxqbZfceMGYMffvgBe/fuxYABAzBo0CB88MEHCAoK0jsjkSmRieYmCRAR3YGZM2eitLTUZG7hQUTmjSNDREREZNZYhoiIiMis8TQZERERmTWODBEREZFZYxkiIiIis8YyRERERGaNZYiIiIjMGssQERERmTWWISIiIjJrLENERERk1liGiIiIyKz9P1m3lW0a/c3hAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = np.arange(-5.0, 5.0, 0.1)\n", + "\n", + "Y = np.log(X)\n", + "\n", + "plt.plot(X,Y) \n", + "plt.ylabel('Dependent Variable')\n", + "plt.xlabel('Independent Variable')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Sigmoidal/Logistic\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = np.arange(-5.0, 5.0, 0.1)\n", + "\n", + "\n", + "Y = 1-4/(1+np.power(3, X-2))\n", + "\n", + "plt.plot(X,Y) \n", + "plt.ylabel('Dependent Variable')\n", + "plt.xlabel('Independent Variable')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Non-Linear Regression example\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2025-10-20 07:48:40 URL:https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n" + ] + }, + { + "data": { + "text/html": [ + "
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919697.871882e+10
\n", + "
" + ], + "text/plain": [ + " Year Value\n", + "0 1960 5.918412e+10\n", + "1 1961 4.955705e+10\n", + "2 1962 4.668518e+10\n", + "3 1963 5.009730e+10\n", + "4 1964 5.906225e+10\n", + "5 1965 6.970915e+10\n", + "6 1966 7.587943e+10\n", + "7 1967 7.205703e+10\n", + "8 1968 6.999350e+10\n", + "9 1969 7.871882e+10" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "#downloading dataset\n", + "!wget -nv -O china_gdp.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv\n", + " \n", + "df = pd.read_csv(\"china_gdp.csv\")\n", + "df.head(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting the Dataset ###\n", + "This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerates slightly in the 2010s.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8,5))\n", + "x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n", + "plt.plot(x_data, y_data, 'ro')\n", + "plt.ylabel('GDP')\n", + "plt.xlabel('Year')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Choosing a model ###\n", + "\n", + "From an initial look at the plot, we determine that the logistic function could be a good approximation,\n", + "since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = np.arange(-5.0, 5.0, 0.1)\n", + "Y = 1.0 / (1.0 + np.exp(-X))\n", + "\n", + "plt.plot(X,Y) \n", + "plt.ylabel('Dependent Variable')\n", + "plt.xlabel('Independent Variable')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "The formula for the logistic function is the following:\n", + "\n", + "$$ \\hat{Y} = \\frac1{1+e^{-\\beta_1(X-\\beta_2)}}$$\n", + "\n", + "$\\beta_1$: Controls the curve's steepness,\n", + "\n", + "$\\beta_2$: Slides the curve on the x-axis.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Building The Model ###\n", + "Now, let's build our regression model and initialize its parameters. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [], + "source": [ + "def sigmoid(x, Beta_1, Beta_2):\n", + " y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n", + " return y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets look at a sample sigmoid line that might fit with the data:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "beta_1 = 0.10\n", + "beta_2 = 1990.0\n", + "\n", + "#logistic function\n", + "Y_pred = sigmoid(x_data, beta_1 , beta_2)\n", + "\n", + "#plot initial prediction against datapoints\n", + "plt.plot(x_data, Y_pred*15000000000000.)\n", + "plt.plot(x_data, y_data, 'ro')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our task here is to find the best parameters for our model. Lets first normalize our x and y:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [], + "source": [ + "# Lets normalize our data\n", + "xdata =x_data/max(x_data)\n", + "ydata =y_data/max(y_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### How we find the best parameters for our fit line?\n", + "we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimize values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n", + "\n", + "popt are our optimized parameters.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " beta_1 = 690.451712, beta_2 = 0.997207\n" + ] + } + ], + "source": [ + "from scipy.optimize import curve_fit\n", + "popt, pcov = curve_fit(sigmoid, xdata, ydata)\n", + "#print the final parameters\n", + "print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we plot our resulting regression model.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(1960, 2015, 55)\n", + "x = x/max(x)\n", + "plt.figure(figsize=(8,5))\n", + "y = sigmoid(x, *popt)\n", + "plt.plot(xdata, ydata, 'ro', label='data')\n", + "plt.plot(x,y, linewidth=3.0, label='fit')\n", + "plt.legend(loc='best')\n", + "plt.ylabel('GDP')\n", + "plt.xlabel('Year')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Practice\n", + "Can you calculate what is the accuracy of our model?\n" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean Absolute Error (MAE): 0.04\n", + "Mean Squared Error (MSE): 0.00\n", + "Root Mean Squared Error (RMSE): 0.04\n", + "R2-score: 0.92\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.metrics import r2_score, mean_squared_error, mean_absolute_error\n", + "from scipy.optimize import curve_fit\n", + "\n", + "# Misal fungsi sigmoid\n", + "def sigmoid(x, beta1, beta2):\n", + " return 1 / (1 + np.exp(-beta1*(x-beta2)))\n", + "\n", + "# split data into train/test\n", + "msk = np.random.rand(len(df)) < 0.8\n", + "train_x = xdata[msk]\n", + "test_x = xdata[~msk]\n", + "train_y = ydata[msk]\n", + "test_y = ydata[~msk]\n", + "\n", + "# build the model using train set\n", + "popt, pcov = curve_fit(sigmoid, train_x, train_y)\n", + "\n", + "# predict using test set\n", + "y_hat = sigmoid(test_x, *popt)\n", + "\n", + "# evaluation metrics\n", + "mae = mean_absolute_error(test_y, y_hat)\n", + "mse = mean_squared_error(test_y, y_hat)\n", + "rmse = np.sqrt(mse)\n", + "r2 = r2_score(test_y, y_hat)\n", + "\n", + "print(\"Mean Absolute Error (MAE): %.2f\" % mae)\n", + "print(\"Mean Squared Error (MSE): %.2f\" % mse)\n", + "print(\"Root Mean Squared Error (RMSE): %.2f\" % rmse)\n", + "print(\"R2-score: %.2f\" % r2)\n", + "\n", + "# Optional: plot actual vs predicted\n", + "plt.scatter(test_x, test_y, label='Actual', color='blue')\n", + "plt.scatter(test_x, y_hat, label='Predicted', color='red')\n", + "plt.xlabel('X')\n", + "plt.ylabel('Y')\n", + "plt.title('Sigmoid Regression: Actual vs Predicted')\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "# split data into train/test\n", + "msk = np.random.rand(len(df)) < 0.8\n", + "train_x = xdata[msk]\n", + "test_x = xdata[~msk]\n", + "train_y = ydata[msk]\n", + "test_y = ydata[~msk]\n", + "\n", + "# build the model using train set\n", + "popt, pcov = curve_fit(sigmoid, train_x, train_y)\n", + "\n", + "# predict using test set\n", + "y_hat = sigmoid(test_x, *popt)\n", + "\n", + "# evaluation\n", + "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n", + "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n", + "from sklearn.metrics import r2_score\n", + "print(\"R2-score: %.2f\" % r2_score(test_y,y_hat) )\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Want to learn more?

\n", + "\n", + "IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: SPSS Modeler\n", + "\n", + "Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at Watson Studio\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thank you for completing this lab!\n", + "\n", + "\n", + "## Author\n", + "\n", + "Saeed Aghabozorgi\n", + "\n", + "\n", + "### Other Contributors\n", + "\n", + "Joseph Santarcangelo\n", + "\n", + "\n", + "##

© IBM Corporation 2020. All rights reserved.

\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python", + "language": "python", + "name": "conda-env-python-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.12" + }, + "prev_pub_hash": "f873d3177bf529d2d648c46bab1627042a257e5ec6ce42ca68028520459f817e" + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb new file mode 100644 index 0000000..c65cdc5 --- /dev/null +++ b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb @@ -0,0 +1,899 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

\n", + " \n", + " \"Skills\n", + " \n", + "

\n", + "\n", + "\n", + "# Polynomial Regression\n", + "\n", + "\n", + "Estimated time needed: **15** minutes\n", + " \n", + "\n", + "## Objectives\n", + "\n", + "After completing this lab you will be able to:\n", + "\n", + "* Use scikit-learn to implement Polynomial Regression\n", + "* Create a model, train it, test it and use the model\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Table of contents

\n", + "\n", + "
\n", + "
    \n", + "
  1. Downloading Data
  2. \n", + "
  3. Polynomial regression
  4. \n", + "
  5. Evaluation
  6. \n", + "
  7. Practice
  8. \n", + "
\n", + "
\n", + "
\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Importing Needed packages\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "import pylab as pl\n", + "import numpy as np\n", + "%matplotlib inline\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Downloading Data

\n", + "To download the data, we will use !wget to download it from IBM Object Storage.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--2025-10-20 07:46:03-- https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv\n", + "Resolving cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)... 169.63.118.104, 169.63.118.104\n", + "Connecting to cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)|169.63.118.104|:443... connected.\n", + "HTTP request sent, awaiting response... 200 OK\n", + "Length: 72629 (71K) [text/csv]\n", + "Saving to: ‘FuelConsumption.csv’\n", + "\n", + "FuelConsumption.csv 100%[===================>] 70.93K --.-KB/s in 0.001s \n", + "\n", + "2025-10-20 07:46:03 (49.8 MB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n", + "\n" + ] + } + ], + "source": [ + "!wget -O FuelConsumption.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](https://www.ibm.com/us-en/cloud/object-storage?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Understanding the Data\n", + "\n", + "### `FuelConsumption.csv`:\n", + "We have downloaded a fuel consumption dataset, **`FuelConsumption.csv`**, which contains model-specific fuel consumption ratings and estimated carbon dioxide emissions for new light-duty vehicles for retail sale in Canada. [Dataset source](http://open.canada.ca/data/en/dataset/98f1a129-f628-4ce4-b24d-6f16bf24dd64)\n", + "\n", + "- **MODELYEAR** e.g. 2014\n", + "- **MAKE** e.g. Acura\n", + "- **MODEL** e.g. ILX\n", + "- **VEHICLE CLASS** e.g. SUV\n", + "- **ENGINE SIZE** e.g. 4.7\n", + "- **CYLINDERS** e.g 6\n", + "- **TRANSMISSION** e.g. A6\n", + "- **FUEL CONSUMPTION in CITY(L/100 km)** e.g. 9.9\n", + "- **FUEL CONSUMPTION in HWY (L/100 km)** e.g. 8.9\n", + "- **FUEL CONSUMPTION COMB (L/100 km)** e.g. 9.2\n", + "- **CO2 EMISSIONS (g/km)** e.g. 182 --> low --> 0\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reading the data in\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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MODELYEARMAKEMODELVEHICLECLASSENGINESIZECYLINDERSTRANSMISSIONFUELTYPEFUELCONSUMPTION_CITYFUELCONSUMPTION_HWYFUELCONSUMPTION_COMBFUELCONSUMPTION_COMB_MPGCO2EMISSIONS
02014ACURAILXCOMPACT2.04AS5Z9.96.78.533196
12014ACURAILXCOMPACT2.44M6Z11.27.79.629221
22014ACURAILX HYBRIDCOMPACT1.54AV7Z6.05.85.948136
32014ACURAMDX 4WDSUV - SMALL3.56AS6Z12.79.111.125255
42014ACURARDX AWDSUV - SMALL3.56AS6Z12.18.710.627244
\n", + "
" + ], + "text/plain": [ + " MODELYEAR MAKE MODEL VEHICLECLASS ENGINESIZE CYLINDERS \\\n", + "0 2014 ACURA ILX COMPACT 2.0 4 \n", + "1 2014 ACURA ILX COMPACT 2.4 4 \n", + "2 2014 ACURA ILX HYBRID COMPACT 1.5 4 \n", + "3 2014 ACURA MDX 4WD SUV - SMALL 3.5 6 \n", + "4 2014 ACURA RDX AWD SUV - SMALL 3.5 6 \n", + "\n", + " TRANSMISSION FUELTYPE FUELCONSUMPTION_CITY FUELCONSUMPTION_HWY \\\n", + "0 AS5 Z 9.9 6.7 \n", + "1 M6 Z 11.2 7.7 \n", + "2 AV7 Z 6.0 5.8 \n", + "3 AS6 Z 12.7 9.1 \n", + "4 AS6 Z 12.1 8.7 \n", + "\n", + " FUELCONSUMPTION_COMB FUELCONSUMPTION_COMB_MPG CO2EMISSIONS \n", + "0 8.5 33 196 \n", + "1 9.6 29 221 \n", + "2 5.9 48 136 \n", + "3 11.1 25 255 \n", + "4 10.6 27 244 " + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_csv(\"FuelConsumption.csv\")\n", + "\n", + "# take a look at the dataset\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's select some features that we want to use for regression.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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ENGINESIZECYLINDERSFUELCONSUMPTION_COMBCO2EMISSIONS
02.048.5196
12.449.6221
21.545.9136
33.5611.1255
43.5610.6244
53.5610.0230
63.5610.1232
73.7611.1255
83.7611.6267
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" + ], + "text/plain": [ + " ENGINESIZE CYLINDERS FUELCONSUMPTION_COMB CO2EMISSIONS\n", + "0 2.0 4 8.5 196\n", + "1 2.4 4 9.6 221\n", + "2 1.5 4 5.9 136\n", + "3 3.5 6 11.1 255\n", + "4 3.5 6 10.6 244\n", + "5 3.5 6 10.0 230\n", + "6 3.5 6 10.1 232\n", + "7 3.7 6 11.1 255\n", + "8 3.7 6 11.6 267" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n", + "cdf.head(9)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's plot Emission values with respect to Engine size:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Creating train and test dataset\n", + "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "msk = np.random.rand(len(df)) < 0.8\n", + "train = cdf[msk]\n", + "test = cdf[~msk]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Polynomial regression

\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sometimes, the trend of data is not really linear, and looks curvy. In this case we can use Polynomial regression methods. In fact, many different regressions exist that can be used to fit whatever the dataset looks like, such as quadratic, cubic, and so on, and it can go on and on to infinite degrees.\n", + "\n", + "In essence, we can call all of these, polynomial regression, where the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Lets say you want to have a polynomial regression (let's make 2 degree polynomial):\n", + "\n", + "\n", + "$$y = b + \\theta_1 x + \\theta_2 x^2$$\n", + "\n", + "\n", + "\n", + "Now, the question is: how we can fit our data on this equation while we have only x values, such as __Engine Size__? \n", + "Well, we can create a few additional features: 1, $x$, and $x^2$.\n", + "\n", + "\n", + "\n", + "__PolynomialFeatures()__ function in Scikit-learn library, drives a new feature sets from the original feature set. That is, a matrix will be generated consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, lets say the original feature set has only one feature, _ENGINESIZE_. Now, if we select the degree of the polynomial to be 2, then it generates 3 features, degree=0, degree=1 and degree=2: \n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1. , 2. , 4. ],\n", + " [ 1. , 2.4 , 5.76],\n", + " [ 1. , 3.5 , 12.25],\n", + " ...,\n", + " [ 1. , 3.2 , 10.24],\n", + " [ 1. , 3. , 9. ],\n", + " [ 1. , 3.2 , 10.24]])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn import linear_model\n", + "train_x = np.asanyarray(train[['ENGINESIZE']])\n", + "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n", + "\n", + "test_x = np.asanyarray(test[['ENGINESIZE']])\n", + "test_y = np.asanyarray(test[['CO2EMISSIONS']])\n", + "\n", + "\n", + "poly = PolynomialFeatures(degree=2)\n", + "train_x_poly = poly.fit_transform(train_x)\n", + "train_x_poly" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**fit_transform** takes our x values, and output a list of our data raised from power of 0 to power of 2 (since we set the degree of our polynomial to 2). \n", + "\n", + "The equation and the sample example is displayed below. \n", + "\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + " v_1\\\\\\\\\\\\\n", + " v_2\\\\\\\\\n", + " \\vdots\\\\\\\\\n", + " v_n\n", + "\\end{bmatrix}\\longrightarrow \\begin{bmatrix}\n", + " [ 1 & v_1 & v_1^2]\\\\\\\\\n", + " [ 1 & v_2 & v_2^2]\\\\\\\\\n", + " \\vdots & \\vdots & \\vdots\\\\\\\\\n", + " [ 1 & v_n & v_n^2]\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "\n", + "\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + " 2.\\\\\\\\\n", + " 2.4\\\\\\\\\n", + " 1.5\\\\\\\\\n", + " \\vdots\n", + "\\end{bmatrix} \\longrightarrow \\begin{bmatrix}\n", + " [ 1 & 2. & 4.]\\\\\\\\\n", + " [ 1 & 2.4 & 5.76]\\\\\\\\\n", + " [ 1 & 1.5 & 2.25]\\\\\\\\\n", + " \\vdots & \\vdots & \\vdots\\\\\\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks like feature sets for multiple linear regression analysis, right? Yes. It Does. \n", + "Indeed, Polynomial regression is a special case of linear regression, with the main idea of how do you select your features. Just consider replacing the $x$ with $x_1$, $x_1^2$ with $x_2$, and so on. Then the 2nd degree equation would be turn into:\n", + "\n", + "$$y = b + \\theta_1 x_1 + \\theta_2 x_2$$\n", + "\n", + "Now, we can deal with it as a 'linear regression' problem. Therefore, this polynomial regression is considered to be a special case of traditional multiple linear regression. So, you can use the same mechanism as linear regression to solve such problems. \n", + "\n", + "\n", + "\n", + "so we can use __LinearRegression()__ function to solve it:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[ 0. 50.57406358 -1.44659762]]\n", + "Intercept: [106.21698993]\n" + ] + } + ], + "source": [ + "clf = linear_model.LinearRegression()\n", + "train_y_ = clf.fit(train_x_poly, train_y)\n", + "# The coefficients\n", + "print ('Coefficients: ', clf.coef_)\n", + "print ('Intercept: ',clf.intercept_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As mentioned before, __Coefficient__ and __Intercept__ , are the parameters of the fit curvy line. \n", + "Given that it is a typical multiple linear regression, with 3 parameters, and knowing that the parameters are the intercept and coefficients of hyperplane, sklearn has estimated them from our new set of feature sets. Lets plot it:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Emission')" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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DW6r6rdHIY9OnA9HRnj9KYu1zANxGbpFOB6xbJ0dufvtNHouMlMkAhwwBfH3d2bsyTenvN4MdMNghKq1cURncVtVvU546SsLq5Q4QQpZw+L//A37+WR6rUUMW6Hz5ZaB8eff2j7gbi4i8m74yuOkWbX1l8MmT1bmPrarfpi5flqMniYnq3F8t9lQvJwC7dwNPPAE8+6wMdCpXlmt0fvsNGDOGgU4pw2CHiEodV1YGt7csg36sPD7edkFPV/K0MhQe68cfgQ4dgE6d5LbxwEDgzTflkNdrr8nXVOow2CGiUseVlcEdqebtylESnQ7Ytw/44gv5bOl7YfVyG86eBZ55BmjeHPjuO7nwa8wYOZLzzjtyZIdKLe7GIqJS58IFddtZY6vqtzUlHSWxtfjanp1VrF5uwe+/y4XHq1cDBQVy2/iLL8pjtWq5u3ekEo7sEFGp88AD6razxlrVb1tKMkoyebIsGzFunCyxNG6cfK1fi6TfWWW6DsfSmiFWLzdx/bpcyf7gg8DKlTLQeeYZIDkZWLGCgY6X4W4scDcWUWmTkyN/+G25cwcICFDnnuZGUSwp6c4m/eJrSyZMANavd2xnlbnPERUlAx1P20HmFLdvyw/73ntAVpY81rYtMHu2XJBMpQq3ntuBwQ5R6bJvH9Cune12e/fK3zEllGQVLtrm/Hk50wEYTwuVNGeNkkKgPj5yIMIWS5+/TGZQvncP+OwzmRQpLU0ea9xYBjmdOrG0QynFDMpE5LXU3lmkdO2LVmscPMTEmD+vJKMkShZfKwl0AMuf3/RzeDUhgI0bgddflxEqILMez5gB9O3L0g5lBIMdIlKds7Maq7mzyFJWYf3aF2sjNHFxQI8e6n7WX35x/FxTZXZnld7Bg3JO8MgR+bp6dZn1+OWXWTa+jOE0FjiNRaQmV2Y1trWzyNaamZJmFXZGnalnngE2b7bdrnx5IDe3ZJ/fa/33vzInztat8nWFCsDEifIRFOTevpGqmEGZiFzOVVmN1dpZVJKswvbuhlIqLExZuzZt5DN3VhVx9SowbJicX9y6VX4Bw4YBv/4q1+ow0CmzGOwQkSpcmdUYkCMnGzYANWsaH4+MVL442NG1PzqdHNExN6pS0gzKDz2krF3XriX//F4jO1uuFo+OBpYvl4uaevcGzpwBli3jfB5xGgvgNBaRGhYulLlgbFmwQAYCainJziJHd3U5YzeYnpLdWFqt3Fbv51dGd1bp5efLnDhvvVW4w6p5czmM2LKle/tGLsHdWETkUq7MalxUSXYWOZpV2Jl1pvz85Poma3l2xo8vXF9bpnZW6QkB7NgBTJokyzwAcnX47NmycCe3kZMJTmMRkSpcmdVYLUXX/lhibu2Ls+tMzZkjf8dN76vVyuNqLfQulU6dAjp3Brp1k4FOSIj8h/Tzz3KxFAMdMoPTWOA0FpEa7J1+8ST27iBTazeYLc7ewl+qXLkiq4+vXCm/dH2hztdfB6pUcXfvyE1K3W6sWbNmQaPRIL7IZL4QAtOmTUNERAQCAgLQtm1bnNUPWf4tNzcXo0ePRrVq1RAYGIhevXrhDyX53IlIVfrpF2uKTr94isREYO7c4kFaQYE8bm5Xla3dYEIAL70EfPml9Urktvj5yfVNH34onz3tu3OJ27eBt9+Wi49XrJBf7vPPA//7n5zrY6BDSggPcPToUVG7dm3RsGFDMXbsWMPx2bNni6CgILFx40aRnJwsnn/+eREeHi4yMzMNbYYPHy5q1qwpdu3aJU6cOCHatWsnGjVqJPLz8xXfPyMjQwAQGRkZan4sojJp0iQhtFoh5K+SfGi18rinyc8XIjLSuK9FHxqNEFFRsp05GzcWP79qVfkoeiwyUrYlO+h0QqxaJUTNmoVf5JNPCvHDD+7uGXkQpb/fbg92srKyRHR0tNi1a5do06aNIdgpKCgQYWFhYvbs2Ya2d+/eFcHBwWLZsmVCCCFu3bolfH19RUJCgqHN5cuXhY+Pj9ixY4fFe969e1dkZGQYHqmpqQx2iFSUmyvEggVCjBoln3Nz3d0j8/butRzoFH3s3Svb5+fLP69bJ5/z842PTZ8uAyRzQZNGw4BHsQMHhGjatPALrF1biPXrhSgocHfPyMMoDXbcPo01cuRIdO/eHR07djQ6npKSgrS0NHTu3NlwzN/fH23atMHhw4cBAElJSbh3755Rm4iICMTExBjamDNr1iwEBwcbHlFRUSp/KqKyrbRMv9izqyoxUa7TadcO6N9fPteuDWzZIndD9e0LfPKJc3LvlBm//QY89xzQujVw/LhMAvjeezIjct++XHxMDnNrsJOQkIATJ05g1qxZxd5L+ztnQmhoqNHx0NBQw3tpaWnw8/NDFZM526JtzJkyZQoyMjIMj9TU1JJ+FCIqhZTuljp/3na25JJkYy7zMjNleYeHH5YZEX18CjMfT54sa2MQlYDbgp3U1FSMHTsWa9euRXkrf5E1JpG8EKLYMVO22vj7+6NSpUpGDyIqe/R5diz950K/q2r5ctsjNpcvK7unI7l33CU7W9bqathQPmdnq3wDnQ747DPgwQflCE5eHtCxo9xevmwZUKOGyjekssptwU5SUhLS09PRpEkTlCtXDuXKlcP+/fvxwQcfoFy5coYRHdMRmvT0dMN7YWFhyMvLw82bNy22ISKyREmNrX/9y3ogox+xuXZN2T1LS+WCxx+Xs0ibNwPJyfI5KEgeV8X+/UDTpnLb2p9/yoBn2zZg506gQQOVbkIkuS3Y6dChA5KTk3Hq1CnDo2nTphgwYABOnTqF+++/H2FhYdi1a5fhnLy8POzfvx8tWrQAADRp0gS+vr5Gba5evYozZ84Y2hARWWOrxlZ0tLLrVK9ue5QoKqp4NmZP9PjjwLFj5t87dqyEAc/Fi3L9Tdu2cgQnOFgmOUpOBnr04Loccgq3lYsICgpCTEyM0bHAwEBUrVrVcDw+Ph4zZ85EdHQ0oqOjMXPmTFSoUAH9+/cHAAQHB2Po0KGYMGECqlatipCQEEycOBENGjQotuCZiMiSuDggNtZ8jal9+5Rdo2ZNOUqkT+JbdNqrNFUiz862HOjoHTsm21WsaMeFb9+W5RzmzgXu3pXrcl5+GXjnHaBatRL12ZMwEaSHcsneMIWKbj0XQm4/nzp1qggLCxP+/v6idevWIjk52eicnJwcMWrUKBESEiICAgJEjx49xKVLl+y6L/PsEJEl+lw85raUm8vFYy73TlRU6dl23ru3su34vXsrvGBBgRCff26cL6ddOyF++smpn8MdSlOOKW+h9Peb5SLAchFEZF1iohyxAcyP2GzYIEeH9EpzJfKGDeWMki0NGgCnT9todOKELOnw/ffyde3awLx5crWzl01XTZ5svXhrma9p5iSlrlwEEZEpnU5OI33xRcnKLpSUrXU9RQMdoLASeb9+8rm0BDqASgVdr12TU1RNm8pAp0IF4N13Zb6cuDivC3Ty8uSyI2vmz5ftyD04sgOO7BB5osREYOxY49w1kZFyXYxpcOEqjo7YlKaRnuxsuevKlqwsM2t28vPlgpW33gIyMuSx/v3ltvLISNX76ikWLgTGjbPdbsECmaaA1KP099ttC5SJiCzRTxuZ/q+YPomfudEUV9CP2NjDE4M2aypWBJo1s75IuVkzM4HO3r3A6NGAvljzo4/KFNotWzqrqx7jwgV125H6OI1FRB5Fp5PBgSeWXbB3Wk0ftFnLvFxSzkj8d/SoDGjMadZMvm9w6ZLcSt6+vQx0QkJkQsDjx8tEoAOoNPVHTsVpLHAai8iT7Nsn607Zsnev/aMsJWHvCI1OJ9fjWiohoc/OnJLi+JSWpXw4xQISB2VnA4MGFW6jXrOmyIhObq5cbDxjBnDnjtxK/sorwNtvy4CnDMnLk8uSrAW/Wq38mrgNXV1coExEpZI9xTmdLS0NCAsDfH2BZ59VPkKj08kZnJLWysrLk+tBRo+Wz0UXuDo18d/fKlYENm2Su642bSoS6GzfDsTEAG+8IX/BW7WSO68WLy5zgQ4gA5jx4623GT+egY47MdghIo+itJyCs8suBAbKe/z5p1x3a465aTV9dXQlC1YBy0Hb5MlytGDcOBlDjBsnX0+ebF/iP1WlpMjsi927yyKdYWHA2rWy9EOjRirfrHSZM0duLzcdpdNque3cE3AaC5zGIvIk+umfy5fNr9tRY/rHlsBAOWBhj717gb/+Mr+w2tZ5ptNxtnK2PPCAssWuvXvLEZkSu3tX/lrPmiX/XK6cnNN76y2A/800wgzKrsXdWERUKumLc7qr7EJamv2BDiCDs9desy/Q0WoB0zJ+SnK2KN3V8+uvyvti0ddfy8SAv/0mX7drJ4eaHnlEhYt7Hz8/bi/3RJzGIiKPY28SPzU9+qhj5127Zn2Njjk6HXD4sPGxJUvU22kWHFyCky9elFNWPXrIQCciAkhIAPbsYaBDpQ5HdojII1krzulMt27Z114/rVa9umP3M12zo2YulqFDHTgpN1cW65wxA8jJkVNW8fFyykpJtkEiD8Rgh4ioiMqV5aJkJYpOqzm6Ccl0obWauVjsTlq8axcwahTwyy/ydZs2wEcfAfXrq9cpIjfgNBYReST9rqZ27WTFgXbt5Gs1EvFZc+qU8rZFp9VatZKv7Sn7FBUlzytqxAj1Rq+UFPQEAFy5Ajz/PNC5swx0QkPlLqu9exnokFdgsENEHscVmYctCQuTW7yt8fOTcUBKSuH6If3CakB5wPPCC8UDGyU5Wxo3Vnb9lBQbDfLz5bBUvXrAl1/KxIBjxgDnzgEDBnhdwU4quxjsEJFbWCq94AnlIm7fthzwVKggl7WYq2ZuaWG1JQkJ5j+HrZwtL76o7PpWp8SOHJFVyceNk1U9mzcHkpJkxFailc1Enod5dsA8O0SuZq30QkiI55SLSEuTu7Nu3ZJreU6dkiM/tugzKCtJLGjtc1jK2VKi8gQ3bwJTpgDLl8vosUoVYPZs4KWX5MgOUSnCPDtE5JFsVTQfO1bZdVxRLiIsTAY8evryDbYSxmm1ctmLEtY+h6WcLfqpLmuJB4uVJxAC+Pxz+ca1a/LYkCFyGKl6dSbDI6/GYIeIXMbWFJVGI3+PlXB2uQjAeGTl7FlZFaGgoPD9iRNl7GCuFICzy17o7zlvnnGftFozfTp3Thbp3LtXvn74YWDpUrnbCjJj8/z5xiNF1j4bUWnDYIeIXObgQdvFMa9dkzlrrl+3Xi7CdBeT2swFAKZ0usLRFdOgQL87y1bZi5J8jubNZbB0+XLhsbAweRyALO0we7Ys85CXBwQEyHw5RYZ9LJWmsPbZiEobTtASkcsonXoaMEA+m24GckW5CKAwAFC6CHr+fOOK5ID13VlqfA79dGDRQAeQu8j79AEOTv9OFuecPl127umn5fDUa68ZAh0lpSnMfTai0obBDhG5jNIpm9hY95WLUBIAmNLp5PreorvKAOeVvbA2HVhVXMMKMRitpnWQOXPCw6FL+BL7Jn2NL47UMeqjktIUOp1sR1SacRqLiFzGnqkdrdY95SIcrU21Zo186HeV6QMZZ5S9MD8dKDAYqzAXE1ENN1AADa48MxInnnkXIycGm935prQ0hZolLIjcgcEOEbmMvRXNtVrnby83VdIfdv2usqIjN2p/DtPpwGj8gmUYjvaQC5B/QkO8jOW4T/sENg62vPNt8GBl91OzhAWRO3Aai4hcqqRTO5aSEaqlpD/sjiY+zMmRZam6dJHPOTmW2+qnA32RhzfwLk6jIdpjL+4gAJMwB01xHEfxBDZssJ6ccdcu2yNMWq3chk5UmjGpIJhUkMgddDr7p3asJSNUax1PRoZMIKgGpYkPe/cGtmwpfjw2Fti8ufhxnQ7oEXIYczP/hfr4GQDwDbpiBJbgIurY1cfnnwfWr7f8/qRJ3I1FnotJBYnIo9k7tWMrGaFaC5ffeKPk19BTsvvMUqADyOO9e5sEPBkZ0Lw2Bd9kLgUApKM6xmIREvACAPtrWdlaNG7Yxk5UinFkBxzZIfJ0Op2seG4pR49+YXNKSskXMHfpAuzcWbJr6OlHdiyNYuXk2C46CgArVwK1agGt/toM7eiRcn85gM/wT0zC+7iJEIf7WL16YUJlU2p+r0TOoPT3m2t2iMjjKUlGmJoq25VUdHTJrwEAUVEyqElMlIFau3ZA//7yuXZteXzSJGXXem3IVVxv1wfaZ58BrlxBZlg02uE7vITPHA50NBrrgQ6g7vdK5E4MdojI4ylNRmipnZJFzfq6V/fuOdhJEy+8IKeh+vQpHqjpp94OHbJ1FYGX8An+i4fRBxtxD+UwE69j8Us/YR8UVEu1QL/zTZ+80RZX1CEjciau2SEij1eSOlNKFjUrKQ1hry++kA9rdcCsbXOvi/NYjpfRDvsAAEfRDP/CJ0jWNELNlfIzWBvtsiYyUgZ2ISHy2RZX1CEjciau2QHX7BB5Op1O7pDKzrbcJigIuHnTeG2JpUXN+pGNDRuAI0esVw93NS3yMQHzMA3TEIC7uI0KeBPv4gOMQQEKP9xTTwHff2/7evp8RtOnyym6omuG9GuhbCV55Jod8lTcjUVEXkOnA+7csd7m9m3ZTv+jrKTC+tixhrW+VjVsCJw+bX+/lWjSBEhKkn9+FCfxGYbiMZwEAOxEJwzDx2a3kx8+rOz6+lEcczvV7E3ySFRacc0OEXm8JUuAggLrbQoKjGs4KVnU/Mcftq8LAP/4B7Bxowwc1DZ3LtCnx13MwOs4hmZ4DCfxF6pgMFaiC761mDdHyZj8yJFyVMbalnxn1e8i8iRuDXaWLl2Khg0bolKlSqhUqRKefPJJfPPNN4b3hwwZAo1GY/RobpL0ITc3F6NHj0a1atUQGBiIXr164Q9HJ7KJyCOdP29/OzUX1V64IH/0L16U28nXrpU7mUyrmevpp38iI623iYoCWmkO4T+/NMLrmIVy0GF/6HNoWuG/WKMZDHN5czQaZdvVARkQKRmVKfrZ1q2Tz7aCJKLSxK3TWJGRkZg9ezbq1q0LAFi1ahViY2Nx8uRJ1K9fHwDQtWtXrFixwnCOn5+f0TXi4+Oxbds2JCQkoGrVqpgwYQJ69OiBpKQkaDn2SuQR8vLkqMuFC7Icw4gRgMm/ymbp89P88ouy+xQd7VBzUa2+hETRRIgBAdanfxYtks+W2lQUWdgb8zq07T6Sb4aFAUuXok3v3pibaP3arVoB335ru9+WAi1z3FGHjMhlhIepUqWK+PTTT4UQQgwePFjExsZabHvr1i3h6+srEhISDMcuX74sfHx8xI4dOyyed/fuXZGRkWF4pKamCgAiIyNDtc9BRNKkSUJotULIn2350GrlcWs2bhQiMtL4PFuPKVMKz8/Pt31+ZKQQPj7W22i1QuTmFl5z714h1q2Tz//5T/F7REXJvlv7HP2r7xTZ1WsVHvjnP4X46y+bn19/7dWrlX0fq1er8U+QyHNlZGQo+v32mAXKOp0O//nPf3D79m08+eSThuP79u1DjRo1ULlyZbRp0wYzZsxAjRo1AABJSUm4d+8eOnfubGgfERGBmJgYHD58GF26dDF7r1mzZmH69OnO/UBEhMmTze900ukKj5uru2RpF5UtRQdztVq5+NfarHaTJkC/ftZ3Y40fL0ehLG1hnz9fTmkVzY4MyHw++mMXLsgFxdd/vYWnNk1E+PbPZKNatYBPPgE6dSp237g4WRvLXOblffuUfR9RUcraEXk9FwVfFp0+fVoEBgYKrVYrgoODxddff214LyEhQXz11VciOTlZbN26VTRq1EjUr19f3L17VwghxOeffy78/PyKXbNTp07i5ZdftnhPjuwQOV9ubvERHWujJnpKRmQsPXbudOz+lkafRo4U4qmnhKha1fz5Go182BrJiYwU4vsp24SIiCg8OGqUEFlZDn23Sr6jqCjZjsibKR3ZcXuwk5ubK86fPy+OHTsmXnvtNVGtWjVx9uxZs22vXLkifH19xca//8tiKdjp2LGjGDZsmOI+KP2yiEi5BQuUBSgLFhift3evY4EOIMTu3Y7fPzdX/nnUKPn8wAPKztdoCgOLjRvl66LvV8ENsRoDCw9ERwtx4ECJv1/9vUzvZy4AI/JWSn+/3b713M/PD3Xr1kXTpk0xa9YsNGrUCIv0K/tMhIeHo1atWjj/95aLsLAw5OXl4ebNm0bt0tPTERoa6vS+E5Fl1rIDW2tXkl1U6emFf7Z3B5efHxAfD3z4IbB4sfL+CyHrR+3bVzyvT29sws94BIOwFjr4YFnQROhO/FQ411UC3DJOpJzbgx1TQgjk5uaafe/GjRtITU1F+N/bLJo0aQJfX1/s2rXL0Obq1as4c+YMWrRo4ZL+EpF5+h1M9rYryS6qoucq3Ylk2i4jQ3mgU9S+fYXreariOtahHzYhDmH4Ez/jYbTAYbyS9T4+/DRAtbIUcXHAmTMym3JUlHxOTmagQ1SMawaazJsyZYo4cOCASElJEadPnxavv/668PHxETt37hRZWVliwoQJ4vDhwyIlJUXs3btXPPnkk6JmzZoiMzPTcI3hw4eLyMhIsXv3bnHixAnRvn170ahRI5Fvx2Q1p7GI1FfSNTum0zNKp5L0Pv1U2bl/b/40eOopx6bQ3nxTPsdhg/gT1YUARD58xEy8JvyRU2wNjxrTTM2ame9Ls2YlvzZRaVAqprH+/PNPDBo0CA899BA6dOiAH3/8ETt27ECnTp2g1WqRnJyM2NhYPPjggxg8eDAefPBB/PDDDwgKCjJcY8GCBejduzf69u2Lp556ChUqVMC2bduYY4fIzfz85E4maxo0AHr2BEaNAnJy5DF9CQNA2eiMpbIGX32lrJ+m7S5dUnZe0ftHRQGdGsvRnI3ogxq4hjOoj+Y4gtcxC7kob3SOvup5YqJ99yrq8ceBY8fMv3fsmHyfiCQWAgULgRI5kz0VxWNjgc2b5Z/NbfUOCCgMiiydp9e5M1BkhtuiTp2AnTsLX7dsqazAJlAYaB2etAlPrBwOTXo68qHFe3gVb+Mt5MHf6rmOFtnMzpaFT23JygIqVrTv2kSlidLfb49bs0NEpV9enhxpGT0aiIgAbt0CFiyQIzgxMZbP27IF6N1b/tm0hMHzz5sPdPTnTZ5sfOzBB5X11bTd118rOw8AYsJv4GLLAWg+Jw6a9HRkRNXHkziC/9PMsBroAIULmw8eVH4/vUGD1G1H5O04sgOO7JB76EshmCaMK+19MjeSo9XKKa3p05XVdbpzR47i6OXlyfOsjQ5ptfI8fRmKkox+1K1rfZFyaCiwa/RWxCweBk1aGuDjA7z6KjB1KhK/9i82ImXNunUysaE9YmKAs2dtt6tfXy5gJvJWHNkh8mCJiUDt2kC7dkD//vK5du2SreHwhD7pMyabBiX6jMlKN0lOmmT8eskS29NgOp1x1fPjx5Xdy1y7X3+1vJusce2bSOsyGA3ejJWBzsMPA0eOADNnAv7+hhGpBQuU3d+R3WeO7jQjKqsY7BC5mL4Ugun/+auxaNWdfcrLkyM61pw6paw/pjlyHMnZk5qq7BxL7X79VU6/Fd3Wnb1hB07kxQCrV8vRnMmTgRMngGbNjM7VauUUnqKq5w6k3FEaNDIDB5HEYIfIhXS64onn9PTH4uOVLeb1tD4pGX1RKjra+LUjOXt++EHZOdbaBQcDhw4Bl85m4VD9YQjs8zRw5Ypc6HPoEPDee0D58mbPtbarzNIOMqUefljddkTejsEOkQsdPGh9LUdJFq26u0+OJOKzxLQw54gRtoMCrVa207tyRdm9bLbbtw9o2BBYvly+jo8HTp4EihQstiQuDpg4UQ4CFeXjI487mvzPke+DqCxjsEPkQkpLIZSkZIK91OqT0tEXa7uxALmNvOjiZEBZzh59dXI9pXsNLLbLyZGBTbt2chFO7dpya9iCBcpWWUNO/82da34N09y5jk9ZOvJ9EJVlDHaIXEjpYtSSlEywl1p9UjrakJQkAxpzzOXL0ZszRy5cNr2HViuPz5ljfLx/f+t9sdru6FGgcePCeaiXXwZOnwbatlV2UVifHtQryZTlnDnFlgoZNGtW/PsgKssY7BC5UKtWzlu06u4+2TPasHmz3CY+cqRM/jdypHxtKdDRmzNHbhUvel5Wlvkfdl9f69cy2y4vD/i//5Mre8+dk0mCvvkG+PhjZfvYi1BjelCnk7NoX3whn4sGRpMnW8+gbJp3iKhMc0HpCo/H2ljkShs3ylpOprWf9MfUqJnkzj5NmlS8JpZWK4+r0c/ISONrW6oztW6dsppW69b9fcKZM0I0blz4Rr9+Qty44XBf7b6/HZ/V0bpjRN6mVNTGIiqL4uKADRvkoEFRNWvK4+6oWK3vU82axscjI+3v05w5cpRGnzF5wQL52nT0xdqohTn2bo9XPD0XWgDMmwc0aSIXHoeEAF9+KbP9hYQou4i565ZgetDWZx0+3P68Q0RlWTl3d4CorPK0hG9xcXLNjBpZnf385HoUS8zVvYqMlEtkzAVWtrbHazTyfrGxhf3VT89dvmz+PI0GaB52EW2mDwEO7JcHu3UDPv1UlUVTSu4fGVl8elDJZ/3Pf5T1Qc0dckSlGUd2iFzME5MK2sPeERlTjnx+R9a/WM1zA4HBYiX232oIzYH9QGCg3Fr+1VeqrQ53NM+Oks+ana2sD0p3yBF5O4dHdm7duoWjR48iPT0dBQUFRu+9+OKLJe4YkTdyZITCVZSMttg7ImPK0c/v6PZ4/fRc0T5XwzWsDhiGp3M2ATmQqZFXrXJKZGDu/oD8zhYuNP+dqZl24KWX1LsWUWnmULCzbds2DBgwALdv30ZQUBA0Rf63RaPRMNghssCeEQo7djmXmH60xTQI0Y+2bNggX9tqYyvgsffz6wuT/vyzss/x55/ynKKBUtHpOc32r/Hkp0Phd/NPuQ3r7bfN72dXkb3Tg2qmHfj008Lt7Z5WdJbIpRxZ/RwdHS3Gjh0rbt++7dDqaU/D3VjkKiXdoeMM+fnFd/2Y7siKjBSiZk3rfY6Kkteyxp7Pb243kpKH2d1Z2dlCDB9e2Kh+fSFOnnTWV1oi+n8epjvjiv7zqFhR2XcxapR9O9iIShun7sa6fPkyxowZgwoKs4gSkeSqpIL2rKtRMtryxx9yBMcaJSUllH6u8+fNr+tRotjan6NHIRo3BpYtk/18bjx0Px4HHn3U5rWuXQPq1AEqVpTP167Z3x97KVnr89xzyq6VnW3+e/zjj9KxPoxILQ4FO126dMHx48fV7guR13NFUsHERFnZoF07mR24XTv52tIPm5prRGwFRC1a2J4+8fGRa4WtZR62Rn/ehLH5KJj2NgqebAHN+fNIRSQ6YDfu+8881K5X3uYPfeXKQI0aslLE7dvyuUYNedzZbKUCWLZMWbbqXbssf49CuL7oLJG7OLRmp3v37pg0aRJ+/vlnNGjQAL4mqUp79eqlSueIvI3+/9r79JGBTdEfopJWwgaUrb0xXVej5hoRWyMfhw/b/nEtKLAdNNlyv/gVa/4YBJ/pRwAAX+AFjMAS3EIVAIUjG5bWGVWuDGRkmL92RoZ8/9atkvXRFltrfcaPL14wtag+fYD1663fwx3rw4jcwpE5Mo1GY/Hh4+Pj0LybO3HNDrmauXUUUVElW0ehZO2NuXU1StaIhIQoWyOydq31Pv773/avwbHvUSD+gc9EFgKFAMQtTbDoh8/tWmeUnq7sXunpjv+zUou1bNVr16rzz4zIkzl1zU5BQYHFh45jokQ2xcXJaZG9e2Wi3r17gZSUkmVPVrrT6cMPjUdXlKwRGTtWWR9Mp11MffaZsus4IgQ3sAF98G8MRUXcxj60QQNxGl/AckVQc+uMHn9c2f2UtgNKnpvIEmvZqpWuL3LFOiQid2NSQSI30Wrl9EG/fvK5pFuBla69GTeu+BoeW2tEXntN2RqRFi2st7E0NWSqXDnr65pq1jTuT0fsQjIa4FkkIg++mIz30BF7kIr7bN4rJcX4tdpBgr1rqOylz1b94Yfy2c9PHq9eXdn5StsRlWYOBzv79+9Hz549UbduXURHR6NXr144aGsrBhE5jT1rb8xlK7Y22qRkrY1OJ9tZU7eusv499ph8tjTS9PLL8n5+yMVcTMAudEYEruK/qIfmOIL3MRk6KIseTUeb1AwS3Jkt29Yom73tiEozh4KdtWvXomPHjqhQoQLGjBmDUaNGISAgAB06dMC6devU7iMRKWBrp1dR+gXMprtxLI02OZrB2NSaNcqus2eP9ZGm6GjgEZzFUTyOCZgPAFiCV9AESTiJx5Td5G+mo01Hjyo7T98uL08uKh89Wj7n5cnjtrJFA87dDaX/+2BNSXf+EZUajiwIqlevnpg/f36x4/PmzRP16tVz5JJuxQXK5C02brS80NjSo3dvIRYsECI31/J19+5Vdq29e2X7/Hz553Xr5HPRRcDNmlm/RrNmhW3NXqegQJwbs1jcQXkhAPEnqovu2ObwoubevYt/3uBg6+cEB8t21hYI2/udOYP+74Pp3wn9MSYWpNJO6e+3Q8GOn5+fOH/+fLHj58+fF/7+/o5c0q0Y7JA3MfcDrOSh/5E2R8mOLf3OJiUZey0FPEUDHbP+/FOI7t0NJ2xHVxGKq2b7Yyvjs/6RlWX+VpYCnqKBjrXr9uih7P7OzpbtjJ1/RJ7CqbuxoqKisGfPnmLH9+zZg6ioqBKNNBGR4xITgblzHZsa0elk3pbJk4u/p7SC95YtytaoHD0KZGUBvXsDDRrI56wsG1NI334LNGwIfP014O+Pn/65CN2xHemaMLP9mT9fwYdG4YJeU7duAenpcjFxYKB8Tk+Xx/PygHnzrF/366+V3V/NPEfmOGPnH1Gp40gktWTJEuHn5yeGDx8uVq9eLdasWSOGDRsm/P39xbJlyxyKztyJIzvkDWzl2bFnhMfSlJa1UQIl91dSP6uYu3eFGDeu8CL16wtx+rTN/ixYoOzzLlhg/3c9d66yawcHKxsNIyLHKP39diiD8iuvvIKwsDDMmzcPX375JQDg4Ycfxvr16xEbG6tiKEbkvdSuRG0rz449/VqyRC6eNWUtq+++fbbvb3fG3v/+V+7XPnVKvh45Ug4/BQTY7M/o0cpuceGCwr4UceiQsnYPPQQcO2Y5W/ZLLwFffslK5ETO5lCwAwDPPPMMnnnmGTX7QlRmJCbKnTpFg4PISDlV5Oj0gpo1rqwFAPodW6aUlnhQ1E4I4NNP5ZeUkwNUqwb8+99Az56K+xMRoaw/StsVVbGisnYPPgi8+mrxf9YhIfJ56tTCYyX9509EljGpIJGLWcq9UtJK1Gqu/XjgAcvvWdpqrVoyvps3gb59ZTKdnBygY0fg9GmzgY4127ap266oQYOUt4uLk8GjPsvxkCHAjRvyUZQrcu8QlVUaIYoOrloWEhKCX375BdWqVUOVKlWgsZLM46+//lKtg66QmZmJ4OBgZGRkoFKlSu7uDnkxnU4udLU23RMVJReQ2julob/25cvGUyb20mplyQFzC3cnT5YLf01z84wfDzRqBAwcaPv6a9cCAwZYePPQITltlZoq0yjPmAFMnChLodspKkrZtF5kpLydPfLygPLlrX/PGg1w9y7w1VfFR3asnRMZ6dg/f6KySOnvt+JprAULFiAoKMjwZ2vBDhGZp2RdjaOVqK1VVLfH+PGWAx1zVbb1u7ief17Z9c1m7NXpZGAzfbose163rtw61KyZzetZWvtUubKyAKNyZcvv5eXJ9UsXLsjRrhEj5Hdz+LDt71cIYPZsYNo05f8shGAlciKncMlyaQuWLFkiGjRoIIKCgkRQUJBo3ry52L59u+H9goICMXXqVBEeHi7Kly8v2rRpI86cOWN0jbt374pRo0aJqlWrigoVKoiePXuK1NRUu/rB3VjkKq6oRO2MPDu5ubavqdUKERHhwG6s1FQhWrcubPTii0JkZir6rNZy+ixfruxzL1+u/HvUf0erVyu7duXKju2Ic3buHSJv4dQ8OydOnEBycrLh9ZYtW9C7d2+8/vrryNNP4CsQGRmJ2bNn4/jx4zh+/Djat2+P2NhYnD17FgAwZ84czJ8/H4sXL8axY8cQFhaGTp06ISsry3CN+Ph4bNq0CQkJCTh06BCys7PRo0cPVl8nj+TsStSO5Nnp3du4WrY5S5Yoq43VubP1Ap4LF5pMz2zZIue/DhyQq37XrAFWrQL+HkW2Vi3c1tqnH36w3l+927eLH9OPYpl+Zv0oltIcPrduKWtnytm5d4jKHEciqaZNm4oNGzYIIYS4cOGC8Pf3F/369RN169YVY8eOdeSSBlWqVBGffvqpKCgoEGFhYWL27NmG9+7evSuCg4MNuXxu3bolfH19RUJCgqHN5cuXhY+Pj9ixY4fFe9y9e1dkZGQYHqmpqRzZIZdw5siOo3l2lIwijBql7FqjRinM2JuTY3zRJk2EMMnKbm3URslnDQlx7LtWMorlrAdz7xDZx6kjO7/88gseffRRAMB//vMftGnTBuvWrcPKlSuxceNGh4IunU6HhIQE3L59G08++SRSUlKQlpaGzp07G9r4+/ujTZs2OPx3aeWkpCTcu3fPqE1ERARiYmIMbcyZNWsWgoODDQ9mfSZXcWYlakfz7CgZRbC2O8u0nc2MvefOAc2bA4sXy9cTJshFMEVKotuqFj5jhu3PqnSfhOl3rWQUyxmKZqLm4mQidTkU7AghUFBQAADYvXs3unXrBkCWkbh+/bpd10pOTkbFihXh7++P4cOHY9OmTXjkkUeQlpYGAAgNDTVqHxoaangvLS0Nfn5+qFKlisU25kyZMgUZGRmGR6q9WzGIHGRvJWpr0zimHMmz4+MjF8TauvY//qHsevp2ZqunCyGnqJo0AX76CaheHdi+Xc67FVkRraRa+MKFyvpj8p+GYsxV/XYkyaAl9mzu1Fd0tzfPjj1/R4jKKoeCnaZNm+Ldd9/FmjVrsH//fnTv3h0AkJKSUiw4seWhhx7CqVOncOTIEbzyyisYPHgwfv75Z8P7pru+hBA2d4LZauPv749KlSoZPYhcoWiNKUv0/2efmCi3krdrJ3djt2snX1vKw+LIOo+CAuDFF21f+403lF3PYrusLHmjIUPkIpn27XHju59QZ8TTqFgRqFOncJ2SrREqIWQqHiVsJXQ3N4qidBRLicxM6+9Pn16yelX2/h0hKqscCnYWLlyIEydOYNSoUXjjjTdQ9+/h5w0bNqBFixZ2XcvPzw9169ZF06ZNMWvWLDRq1AiLFi1CWJgs7mc6QpOenm4IqMLCwpCXl4ebJv/lK9qGqDSyNY1j7sesVSvlmX3NsXbt8+eVXcNsu1On5GjO2rUyspgxAyHHd6Jag3BcvChjn4sXgRo15DZwNTNBO/L/MSNGqHd/W06cMBn9soMjf0eIyiw1Fwrl5OSIvLy8El2jffv2YvDgwYYFyu+9957hvdzcXLMLlNevX29oc+XKFZsLlE1x6zm5Sn6+EOXLW1+k6u9vffGtpUWsubmWi06WdIHsyJHKzh85sshJBQVCLF4shJ+fEIDIqREldk49JAIDrV/D1vv2PCpVsv5+1arFP+utW65dlHznjmN/jxz5O0LkbZT+fjsU7Fy6dMkol82PP/4oxo4dKz7++GO7rjNlyhRx4MABkZKSIk6fPi1ef/114ePjI3bu3CmEEGL27NkiODhYJCYmiuTkZNGvXz8RHh4uMovk4Bg+fLiIjIwUu3fvFidOnBDt27cXjRo1Evl2/FvOYIdcZft29X4k9+41vrbSStyOXDsrS9l5WVl/n3DzphBxcYY3vi3fS1TBDcX3j4iwXi08MtL2bqzq1ZXda/du48/aooVrgx2jAFGhvXsd++dI5G2cWvW8f//+ePnllzFo0CCkpaWhU6dOqF+/PtauXYu0tDS89dZbiq7z559/YtCgQbh69SqCg4PRsGFD7NixA506dQIATJ48GTk5ORgxYgRu3ryJJ554Ajt37jRkcgZkNudy5cqhb9++yMnJQYcOHbBy5UpouZ2hTFG7griepQy6jlKan0UJ0+kepZW4Hbn28ePKzjt+HGgb8CPwwgvAxYsoKOeL8fnvY9HdMQCUZ12/d08+W6oWrl/31KePfDbXpk0bueDXln37gA4dCl8rnbJTiyP3UzrVp+aUIFGp5kgkVblyZfG///1PCCHEokWLRIsWLYQQQnz77beiTp06jlzSrTiyU7pZy8dSEtYy6DqqaVPnjb4MHKjetU1HO5TlByoQx/vPFaJcOSEAUXD//aJbjWMO3T8wUFm+HmttXntN2b1ee834sz74IEd2iEoLp+bZuXfvHvz9/QHIree9evUCANSrVw9X+b8S5ELOWqRpK4Pu5MmOXbdpU2XtAgOtZyI2t2VaaSVuR9jK6ByCG9iKXmiybiKQnw889xwOLTqB7ekKP7CJ6tUV5OuB9TZKsxebtps716EuO8xcvTFb9CkM7P07QlRWORTs1K9fH8uWLcPBgwexa9cudO3aFQBw5coVVK1aVdUOElmiJB9LfLz9eUfy8mxPN82fL9vZS+k01iefyGfTHzNriefatrX842evK1eMX1v717o5fsBJNEZPfAWdr7+c91u/Hn9kBTt8/6NH5bPZfD0mLLVRWijdtF23branQLVa68GGUrGxQECA/ecVTWFgz98RorLKoWDnvffew8cff4y2bduiX79+aNSoEQBg69atePzxx1XtIJElSvKx6CtI20NpHaglS+y7LiB/2GwV8m7WTP5wb9hQPLuvtcRzSipxK/Xjj8avb9wo3kaDAkzAXBxAa9yHVPyCaCSMPQK88gqg0Thc3yk4WI7sACVLmBcd7Vg7rRb48kvr53z5peVgQ6nYWGDzZsfOBeTfAXv/jhCVWY7Ok+Xn54u//vrL6FhKSor4888/Hb2k23DNTum0bp2ydQv2VpC2pw6UvfLzlVUP128mzM+X6y7WrZPP1jYZKv0+lDxGjDC+tumanRBcF1vRw3BgHV4QFZFpVGcqP1+IihXtu29wcOH5JV2LpbRSe26u+fM3bhQiPNy4fUSE7TVDVasWr8sVESFE165CdO4s1+g4st3cEnv+jhB5G6fuxgIArVZbrExD7dq1SxZ5EdlB6ciBvSMM9tSBstc33ygbNfrmG6BHj8IpGiVq1LC/P5aYjnYUHT14AkewHs+jFi7hLvwxFouwHC8D0Bi10+lkJXVbfH2BkBCZe/DvXKKGtVimI1X6tVhKRi78/IDx462viRk/3vLuurg4OfpibZefaZvz54GpU4tf6+pV+XDGiIs9f0eIyiqNEMoGvh977DHs2bMHVapUQePGja2WYzhx4oRqHXSFzMxMBAcHIyMjg6UjSpG8PKBCBevBg1Yrf3Dt2S6ekyOva8udO/avt3jwQWVbjaOjgV9+se/ae/YAHTvad44lWVnG2Zh1OqB2LYE+lxdiDibDF/k4j7p4Dv/BT3gUgFwQm5JSGAwsXAiMG6f8npGRcmooNlaWPLA0RanRyLZF72XN5MnAvHmyNIaeVisDnTlzlPfPFp1O3X4TkW1Kf78Vj+zExsYadmD17t27xB0kKqnDh5WNkhw+bN//+ZquV7HWzt7/ozZd+FvSdkWlp9t/jiWffioXd+tps25he4V/ogE2AQDWoy/+hU+QhcL/uLzwgvGPuL0FNfWjNtOmKV+LpeT7b95cjspcvlx4LCxMHleTPWvIOBJD5FqKg52pRcZmp5obpyVyMWclVnNmwrYKFWQtKCXt7OXogmBzzp0r8iIpCeK559AgJQW58MM4LMBSvALTJIEJCcCsWYUBj73TfELI0Q9bhVL1Nm6Uz9YSSFqaDrtyRfl0mFJM9EfkuRzajVVUdnY2MjMzjR5EruCsNTvOui4gq3ur2a4ofe4VNSQnQ0YIS5cCLVpAk5KC31AHT+F7LMUImMuGbLrzbcQI+6drhAD++ktZ28WLZZXvWrXM51NSIzVBXp6cjhs9Wj5bSzfgzL831pRkxxpRmeHI6ufffvtNdOvWTVSoUEH4+PgYHhqNRvj4+DhySbfibqzSSV8M0VoNJUeKITrrukII0bGjsl1JHTvaf20hZHZnNXZj9WibJUS/foYDqU1iRWX8ZfM8051vjvYnJMT+oqamu7RKmmXY3gzazvx7Y4mzsocTlRZO3Y01YMAAAMC///1vhIaGWl2sTOQs+sRqffpYrqHkSGI1e69rT10upRsWHdnYqNPJgZiSegRnMe9AH6DgfxBaLTTvvYdfHxuPW+1t/3tuOmqhXwA8f759Iw5jx8q1O6bfvzUvvywXN+u/+5JMK+kzaJvSZ9AGii9udtbfR0vU2LFGVGY4EkkFBgYaamN5A47slG5Kaig567r2/p919+7KRhu6d7e/vzt3lnxEZwDWiGxUkKM5qCla4JBo1qzkoxa5uUIsWCDz91SqZPn+Ra9j7ru19Sha08vRkR018vM44+9jUfp/Hkq+RyJvpvT326Fgp23btmLXrl0OdcwTMdgp/ZyVWM3adTduNP/jr9HIh7kft9q1lf0A165tf18HDXI8yPFHjliKYYYD36KTqIZ0w/vNmhV+XtPPbO3zmmPPdfTff+/eyj7Hm28an+tIgLZggbJ7LVhg+TM6O9EfC4ESSU6dxvr0008xfPhwXL58GTExMfD19TV6v2HDhiUecSKyh7MSq1m6rq3FrxqNXPxadFoFUJ7vx1o7S9Nmju4NqI0U/AfPoSmSUAAN3sZbeAf/hwIUdvzYMaBzZzk1Mnas8RbryEg5PWNtysS0z+vXyzw3tq6j//737LG/tIKj00pKt8xba+fsRH/c+UVkH4eCnWvXruHChQv4xz/+YTim0WgghIBGo4GO2wHIyzmaUyU2VlmV69hY88cTE80HG4sWARERirpupBu+xhoMQghu4jqqYiDW4lt0Ndt20CBg0ybbWYWV9nnBAqBaNWXXadsWePdd25/HNMDQ14+yJ0BzZgZttbhr5xdRaaU4g3JRjzzyCB5++GFMnjzZ7ALlWrVqqdZBV2AGZbLXF18A/fvbbrdunSzqqac0y/Hu3UCHDsbHLC1I1f/rN2oU8OGHtq8NAD7QYTqm4k3MAAAcwRPoiy+RivssntOgAXD6tLLr2+qzvt9KF9HqdEBoqPmCpHpVqwJ//mk+YLJnEbmzMnOrSZ+t+fJly98tszVTWaB6BuWifv/9d2zduhV169Z1uINEpZnSOlSm7Vq0UHaevp3+R/ryZVl6wdq02RdfKLt2NVzDF+iHjtgDAPgQozAB83AP1n+57R3JsDbVB8jj5qb6zNFqgeXLgWeftdxm+XLL17FnWsnPD3jsMTl1Z8ljj7kv0AFcv/OLqLRzKKlg+/bt8dNPP6ndFyKv9/HHytslJsr/e2/XDhg4ELh2zXJ7IYDr121f9wkcwQk8ho7Yg9uogH5YhzH40GagAwBr1ijru56tqT6geCJCa44cKdn7SuXlAbbK+504YT3BoCvop+iKFl8F5IgOt50TGXNoZKdnz54YN24ckpOT0aBBg2ILlHv16qVK54g8ldI6VKbtlC5+/fZb+bB/ktkSgZH4CPMxHn64h//hITyLjfgZ9RWd3ayZcWFQJVJT1WuXlydz9Vgzf75c11PSEZclS5TVXFuyxLh+mDsoqcxORA4GO8OHDwcAvP3228Xe4wJlKgscXSCqNFng4cPqBToVcBvL8TIGYB0A4Es8h6H4DNkIUnR+s2bA0aP239eegqqDBllvU9IAxJ41O2rsxnIlZ+/8IvIGDk1jFRQUWHww0KGyQF+HylLycI0GiIqS7Ypq0EDZ9e3dRq7RyJ1NpqLxC46gOQZgHfKhxTjMx/NYbzPQCQgAevcGsrIcC3QA5cGaknYlCUCKTgf27y+fa9c2X08LKB27sYjIPnYFO926dUNGRobh9YwZM3Dr1i3D6xs3buCRRx5RrXNEnkq/QBQoHvBYWyBqbTeRo/T3+7uKi0EsNuMYmqEBzuAqwtAe32EhxsFcEU9Tjz0mt5nbO3VVVHS0eu0cDUD0u8FM1w7pSyqYC3iUFDDVamU7Iiod7Ap2vv32W+Tm5hpev/fee/irSIni/Px8nDt3Tr3eEXkwRxaIVq6sfj98fICJEwv74QMdZmIKNuMZBCMTB9ESj+EEDqK14mvWq1fyfqkZNAwbpuyeRds5WvXcz08mPLRm/Hj37sYiIvvYtWbHNCWPAyl6iDya6dqOFi3k+hlLaz3sXSC6datz+jx3LtCypdxWvg790Qm7AQALEI/JmIN8+Nq4irE7d6zfT8nn1QcN1pIoKg0a7Fn/o1+/4mjiR8ByAVOtVvbZtAgoEXk2hxYoE3kjc5l+TXOYRETIxH3mShoo4cxFreLoMSThWdyHVNxGBQzFZ1iPFxy61rlzwL59xQMZaxmczY1kqRU0XL5sf7uSllSYM0fu7lqyRP5ze+ABOQrlaSM69iy+Jiqr7Ap2NBpNsWzJpq+JSiNLmX5NX1+5IhPbbdzoWB6TwEDH+2jNP8RnWJI7Av7Iwy+IxjPYpHhbuTknTsiFvEUDGUvfkX79i6WpOzWCBms5hiy1U6Okgp+f+7eXW2Nv8ElUVtlVLsLHxwdPP/00/P39AQDbtm1D+/btEfj3f8Fzc3OxY8eOUrcji+UiyjZ96n1bCfCKqlgRuHXL/v+D/uwz4KWXbLcLDARu37bdzg+5+ABjMAzLAQCbEYvBWIVMBNvXMQv0/y/z5Zcyg7Ol78jZ5Qk+/1wmVrRl7drChdreXlLBVvkQJhakskDp77ddC5QHDx6MGjVqIDg4GMHBwRg4cCAiIiIMr2vUqIEXX3yxxJ0nciUlmX5NZWfLOlf2Urr2JD/fdpua+AMH0BrDsBwF0OANvIs4JKoW6ACFP6QjRihf/+IMpovAlbRzdMdcaeDo4muissquaawVK1Y4qx9EbqN0bYepNWuAzp3tO2f3bmXtimx6NKs19uNL9EUo0vEXqqA/vsB3vl0g7tnXHyWEUD6N5Oh3aYs+r5G1gMtcXiNHqp6XBiVZfE1UFjmUVJDImyhd22EqO9v+c3JyHLtXIYExWIQ96IBQpOMUGqEpjuNbdDGbVNDVHP0ubdGP0mg05kdpNBrLozRxccDFi8DevbIK/d69cuqqtAY6QMkXXxOVNQx2qMxr3Nix81q2tP+cxx937F4AEIA7WI0XsQjxKAcdPkd/tMBhXNLeD8D5P2zVqtmfMVpNJSl8qd8x16+ffC6NU1dFqbH4mqgssWuBsrfiAuWy7ZlngM2b7TvHx0eO0vj52bf1NzsbCFJQkiokBCiSrxO1cBGJiMNjOIl8aDHFdx7OtB+DHd+6bjfk1KmAvhxe0f9quHpBLLdae//iayKlnLJAmcgbOZL7ZsIEGejYW3fJkR+eDtiN42iKx3AS6aiOjtiNuffGujTQAeSWcUdHVtTkbaM0jvDmxddEzuDWYGfWrFlo1qwZgoKCUKNGDfTu3btYuYkhQ4YY8vvoH82bNzdqk5ubi9GjR6NatWoIDAxEr1698Ie922uozLKnoKNWC0yaJHPHOFJ3adIkZfeRozoCEzBXrsfBDRxDUzRBEvajrfIOq+jHH71z/UtpVZJpPaKyxq3Bzv79+zFy5EgcOXIEu3btQn5+Pjp37ozbJglGunbtiqtXrxoe27dvN3o/Pj4emzZtQkJCAg4dOoTs7Gz06NGj1OX7IfdYuVJZu5kzZRmFOXMc3/r7yy/K7hWAO/gcAzAXk6BFAVZiMFrhIP5AlLILOIH+s3BkxXMw+CRSxq3lInbs2GH0esWKFahRowaSkpLQunVh0UJ/f3+EhYWZvUZGRgY+++wzrFmzBh07dgQArF27FlFRUdi9eze6dOlS7Jzc3FyjgqaZmZlqfBxyo5wcOWpy/rysov3++0BAgLJzT55U1u7JJwuz/jq69VdJBuVauIhNeAaNcQr3UA7jsAAfYSSUVCt3JgY15rl7DZE95UqIyiqPWrOTkZEBAAgJCTE6vm/fPtSoUQMPPvgg/vWvfyE9Pd3wXlJSEu7du4fORRKeREREICYmBocPHzZ7n1mzZhkSIQYHByMqyn3/t0wl17s3UKEC8NFHwM6d8rlCBXlcCUe28Tq69ddWn9rhOxxHUzTGKaSjOjpgDz7CKLg70AGAZs3c3QPPY++aLSJyD48JdoQQGD9+PFq2bImYmBjD8aeffhqff/45vvvuO8ybNw/Hjh1D+/btDSMzaWlp8PPzQ5UqVYyuFxoairS0NLP3mjJlCjIyMgyP1NRU530wcqrevYEtW8y/t2WLsoDHkW28jm79rVXLUkuBsViInehstD7nIFpbOsHlbt50dw88iyNrtojIPTym6vmoUaNw+vRpHDp0yOj4888/b/hzTEwMmjZtilq1auHrr79GnJWJaSGExSKl/v7+hvpeVHrl5FgOdPS2bJHtrE1pPfGEsvsVbafP6Gtr669p3hlz9yqPHCzDcAzGagDAKryIYfgYuSivrGMuUrWqu3vgOWyt2dJo5Jqt2FhO/xF5Ao8Y2Rk9ejS2bt2KvXv3IjIy0mrb8PBw1KpVC+fPnwcAhIWFIS8vDzdN/rczPT0doaGhTuszuZ/SnU222n38sbLrFG3n6NZf03vp61sNxmrkQ4uxWIghWOlxgQ4A3Ljh7h54DnvWbBGR+7k12BFCYNSoUUhMTMR3332HOnXq2Dznxo0bSE1NRfjf8wNNmjSBr68vdu3aZWhz9epVnDlzBi1atHBa38n9/o53S9zO0es4svW36DWexGEcR1M0w3HcQAi64Ft8gLEANPDEgUeO7BRiuQai0sWt01gjR47EunXrsGXLFgQFBRnW2AQHByMgIADZ2dmYNm0ann32WYSHh+PixYt4/fXXUa1aNTzzzDOGtkOHDsWECRNQtWpVhISEYOLEiWjQoIFhdxZ5JwWxsaJ2lkogmPrpJyAvr3BHFiADmthY5btx9Pcaik+xBCPgh3s4jQaIxRZchMIPBKBcOWWV0dXEkZ1CLNdAVLq4NdhZunQpAKCtyb7JFStWYMiQIdBqtUhOTsbq1atx69YthIeHo127dli/fj2CiuTcX7BgAcqVK4e+ffsiJycHHTp0wMqVK6HlZLlXUyvYeeIJuYPLlu+/l7u8xo+XuXb07Nn627zJPdTDOIyCvOF/0Af/wArcRkWjdraqnrs60AGA6tVdf09P5eiaLSJyD7cGO7bKcgUEBODbb7+1eZ3y5cvjww8/xIcffqhW16gUUJok21Y7ezIP6HQyhw9QGPAozrNy/Tq6f/AcqmAfAOANvIuZeB2esK1cCdPpurJMv2arTx8Z2JirFcZyDUSewyMWKBM5onZtddrp/y/dHvPnyyktxXlWTp8GmjZFlVP7kKUJQi9swUy8AXOBjieOoDi7onlpxHINRKUHgx0qtRo0UKedVgs0aWLfvXU6YPhw83lW/vjDJM9KYiLQogXw++9A3bp4qf4RbEMvi9euVUv+YFpaS6TRAFaK+6pOo+EohSUs10BUOjDYoVLr2jV12uXlAV99Zf/9//Mf8+s1AHl83NgCFLw1DXj2WeD2baBjR+Ts+xFfnnnE6nWPH5dTZNau/eST9vfXFh8foKLx0iFERXGUwhbWCiPyfB6TVJDKnpLWFFIr2FmypHjBTiWysy2/F4hszP9jMHze+Xt4Jz4eeP99TIpX9q/c6tXW31e6g0yJOnWAMWOAESPk9+/OOk9ERM7AYIfcIjFRZqAtOgUUGSkXfSodRVBSVFNJu3PnlF1HqfvwO7aiFxrhNHTl/KBdvgz4xz8AKK96vnev5fc0GuDoURU6+rfAQBmL6bGoJBF5G05jkcupVVPogw+UtZs50/rITXKysusUZWkR8VM4hGNohkY4jTSEYmGvvYZAB1AeoFnbei4E8NdfdnTWhuBg9a5FROSJGOyQS9mqKQTIUQYl00pKC1NevGi9ErUj2YqvXy9+7J/4DN+hPWrgGk6gMZrhGH4LM87i3aOH/feyRK2prKFD1bkOEZGnYrBDLqVmTSFfX+X3tTZqZCuBnzlFgzUt8jEf4/AZXoIf7uFLPIdWOIg/EIXoaOPzTp60/15K+lASSpMzEhGVVgx2yKXUrCnUurXy+1obNXrgAeXXMRWMW/gKPTAOCwEAb2E6nsd63IGcrxo2zLi90szHgYHWt56rWadKadV3IqLSisEOuZSaNYUuXLDv3pZGjRQk6TarLs7jCJqjK77FbVTAs9iAd/AWiiYK/PFH43P+/FPZtevXl8+WKqqPGeNYn81ZskS9axEReSIGO+RSSrIVK83W6+Pg317TUaO7d+2/Rgfsxo94AvVwDpcQhZY4hEQ8W6xdaqrx62rVlF2/YUPr2XnfeMP+rM+WHDqkznWIiDwVgx1yKa1WJl+z5oUXlOV2UbqN25TpqFH58vad/wqWYAe6IgQ38QOa43EcxSk0NtvW0ZGdP/+0np1XyfeolGkiQSIib8Ngh1xKpwO++MJ6m4QEx5L82aLRmB816tpV2fla5ONDjMISjEQ56LAag9AOe/EnwiyeY7qIWOkOKn07S9l5lXyPSg0apM51iIg8FYMdcilbu7EA5buxzG3/tsRaJeqkJNvnV8ZNfIOnMQofoQAavIZZGIxVyIX1YSHT3VhKR1FstVPyPSq9T4cOJb8OEZEnYwZlcqnLl9Vrp9UqHwGKjJSBjrnszLa2cNfFeWxDT9TDOdxGBQzA59iC3or6N2KE8bGgIGX9tdVO6a42Wzp0YDkIIvJ+DHbIpdSqZwUAVaooWwNTpYpc62LpRz06Gjh71vx7bbEXG/EsQnATlxCFXtiKn/AoAJmM0FqOnvHjAT8/42NKAwtb7ZTuarPlq69kIVTTfhIReRNOY5FLKc0Po6Tdd98pu9ahQ9aDh5UrzR9/CZ9gJzojBDdxBE/gcRw1BDr6Pk6aVPzaWq08PmdO8WuaTmtZYqudfldbSbMo63Tcek5E3o/BDrnUjRv2tcvLk9NPo0fL57y8wjbPP6/sWrbamWY19oEO8zAen+Bl+CIf69APbbGv2ELkkBAZ0Ny5AyxYAIwaJZ/v3DEf6ACFlcWtMTf9Za7NokXyzyUNeOzNV0REVNpwGotcylIBTXPtJk8G5s83XpczcaKcHpozB7hyRdm1bLUruv6lIrLwBfqhB74GIDMiv4P/Q9FEgXr6SuF+fsZVw63x85P9f/99y23MTX+ZExcnc+6YVo+3V0kySBMRlQYMdsilwizv0jaydSvw5ZfFj+t0hYFCRISy6t8REdbfr1xZPkfhEr5CDzREMnJQHoOxCv9BX4vnRUXZvrc5+lGfefOAgoLC4z4+wIQJlkeFzImLA2Jj5e6siROV7SwrSskoEhFRacdpLPJIGzZYf3/+fGDKFGXXevNN6+8nJgKP40ccxeNoiGSkIRRtsN9qoAMAJ04ou785zZsXX2QcHi6P20ufi2ffPvvPVTqKRERUmjHYIafQ6eSP7xdfyGf9VFR6urLzi454WLr+9OnKrvXpp9bfL5f4JfahLcLwJ35CQzyOoziGx21e9/PPC/ti7rNakpgIPPts8e31ly/L4+YqsytRsaLyKSlri6iJiLwNgx1SXWIiULs20K4d0L+/fK5dWx6vUUO9+yhd7Gwx+aAQwLvvYulfzyMAd7ENPdASh5CK+xRdNy/P+mc1R6cDXn7Z+nVfftmxDNI6nfWt8IAMiObNs76ImojI2zDYIVUlJgJ9+hRfMHv5sjyuJDOyUrZ+2PXMJuDLzQUGDwb+7/8AAPMwHr2xGdlQmPUPwH33Wf+s5gKefftsB2k3bjg2JaUkq3J2NvDYY5y6IqKyhcEOqUankzuDzGUk1h/78ENl17K1nVqrBQIDHbzW9etAp07AmjWAVoucBcswEfNQAPtSCf/8s/XPGh9ffIRGaW4gpe2KUppVWa3sy0REpQWDHVKNrZEFIZTtngKAvtbXBmP8eOOcO9YYjQCdOydXAR88CFSqBHzzDT7GMGUXKuKpp6xvaRfCfI2vS5eUXV9pu6KUZlVWK/syEVFpwWCHVKN0xEDJqM3q1XJLtTmxsXK9id3ZmPftA558UmbRq10b+OEHoFMn/Pe/yq6jFxwMjByprK3pd3KfsuVAitsV1aKFsoSFLVrYf20iotKMwQ6pRumIga3CmzodMHu2zLVjSqORxxMTgd9+U3a/334DsGoV0LkzcPOmHNk5cgR45BEAlutiWZKRAbz9trK2pt9J+/bKzlParqjDh20vbNbpZDsiorKEwQ6pRsnIglLz51teDyOEXA9ja3v632dgWsH/AUOGAPfuyfmx774DQkMNLQIC7O/f//4nAxlLo1QajUw62KqV8fG2bW2PSFWtKtvZi2t2iIjMY7BDqlEysqBURob191NTbQdW/riLdeiP/8O78sDrr8tkOCbRzUMPOdbHyEj5bBrw6F8vXGi+SOjy5davu3y5Y0Ej1+wQEZnHYIdU4+oRA2vZhqviOnajI/ohAfmacsC//w3MmCFrMpiwVqfKmjt3ZKbnmjWNj0dGyuNxcebPi4sDNm4sDJaKnrdxo+XzbLFVCd3SaBMRkbdjbSxSjaeMGETjF2xHN9TFBdxEZazptRFj/mF5EUxAgFz0vGWLffe5fdu4NtXVq/I7aNXK9siMo+dZo6+E/uyz5t8XwvxoExGRt2OwQ6rRjyxY234eEaG8Wrkt9esD339vfKwlDmIzeqMq/sJvqIPu+BqvP/uwzWs9+KD9969TRz7ra1PZy9HziIjIPm6dxpo1axaaNWuGoKAg1KhRA71798a5c+eM2gghMG3aNERERCAgIABt27bFWZPtM7m5uRg9ejSqVauGwMBA9OrVC3/YSiVLqtNqgX79rLfp18/2yIKZmSazTLdn98fn2I2OqIq/cARPoDmO4H942FDV3JK8PGDuXGX3LKpePfvPcSZ9UkdLNBrziQ6JiLydW4Od/fv3Y+TIkThy5Ah27dqF/Px8dO7cGbdv3za0mTNnDubPn4/Fixfj2LFjCAsLQ6dOnZCVlWVoEx8fj02bNiEhIQGHDh1CdnY2evToAR3/q+5SOp1c/2vNypW2f2yV7bKSu8klgTfwLj7HQPgjDxvwLNrjO1yDLMT1zjvWr/PBB7a3w5vTq5f95ziTkqSO5hIdEhF5PeFB0tPTBQCxf/9+IYQQBQUFIiwsTMyePdvQ5u7duyI4OFgsW7ZMCCHErVu3hK+vr0hISDC0uXz5svDx8RE7duwwe5+7d++KjIwMwyM1NVUAEBkZGU78dN5v7179xnDXPHx8hCiHPPEp/mk4+D4mCA10Ru18fa33+6mnHLv/unUu+VoVW7eudPabiMhRGRkZin6/PWo3Vsbf+41DQkIAACkpKUhLS0Pnzp0Nbfz9/dGmTRsc/jszWlJSEu7du2fUJiIiAjExMYY2pmbNmoXg4GDDIyoqylkfqUxx9W6sigUZ2I5uGIp/QwcfjMBHmIS5ECYDlrZGihwZ1QGUZ3B2FW49JyIyz2OCHSEExo8fj5YtWyImJgYAkJaWBgAILZIATv9a/15aWhr8/PxQpUoVi21MTZkyBRkZGYZHamqq2h+nTHLlj2gULuF7TUt0wm5kIxC9sBVLMcJsWz8/61NnjgYtycmOnecs3HpORGSexwQ7o0aNwunTp/GFmUUfGpP/egshih0zZa2Nv78/KlWqZPSgklMzg7I1j+IkjqA5YsQZXEE4WuMAtqO7xfY5ObIUVmKi+fdN8+QopbRchavot54D9iU6JCLydh4R7IwePRpbt27F3r17EVkk01pYWBgAFBuhSU9PN4z2hIWFIS8vDzdv3rTYhlxDzQzKlnTFNziA1ojAVZxBfTTHEZzEYzbPu3wZ6NPHfMDj6I+/rYKm7hAXJxMaRkQYH69Z03qiQyIib+bWYEcIgVGjRiExMRHfffcd6ugTl/ytTp06CAsLw65duwzH8vLysH//frT4u3RzkyZN4Ovra9Tm6tWrOHPmjKENuYaz1+wMxafYhp4IQjb2oD1a4hBSoaw8uH5djrmt10884Vh/HD3PFTwxECMiche3BjsjR47E2rVrsW7dOgQFBSEtLQ1paWnIyckBIKev4uPjMXPmTGzatAlnzpzBkCFDUKFCBfTv3x8AEBwcjKFDh2LChAnYs2cPTp48iYEDB6JBgwbo2LGjOz9emeO8NTsC7+BNfIp/oRx0WIUX8TS+wR3fyvZdxcLWa0fXp3viuvbERDmCZboF/Y8/LI9sERF5PRfsDLMIgNnHihUrDG0KCgrE1KlTRVhYmPD39xetW7cWycnJRtfJyckRo0aNEiEhISIgIED06NFDXLp0SXE/lG5dI+vu3FF/e7kvcsVqDDQcmIa3BFAgACE0GnW2jOfnCxEZad81tFohcnPd8z1bouRzREXJdkRE3kDp77dGCEc33nqPzMxMBAcHIyMjg4uVS2DhQmDcOPWuVwkZSEQcOuA75EOLl7EcK/DPEl93797iZRomT7a/IKi567jTvn1Au3a223lav4mIHKX095u1sUg1Fy6od61IpGI7uqEBziALFdEHG7ATXUp0TY1Gbs023XqtJPOzOa7OK2TL77+r246IyFt4xG4s8g4PPKDOdRrgNH7Ak2iAwq3l5gKdatWUX9Pa1mtbZRYs8bTkfJs3q9uOiMhbMNgh1YwYUfIcLu2xB4fQEpG4jJ/xMJ7EDziFxmbbli+v/LqRkZa3XjsyQlO1qucl5ytSUk6VdkRE3oLBDqnGzw94zHbKG4sGYC12oCsqIQv70RpP4XtcQi2L7U2rnlvyyitASorlHDM1atjf19xc+89xtgcfVLcdEZG3YLBDqsnLA06ccORMgVcxG2sxCL7IRwKeR2fsxC1UsXrWmDHKrt6tm/pZg7Oz5YJgT6J0gbW9C7GJiEo7BjukmiVL7M+g7AMdPsJIzMYUAMBcTEB/rEMe/G2e+9Zbyu7xwQfW309PV3YdU54W7AQEALGx1tvExsp2RERlCYMdUs3Zs/a1L48cbEAfjMBSFECDsVhotmq5JX/9pew+JpVEinFkGstTbd5sOeCJjeXiZCIqm7j1nFRz5IjytiG4gW3oiRb4AXfhj4FYi43oY9f9KlRQ1q4k64is8dRcNZs3y+KnkyYB588D0dFy6oojOkRUVjHYIZerhYvYga6oh3O4icroiW34Hi3tvk5YGHDpku12trbEOzKNVbWq5wY7gAxsFi92dy+IiDwDgx1SzX33AWfOWG/zKE5iO7ohHGm4hCh0xQ78F484dD9fX2XtbCXRcyRfzvLl6i96VpNOJ/MHXb0qP1+rVp7dXyIiZ+KaHXKZjtiFA2iNcKThJzTEk/jB4UDHxweIiVHW1lYF8FatZB4eb6kUnpgI1K4tS0f07y+fa9dmEVAiKrsY7JBqrE0p9cfn2I5uCEI2vkM7tMYBXEFNh+/l7w888YSyts2aWX9fqwUWLZJ/VhrwDB5s/84zV7BU9fzyZVY9J6Kyi8EOqSY42NxRgQmYi88x0JBD52l8g0yYbaxYTg5w9KiytrZ2YwEy4eCGDUBNhfFXdjawZ4+ytq6i0wFjx8r65qb0x+LjPTNIIyJyJgY7pJqhQ41fa1CA+RiPuZgEAJiPcYpz6CihtMxD9erK2sXFARcvAh07Kmu/Zo2ydq5iq8aXEEBqqmxHRFSWcIEyqaZo+QY/5GIVBuMFrAcATMBczMcEVe8XFKSsndLRGkBOaVWsqKxtdrby67qC0uDP06q1ExE5G0d2SDX66ZEgZOJrdMcLWI97KIcBWKt6oAMAgwbJhcXWREXZX7CzpcJd8ErbuYrS5IjelESRiEgJBjukmoMHgVCkYR/aoiP2IAsV0Q3bsQ4D7L6WrYSBFSsCHToA/fpZb/fCC/ZvuR492vZCZY1GtiMiIs/HYIdUE/LXrziMFngMJ5GO6miLfdiNTnZf5/77bWf79feXI0lffGG9XUKC/QtytVogMNB6m8BAz8tbozQ5oqO1wIiISisGO6SOpCSMXNcC9yMFF3A/WuAwTqCJQ5caPBi4ccN6mxs3ZOFRawtyAccW5B48aHs9Tna25y30VZoc0ZEkikREpRmDHSq53buBtm3hd+saTqAxWuAwLqCuQ5fSaApz3thy/ryydvYuyE1NVbedq9hKjqjROLaGiYiotGOwQyWzfj3QrRuQnY3fozugLfYhHaEOX04I5dXM8/KUtatc2b4+/Pijuu1cxVpyRP3rhQs9b/qNiMjZGOyQ4z78UK4QvncP6NsXE+t9jSxUctntjx9X1m7zZvuuay4pX0nauZKl5IiRkfJ4XJx7+kVE5E7Ms0P2EwJ4801g5kz5etQoYNEiBAxxbeyspOI5AOzfb991o6PVbedqcXFAbCwLgRIR6WmE8MT/P3WtzMxMBAcHIyMjA5UquW5kolTKz0fB8Ffg89mnAIDfhr6LWsteh7acBrt2AZ07l/wWVavaXqAMyCSGSgKemBggOVn5/fPy5NZ3a7u4tFrgzh3Az0/5dYmISF1Kf785jUXK3b2Lyy37wuezT6GDD/6F5XjgszdQu44GiYlA+/bKsw9b06GDsnb16ytr17y5fff38wPGj7feZvx4BjpERKUFgx1SJiMD15p2Rc0fN+Eu/NEHG/Ap/gWgsKL2li3AqlUlv9WuXSW/RlFVqth/zpw5wKRJxad+tFp5fM4cdfpGRETOx2kscBrLprQ0iKefhubUKWSgEmKxBfvR1qiJRiMXwaakyKBn9GjgyhXndisiQtk9OnZ0PIDKy5P5fC5cAB54ABgxgiM6RESeQunvNxcok3W//QZ07gzNhQtIQyi6Ygd+wqPFmplW1PZxwZhhTo667czx8wPi4x0/n4iI3I/TWGTZ6dPAU08BFy4gu3odtMQhs4FOUVu2yCktW5mN1RAcrKxd7dpO7QYREXk4Bjtk3qFDQOvWQFoa0LAhTi/9XlFW5M8/L1n+GY1G7sZSYuhQZe1efNHx/hARUenHYIeK+/proFMnICMDaNkS2L8fT/QOt1mKoHp14Nq1kt9+1Chl7R5/3PbuL311dCIiKrsY7JCxtWtlRrq7d4EePYBvvwUqV1ZUimDAgJLdWqsFJk4EHnpIWfsbN2zv/lq1isn0iIjKOgY7VOiDD4BBg2Q2vUGDgMREmV3vb7ZKEcTGluz2BQXA3LnKC3yGh8s+bdwod2YVVbOmPM7yCERE5NZg58CBA+jZsyciIiKg0Wiw2aSI0ZAhQ6DRaIwezU0yxOXm5mL06NGoVq0aAgMD0atXL/zhitWx3kQI4K23gLFj5ev4eGDlSsDXt1jTuDjg4kVg715g3Tr5nJIij9uqug0A1aoBISGWuwEAn3xiX/XuuDiZSblon37/nYEOERFJbg12bt++jUaNGmHx4sUW23Tt2hVXr141PLZv3270fnx8PDZt2oSEhAQcOnQI2dnZ6NGjB3TWcv1ToYICuUjmnXcAAPnT3sHC++Zj9FgfLFyovLI4YLvqtkYj8+9Yq2ouhNzJ9a9/Wb4OULx6t1YLtG0r65K2bcupKyIiKkJ4CABi06ZNRscGDx4sYmNjLZ5z69Yt4evrKxISEgzHLl++LHx8fMSOHTssnnf37l2RkZFheKSmpgoAIiMjo6Qfo3TJyxOiXz8hACE0GrGx4xKh1cqX+odWK8SkSYWnbNwoRGSkcZvISHncWpuoKHl83Trj45Ye69ZZvw4REVFGRoai32+PTyq4b98+1KhRA5UrV0abNm0wY8YM1KhRAwCQlJSEe/fuoXOR6pMRERGIiYnB4cOH0aVLF7PXnDVrFqZPn+6S/nusO3eA554Dtm8HypXD513XYOBXLxRrptMB778v/9y8ucyhY7q1XF8uYsMGOXVkqeo2AHz4obLuhYfLERql1bt1OnWqfKt1HSIi8iAuCr5sgpmRnYSEBPHVV1+J5ORksXXrVtGoUSNRv359cffuXSGEEJ9//rnw8/Mrdq1OnTqJl19+2eK9yvzIzs2bQrRsKYdKAgJE3pbtxUZ0TB9arRAREZbf12jkqEt+vvlbmhulceQ6Sq9tOtrkyusQEZFreMXIzvPPP2/4c0xMDJo2bYpatWrh66+/RpyV1adCCGisrJL19/eHv7+/qn0tNf78E+jaFTh1SqYg/uorfHS8JWwtcdLprNeh0peLmDZN5rUpOiKSmGh+RMiUpfU41li6tulok6uuQ0REnqdUbT0PDw9HrVq1cP7vvclhYWHIy8vDzZs3jdqlp6cjNDTUHV30bL//LqOQU6eAGjWA/fuBli1x4YJ6t3j3XaBdO1miITFRBkljxyrLqqzfwq40qLB2bf2x+HgoCuSsXUcIZdchIiLPVKqCnRs3biA1NRXh4eEAgCZNmsDX1xe7ipS0vnr1Ks6cOYMWLVq4q5ue6X//k9mQz58HatWS5SAaNQIgq3mrTT8iMmOGsjpZCxYUbmFX6uBB69c2LU7q6HUAZdchIiLP5NZgJzs7G6dOncKpU6cAACkpKTh16hQuXbqE7OxsTJw4ET/88AMuXryIffv2oWfPnqhWrRqeeeYZAEBwcDCGDh2KCRMmYM+ePTh58iQGDhyIBg0aoGPHjm78ZB7mxAk5ovPHH0C9ejLQiY42vD1ihO1pI61WJu6zlkOnKP0oyQcfKGsfGmr/QuCrV9Vpd/mysusobUdERJ7FrcHO8ePH0bhxYzRu3BgAMH78eDRu3BhvvfUWtFotkpOTERsbiwcffBCDBw/Ggw8+iB9++AFBQUGGayxYsAC9e/dG37598dRTT6FChQrYtm0btNxCIx08KOeVrl8HmjQBDhyQ80VF+PkB48dbv8z48YU7qewJeG7cUNb278E6uyg9x1Y7pfW8NmywL+8QERF5Bo0QJalR7R0yMzMRHByMjIwMVKpUyd3dUc8338h5obt3ZQXzbdsAK59v8mRg/nzjtSlarQx05syRrxMT5foWe5JUh4QAN2+aXxOj0cjYKyXF/pEdnU6uDbLWl6go29f+/HNg4EBl9zT9PoiIyH2U/n6XqjU7ZIcvvwR69ZKBTvfuwI4dVgMdQP6A37kj18+MGiWf79wx/mEvWi7izTeVdUVfhUJpNmSltFqZMdmaF16wfW3TWl/W6PMOTZ6s/BwiInIvjuzAC0d2PvsMePllWQrihReA1avN1rkqKf3IyuXLtkdttmwpPiIUFSUDHUe3dKs1sqPkOqa0WhkI+vkpP4eIiNTFkZ2yasEC4KWXZKDz8svA2rVOCXQA27WwgMJRG2sFRB2l1i4q/edQuhYJkAHSkiXK2xMRkfsw2PEWQgDTpxeuNJ40CVi2zOm1DuLi5MJd06kgczlz1C7WqdZuLKDwc5is3bZKzfxERETkPAx2vIEQwIQJMn0xIDP7vfeefUMVJeCMURsl1NqNpaf/HCNHKmvvjPxERESkPq7ZQSlfs6PTAcOHA59+Kl8vWgSMGePePrmIPWuG7BlFyssDKlSwnjGZa3aIiNyPa3bKgnv3gAEDZKDj4wP8+99lJtAB7FszZA8/P6BHD+ttevRgoENEVFow2Cmt7t6V8y7r18sFyAkJwD/+4e5euZw9a4aU0umApCTrbU6cYK0sIqLSwqOrnpMF2dlAbCzw3XdA+fIy09/TT7u7V24TFye/joMH5WLk8HDjquv2smeXV9u2jt2DiIhch8FOaXPrFtCtG/DDD0DFisBXXwFt2ri7V06j0ykLYvQ7vdSg5i4vIiJyPwY7pcm1a0CXLsDJk0CVKjIr8uOPu7tXZikNUqwxV5oiMlKu03HmTi+1d3kREZF7cc1OaXHlihy6OHkSqFED2LfPYwOdxES5S6pdO6B/f/lcu7Y8bs81+vQpPp10+bI8bs+17NWqlQyqLO3c12hkZuZWrZzXByIiUg+DndLg999lIc+ff5a/wgcOAA0burtXZqkRpOh0ckTH3HZy/bH4eOctEHbWLi8iInIPBjue7vx5OYRw4QJw//1ybuihh9zdK7PUClJsLRAWQlkZiJJwxi4vIiJyD67Z8WRnzwIdOwJpaUC9esDu3faV6HYxe4IUa4uJPWWBsNq7vIiIyD0Y7HiqEyeAzp2BGzeARo2AnTvlWh0PplaQ4kkLhNXc5UVERO7BaSxP9MMPQPv2MtB5/HFZbMrDAx1AvSCFC4SJiEhNDHY8zb59QKdOQEaGXJS8a5fcZl4KqBWkcIEwERGpicGOJ/n2W5kJ+fZtGfB88w1QigqTqhmkcIEwERGphVXP4SFVz7dsAfr2lSW3e/YEvvxSloIohcwlA4yKkoGOvUGKGskJiYjIOyn9/WawAw8IdtavBwYOBPLzZTKazz8v9SW1GaQQEZGzKf395m4sd1u9WlYrLyiQAc+KFUC50v+PhbuYiIjIU3DNjjstXw4MGSIDnZdeAlat8opAh4iIyJPwl9VdPvwQGDNG/nnUKLmy14expyml02GcNiMiIksY7LjD3LnApEnyzxMmAO+/b3m/thexNyBRWvXcXdXRiYiodOBQgqvNmFEY6LzxRpkJdOythK60oKg7q6MTEVHpwN1YcNFuLCGAqVOBd96Rr995B3jzTefcy8PoAxLTv2n6GM80b45OJwMhS3W2NBo5cvPrr8ADD9hul5LCKS0iIm+k9PebIzuuIATw2muFgc6cOWUm0HGkErrSgqJLlri/OjoREXk+BjvOJgQwbpwMcAC5kEQ/jVUG2FMJXU9pQdELF5S1c3Z1dCIi8mxcoOxMBQVyp9XSpfL10qXA8OHu7ZOLOVIJXWlB0QceUNbOFdXRiYjIc3Fkx1mEkIHN0qVy8chnn5W5QAdwrBK60oKiI0awOjoREdnGYMdZNBqgXj2ZO2f1auCf/3R3j9zCkUroSguK+vmxOjoREdnGYMeZxo8Hzp6VZSDKKEcroSutes7q6EREZItbg50DBw6gZ8+eiIiIgEajwebNm43eF0Jg2rRpiIiIQEBAANq2bYuzZ88atcnNzcXo0aNRrVo1BAYGolevXvjD2opYV6tXz909cDtHA5K4OODiRWDvXmDdOvmcklK8vdJ2RERUNrk12Ll9+zYaNWqExYsXm31/zpw5mD9/PhYvXoxjx44hLCwMnTp1QlZWlqFNfHw8Nm3ahISEBBw6dAjZ2dno0aMHdEX3MpPbORqQ6AuK9usnny1NSSltR0REZY/HJBXUaDTYtGkTevfuDUCO6kRERCA+Ph6vvvoqADmKExoaivfeew/Dhg1DRkYGqlevjjVr1uD5558HAFy5cgVRUVHYvn07unTpYvZeubm5yM3NNbzOzMxEVFSUc5MKEhERkapKfVLBlJQUpKWloXPnzoZj/v7+aNOmDQ4fPgwASEpKwr1794zaREREICYmxtDGnFmzZiE4ONjwiIqKct4HISIiIrfy2GAnLS0NABAaGmp0PDQ01PBeWloa/Pz8UKVKFYttzJkyZQoyMjIMj9TUVJV7T0RERJ7C45MKaky28Aghih0zZauNv78//P39VekfEREReTaPHdkJCwsDgGIjNOnp6YbRnrCwMOTl5eHmzZsW2xAREVHZ5rHBTp06dRAWFoZdu3YZjuXl5WH//v1o0aIFAKBJkybw9fU1anP16lWcOXPG0IaIiIjKNrdOY2VnZ+PXX381vE5JScGpU6cQEhKC++67D/Hx8Zg5cyaio6MRHR2NmTNnokKFCujfvz8AIDg4GEOHDsWECRNQtWpVhISEYOLEiWjQoAE6duzoro9FREREHsStwc7x48fRrl07w+vx48cDAAYPHoyVK1di8uTJyMnJwYgRI3Dz5k088cQT2LlzJ4KCggznLFiwAOXKlUPfvn2Rk5ODDh06YOXKldAy0QoRERHBg/LsuJPSffpERETkOUp9nh0iIiIiNTDYISIiIq/GYIeIiIi8mscnFXQF/bKlzMxMN/eEiIiIlNL/bttafsxgBzBUUWeNLCIiotInKysLwcHBFt/nbiwABQUFuHLlCoKCgmyWorCHvpp6amoqd3m5AL9v1+F37Tr8rl2H37XrqPVdCyGQlZWFiIgI+PhYXpnDkR0APj4+iIyMdNr1K1WqxH9xXIjft+vwu3Ydfteuw+/addT4rq2N6OhxgTIRERF5NQY7RERE5NUY7DiRv78/pk6dCn9/f3d3pUzg9+06/K5dh9+16/C7dh1Xf9dcoExERERejSM7RERE5NUY7BAREZFXY7BDREREXo3BDhEREXk1BjtOtGTJEtSpUwfly5dHkyZNcPDgQXd3yevMmjULzZo1Q1BQEGrUqIHevXvj3Llz7u5WmTBr1ixoNBrEx8e7uyte6fLlyxg4cCCqVq2KChUq4NFHH0VSUpK7u+V18vPz8eabb6JOnToICAjA/fffj7fffhsFBQXu7ppXOHDgAHr27ImIiAhoNBps3rzZ6H0hBKZNm4aIiAgEBASgbdu2OHv2rOr9YLDjJOvXr0d8fDzeeOMNnDx5Eq1atcLTTz+NS5cuubtrXmX//v0YOXIkjhw5gl27diE/Px+dO3fG7du33d01r3bs2DEsX74cDRs2dHdXvNLNmzfx1FNPwdfXF9988w1+/vlnzJs3D5UrV3Z317zOe++9h2XLlmHx4sX473//izlz5uD999/Hhx9+6O6ueYXbt2+jUaNGWLx4sdn358yZg/nz52Px4sU4duwYwsLC0KlTJ0PNStUIcorHH39cDB8+3OhYvXr1xGuvveamHpUN6enpAoDYv3+/u7vitbKyskR0dLTYtWuXaNOmjRg7dqy7u+R1Xn31VdGyZUt3d6NM6N69u/jnP/9pdCwuLk4MHDjQTT3yXgDEpk2bDK8LCgpEWFiYmD17tuHY3bt3RXBwsFi2bJmq9+bIjhPk5eUhKSkJnTt3NjreuXNnHD582E29KhsyMjIAACEhIW7uifcaOXIkunfvjo4dO7q7K15r69ataNq0KZ577jnUqFEDjRs3xieffOLubnmlli1bYs+ePfjll18AAD/99BMOHTqEbt26ubln3i8lJQVpaWlGv5X+/v5o06aN6r+VLATqBNevX4dOp0NoaKjR8dDQUKSlpbmpV95PCIHx48ejZcuWiImJcXd3vFJCQgJOnDiBY8eOubsrXu23337D0qVLMX78eLz++us4evQoxowZA39/f7z44ovu7p5XefXVV5GRkYF69epBq9VCp9NhxowZ6Nevn7u75vX0v4fmfit///13Ve/FYMeJNBqN0WshRLFjpJ5Ro0bh9OnTOHTokLu74pVSU1MxduxY7Ny5E+XLl3d3d7xaQUEBmjZtipkzZwIAGjdujLNnz2Lp0qUMdlS2fv16rF27FuvWrUP9+vVx6tQpxMfHIyIiAoMHD3Z398oEV/xWMthxgmrVqkGr1RYbxUlPTy8WwZI6Ro8eja1bt+LAgQOIjIx0d3e8UlJSEtLT09GkSRPDMZ1OhwMHDmDx4sXIzc2FVqt1Yw+9R3h4OB555BGjYw8//DA2btzoph55r0mTJuG1117DCy+8AABo0KABfv/9d8yaNYvBjpOFhYUBkCM84eHhhuPO+K3kmh0n8PPzQ5MmTbBr1y6j47t27UKLFi3c1CvvJITAqFGjkJiYiO+++w516tRxd5e8VocOHZCcnIxTp04ZHk2bNsWAAQNw6tQpBjoqeuqpp4qlUPjll19Qq1YtN/XIe925cwc+PsY/hVqtllvPXaBOnToICwsz+q3My8vD/v37Vf+t5MiOk4wfPx6DBg1C06ZN8eSTT2L58uW4dOkShg8f7u6ueZWRI0di3bp12LJlC4KCggyjacHBwQgICHBz77xLUFBQsbVQgYGBqFq1KtdIqWzcuHFo0aIFZs6cib59++Lo0aNYvnw5li9f7u6ueZ2ePXtixowZuO+++1C/fn2cPHkS8+fPxz//+U93d80rZGdn49dffzW8TklJwalTpxASEoL77rsP8fHxmDlzJqKjoxEdHY2ZM2eiQoUK6N+/v7odUXVvFxn56KOPRK1atYSfn5947LHHuB3aCQCYfaxYscLdXSsTuPXcebZt2yZiYmKEv7+/qFevnli+fLm7u+SVMjMzxdixY8V9990nypcvL+6//37xxhtviNzcXHd3zSvs3bvX7H+jBw8eLISQ28+nTp0qwsLChL+/v2jdurVITk5WvR8aIYRQN3wiIiIi8hxcs0NERERejcEOEREReTUGO0REROTVGOwQERGRV2OwQ0RERF6NwQ4RERF5NQY7RERE5NUY7BAREZFXY7BDRKXOypUrUblyZbf2oW3btoiPj3drH4hIGWZQJiLVDBkyBKtWrSp2vEuXLtixY4dq98nJyUFWVhZq1Kih2jXt9ddff8HX1xdBQUFu6wMRKcNCoESkqq5du2LFihVGx/z9/VW9R0BAgNsLvYaEhLj1/kSkHKexiEhV/v7+CAsLM3pUqVLF8L5Go8Gnn36KZ555BhUqVEB0dDS2bt1qdI2tW7ciOjoaAQEBaNeuHVatWgWNRoNbt24BKD6NNW3aNDz66KNYs2YNateujeDgYLzwwgvIysoytBFCYM6cObj//vsREBCARo0aYcOGDVY/y5IlSxAdHY3y5csjNDQUffr0MbxXdBpr37590Gg0xR5DhgwxtN+2bRuaNGmC8uXL4/7778f06dORn59v57dLRI5gsENELjd9+nT07dsXp0+fRrdu3TBgwAD89ddfAICLFy+iT58+6N27N06dOoVhw4bhjTfesHnNCxcuYPPmzfjqq6/w1VdfYf/+/Zg9e7bh/TfffBMrVqzA0qVLcfbsWYwbNw4DBw7E/v37zV7v+PHjGDNmDN5++22cO3cOO3bsQOvWrc22bdGiBa5evWp4fPfddyhfvryh/bfffouBAwdizJgx+Pnnn/Hxxx9j5cqVmDFjhr1fHRE5QvU66kRUZg0ePFhotVoRGBho9Hj77bcNbQCIN9980/A6OztbaDQa8c033wghhHj11VdFTEyM0XXfeOMNAUDcvHlTCCHEihUrRHBwsOH9qVOnigoVKojMzEzDsUmTJoknnnjCcI/y5cuLw4cPG1136NChol+/fmY/y8aNG0WlSpWMrllUmzZtxNixY4sdv379unjggQfEiBEjDMdatWolZs6cadRuzZo1Ijw83Oy1iUhdXLNDRKpq164dli5danTMdH1Lw4YNDX8ODAxEUFAQ0tPTAQDnzp1Ds2bNjNo//vjjNu9bu3Zto8XC4eHhhmv+/PPPuHv3Ljp16mR0Tl5eHho3bmz2ep06dUKtWrVw//33o2vXrujatath6s2Se/fu4dlnn8V9992HRYsWGY4nJSXh2LFjRiM5Op0Od+/exZ07d6xek4hKjsEOEakqMDAQdevWtdrG19fX6LVGo0FBQQEAubZGo9EYvS8UbBq1dk3989dff42aNWsatbO0eDooKAgnTpzAvn37sHPnTrz11luYNm0ajh07ZnHb+yuvvIJLly7h2LFjKFeu8D+vBQUFmD59OuLi4oqdU758eZufjYhKhsEOEXmUevXqYfv27UbHjh8/XqJrPvLII/D398elS5fQpk0bxeeVK1cOHTt2RMeOHTF16lRUrlwZ3333ndmgZf78+Vi/fj1++OEHVK1a1ei9xx57DOfOnbMZBBKRczDYISJV5ebmIi0tzehYuXLlUK1aNUXnDxs2DPPnz8err76KoUOH4tSpU1i5ciUAFBvxUSooKAgTJ07EuHHjUFBQgJYtWyIzMxOHDx9GxYoVMXjw4GLnfPXVV/jtt9/QunVrVKlSBdu3b0dBQQEeeuihYm13796NyZMn46OPPkK1atUMnz8gIADBwcF466230KNHD0RFReG5556Dj48PTp8+jeTkZLz77rsOfSYiUo67sYhIVTt27EB4eLjRo2XLlorPr1OnDjZs2IDExEQ0bNgQS5cuNezGKkm+nnfeeQdvvfUWZs2ahYcffhhdunTBtm3bUKdOHbPtK1eujMTERLRv3x4PP/wwli1bhi+++AL169cv1vbQoUPQ6XQYPny40eceO3YsAJlU8auvvsKuXbvQrFkzNG/eHPPnz0etWrUc/jxEpBwzKBORx5sxYwaWLVuG1NRUd3eFiEohTmMRkcdZsmQJmjVrhqpVq+L777/H+++/j1GjRrm7W0RUSjHYISKPc/78ebz77rv466+/cN9992HChAmYMmWKu7tFRKUUp7GIiIjIq3GBMhEREXk1BjtERETk1RjsEBERkVdjsENERERejcEOEREReTUGO0REROTVGOwQERGRV2OwQ0RERF7t/wFxYI24uoS1LgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS, color='blue')\n", + "XX = np.arange(0.0, 10.0, 0.1)\n", + "yy = clf.intercept_[0]+ clf.coef_[0][1]*XX+ clf.coef_[0][2]*np.power(XX, 2)\n", + "plt.plot(XX, yy, '-r' )\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Evaluation

\n" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean absolute error: 22.32\n", + "Residual sum of squares (MSE): 843.55\n", + "R2-score: 0.76\n" + ] + } + ], + "source": [ + "from sklearn.metrics import r2_score\n", + "\n", + "test_x_poly = poly.transform(test_x)\n", + "test_y_ = clf.predict(test_x_poly)\n", + "\n", + "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))\n", + "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y_ - test_y) ** 2))\n", + "print(\"R2-score: %.2f\" % r2_score(test_y,test_y_ ) )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Practice

\n", + "Try to use a polynomial regression with the dataset but this time with degree three (cubic). Does it result in better accuracy?\n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[ 0. 29.80281416 4.22812695 -0.46674758]]\n", + "Intercept: [128.48038184]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean absolute error: 22.33\n", + "Residual sum of squares (MSE): 840.89\n", + "R2-score: 0.76\n" + ] + } + ], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn import linear_model\n", + "from sklearn.metrics import r2_score\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "poly3 = PolynomialFeatures(degree=3)\n", + "train_x_poly3 = poly3.fit_transform(train_x)\n", + "\n", + "clf3 = linear_model.LinearRegression()\n", + "clf3.fit(train_x_poly3, train_y)\n", + "\n", + "print('Coefficients: ', clf3.coef_)\n", + "print('Intercept: ', clf3.intercept_)\n", + "\n", + "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS, color='blue')\n", + "XX = np.arange(min(train.ENGINESIZE), max(train.ENGINESIZE), 0.1)\n", + "yy = clf3.intercept_[0] + clf3.coef_[0][1]*XX + clf3.coef_[0][2]*np.power(XX,2) + clf3.coef_[0][3]*np.power(XX,3)\n", + "plt.plot(XX, yy, '-r')\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"CO2 Emission\")\n", + "plt.show()\n", + "\n", + "test_x_poly3 = poly3.transform(test_x)\n", + "test_y3_ = clf3.predict(test_x_poly3)\n", + "\n", + "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y3_ - test_y)))\n", + "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y3_ - test_y) ** 2))\n", + "print(\"R2-score: %.2f\" % r2_score(test_y, test_y3_))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "poly3 = PolynomialFeatures(degree=3)\n", + "train_x_poly3 = poly3.fit_transform(train_x)\n", + "clf3 = linear_model.LinearRegression()\n", + "train_y3_ = clf3.fit(train_x_poly3, train_y)\n", + "\n", + "# The coefficients\n", + "print ('Coefficients: ', clf3.coef_)\n", + "print ('Intercept: ',clf3.intercept_)\n", + "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS, color='blue')\n", + "XX = np.arange(0.0, 10.0, 0.1)\n", + "yy = clf3.intercept_[0]+ clf3.coef_[0][1]*XX + clf3.coef_[0][2]*np.power(XX, 2) + clf3.coef_[0][3]*np.power(XX, 3)\n", + "plt.plot(XX, yy, '-r' )\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")\n", + "test_x_poly3 = poly3.transform(test_x)\n", + "test_y3_ = clf3.predict(test_x_poly3)\n", + "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y3_ - test_y)))\n", + "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y3_ - test_y) ** 2))\n", + "print(\"R2-score: %.2f\" % r2_score(test_y,test_y3_ ) )\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Want to learn more?

\n", + "\n", + "IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: SPSS Modeler\n", + "\n", + "Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at Watson Studio\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thank you for completing this lab!\n", + "\n", + "\n", + "## Author\n", + "\n", + "Saeed Aghabozorgi\n", + "\n", + "\n", + "### Other Contributors\n", + "\n", + "Joseph Santarcangelo\n", + "\n", + "\n", + "##

© IBM Corporation 2020. All rights reserved.

\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python", + "language": "python", + "name": "conda-env-python-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.12" + }, + "prev_pub_hash": "4dc110debac287dfd374a575573c16e62a80a935b3bbe2b2f6d5a0598e6e33f6" + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb new file mode 100644 index 0000000..5d1576a --- /dev/null +++ b/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb @@ -0,0 +1,1467 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

\n", + " \n", + " \"Skills\n", + " \n", + "

\n", + "\n", + "\n", + "# Simple Linear Regression\n", + "\n", + "\n", + "Estimated time needed: **15** minutes\n", + " \n", + "\n", + "## Objectives\n", + "\n", + "After completing this lab you will be able to:\n", + "\n", + "* Use scikit-learn to implement simple Linear Regression\n", + "* Create a model, train it, test it and use the model\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Importing Needed packages\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "import pylab as pl\n", + "import numpy as np\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Downloading Data\n", + "To download the data, we will use !wget to download it from IBM Object Storage.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--2025-10-20 06:58:57-- https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv\n", + "Resolving cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)... 169.63.118.104, 169.63.118.104\n", + "Connecting to cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)|169.63.118.104|:443... connected.\n", + "HTTP request sent, awaiting response... 200 OK\n", + "Length: 72629 (71K) [text/csv]\n", + "Saving to: ‘FuelConsumption.csv’\n", + "\n", + "FuelConsumption.csv 100%[===================>] 70.93K --.-KB/s in 0.001s \n", + "\n", + "2025-10-20 06:58:57 (51.0 MB/s) - ‘FuelConsumption.csv’ saved [72629/72629]\n", + "\n" + ] + } + ], + "source": [ + "!wget -O FuelConsumption.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In case you're working **locally** uncomment the below line. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "#!curl https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv -o FuelConsumptionCo2.csv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Understanding the Data\n", + "\n", + "### `FuelConsumption.csv`:\n", + "We have downloaded a fuel consumption dataset, **`FuelConsumption.csv`**, which contains model-specific fuel consumption ratings and estimated carbon dioxide emissions for new light-duty vehicles for retail sale in Canada. [Dataset source](http://open.canada.ca/data/en/dataset/98f1a129-f628-4ce4-b24d-6f16bf24dd64)\n", + "\n", + "- **MODELYEAR** e.g. 2014\n", + "- **MAKE** e.g. Acura\n", + "- **MODEL** e.g. ILX\n", + "- **VEHICLE CLASS** e.g. SUV\n", + "- **ENGINE SIZE** e.g. 4.7\n", + "- **CYLINDERS** e.g 6\n", + "- **TRANSMISSION** e.g. A6\n", + "- **FUEL CONSUMPTION in CITY(L/100 km)** e.g. 9.9\n", + "- **FUEL CONSUMPTION in HWY (L/100 km)** e.g. 8.9\n", + "- **FUEL CONSUMPTION COMB (L/100 km)** e.g. 9.2\n", + "- **CO2 EMISSIONS (g/km)** e.g. 182 --> low --> 0\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reading the data in\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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MODELYEARMAKEMODELVEHICLECLASSENGINESIZECYLINDERSTRANSMISSIONFUELTYPEFUELCONSUMPTION_CITYFUELCONSUMPTION_HWYFUELCONSUMPTION_COMBFUELCONSUMPTION_COMB_MPGCO2EMISSIONS
02014ACURAILXCOMPACT2.04AS5Z9.96.78.533196
12014ACURAILXCOMPACT2.44M6Z11.27.79.629221
22014ACURAILX HYBRIDCOMPACT1.54AV7Z6.05.85.948136
32014ACURAMDX 4WDSUV - SMALL3.56AS6Z12.79.111.125255
42014ACURARDX AWDSUV - SMALL3.56AS6Z12.18.710.627244
\n", + "
" + ], + "text/plain": [ + " MODELYEAR MAKE MODEL VEHICLECLASS ENGINESIZE CYLINDERS \\\n", + "0 2014 ACURA ILX COMPACT 2.0 4 \n", + "1 2014 ACURA ILX COMPACT 2.4 4 \n", + "2 2014 ACURA ILX HYBRID COMPACT 1.5 4 \n", + "3 2014 ACURA MDX 4WD SUV - SMALL 3.5 6 \n", + "4 2014 ACURA RDX AWD SUV - SMALL 3.5 6 \n", + "\n", + " TRANSMISSION FUELTYPE FUELCONSUMPTION_CITY FUELCONSUMPTION_HWY \\\n", + "0 AS5 Z 9.9 6.7 \n", + "1 M6 Z 11.2 7.7 \n", + "2 AV7 Z 6.0 5.8 \n", + "3 AS6 Z 12.7 9.1 \n", + "4 AS6 Z 12.1 8.7 \n", + "\n", + " FUELCONSUMPTION_COMB FUELCONSUMPTION_COMB_MPG CO2EMISSIONS \n", + "0 8.5 33 196 \n", + "1 9.6 29 221 \n", + "2 5.9 48 136 \n", + "3 11.1 25 255 \n", + "4 10.6 27 244 " + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_csv(\"FuelConsumption.csv\")\n", + "\n", + "# take a look at the dataset\n", + "df.head()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Data Exploration\n", + "Let's first have a descriptive exploration on our data.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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MODELYEARENGINESIZECYLINDERSFUELCONSUMPTION_CITYFUELCONSUMPTION_HWYFUELCONSUMPTION_COMBFUELCONSUMPTION_COMB_MPGCO2EMISSIONS
count1067.01067.0000001067.0000001067.0000001067.0000001067.0000001067.0000001067.000000
mean2014.03.3462985.79475213.2965329.47460211.58088126.441425256.228679
std0.01.4158951.7974474.1012532.7945103.4855957.46870263.372304
min2014.01.0000003.0000004.6000004.9000004.70000011.000000108.000000
25%2014.02.0000004.00000010.2500007.5000009.00000021.000000207.000000
50%2014.03.4000006.00000012.6000008.80000010.90000026.000000251.000000
75%2014.04.3000008.00000015.55000010.85000013.35000031.000000294.000000
max2014.08.40000012.00000030.20000020.50000025.80000060.000000488.000000
\n", + "
" + ], + "text/plain": [ + " MODELYEAR ENGINESIZE CYLINDERS FUELCONSUMPTION_CITY \\\n", + "count 1067.0 1067.000000 1067.000000 1067.000000 \n", + "mean 2014.0 3.346298 5.794752 13.296532 \n", + "std 0.0 1.415895 1.797447 4.101253 \n", + "min 2014.0 1.000000 3.000000 4.600000 \n", + "25% 2014.0 2.000000 4.000000 10.250000 \n", + "50% 2014.0 3.400000 6.000000 12.600000 \n", + "75% 2014.0 4.300000 8.000000 15.550000 \n", + "max 2014.0 8.400000 12.000000 30.200000 \n", + "\n", + " FUELCONSUMPTION_HWY FUELCONSUMPTION_COMB FUELCONSUMPTION_COMB_MPG \\\n", + "count 1067.000000 1067.000000 1067.000000 \n", + "mean 9.474602 11.580881 26.441425 \n", + "std 2.794510 3.485595 7.468702 \n", + "min 4.900000 4.700000 11.000000 \n", + "25% 7.500000 9.000000 21.000000 \n", + "50% 8.800000 10.900000 26.000000 \n", + "75% 10.850000 13.350000 31.000000 \n", + "max 20.500000 25.800000 60.000000 \n", + "\n", + " CO2EMISSIONS \n", + "count 1067.000000 \n", + "mean 256.228679 \n", + "std 63.372304 \n", + "min 108.000000 \n", + "25% 207.000000 \n", + "50% 251.000000 \n", + "75% 294.000000 \n", + "max 488.000000 " + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# summarize the data\n", + "df.describe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's select some features to explore more.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
ENGINESIZECYLINDERSFUELCONSUMPTION_COMBCO2EMISSIONS
02.048.5196
12.449.6221
21.545.9136
33.5611.1255
43.5610.6244
53.5610.0230
63.5610.1232
73.7611.1255
83.7611.6267
\n", + "
" + ], + "text/plain": [ + " ENGINESIZE CYLINDERS FUELCONSUMPTION_COMB CO2EMISSIONS\n", + "0 2.0 4 8.5 196\n", + "1 2.4 4 9.6 221\n", + "2 1.5 4 5.9 136\n", + "3 3.5 6 11.1 255\n", + "4 3.5 6 10.6 244\n", + "5 3.5 6 10.0 230\n", + "6 3.5 6 10.1 232\n", + "7 3.7 6 11.1 255\n", + "8 3.7 6 11.6 267" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n", + "cdf.head(9)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can plot each of these features:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ZudgmeWirNrW2f7k5f7AmIiIi2WHSQkRERLLApIWIiIhkgUkLERERyYIsL8S1px6Lv4DKWSD1HiBcsw/a+tZfrPjzynE2jIyI5K7H4i+Mlre2z2EfQx0Nz7QQERGRLDBpISIiIllg0kJERESyYFXSkpKSAoVCgYSEBKlMCAGNRoOAgAC4u7sjOjoap06d0nudVqvFvHnz0LVrV3h6emLixIk4f/68NaEQERFRB9fqpKWgoADr169H//799cpTU1ORlpaGjIwMFBQUQK1WIyYmBlVVVVKdhIQEZGVlITMzE3l5ebhy5QrGjx+P+vr61reEiIiIOrRWJS1XrlzB448/jvfeew+dO3eWyoUQWLNmDZYuXYrJkycjPDwcmzdvRnV1NbZt2wYAqKiowIYNG/Dmm29i9OjRGDhwILZu3YoTJ05g//79tmkVERERdTituuV5zpw5GDduHEaPHo1XX31VKi8uLkZpaSliY2OlMpVKhREjRiA/Px+zZs1CUVERdDqdXp2AgACEh4cjPz8fY8aMMdieVquFVquVnldWVgK4PieCTqdrTRNaTeUsoHIS1///339bqz1ib9xGe++n1mK8bcfcWOXQFiK6OVmctGRmZuKbb75BQUGBwbLS0lIAgJ+fn165n58fzpw5I9VxdXXVO0PTWKfx9U2lpKRgxYoVBuXZ2dnw8PCwtAlWSb3nf/9/JbLBqnXt2bPHymjMl5OT027bsgXG23ZairW6urqdIiEisoxFScu5c+cwf/58ZGdnw83NzWS9prM3CiFanNGxuTpLlixBYmKi9LxxauvY2Nh2n4E1XLMPKieBVyIbsKzQCdqG1g8ud1JjeFbJ1nQ6HXJychATEyOLWUcZb9sxN9bGM5lENzI18F1r/fBKbMuViJqwKGkpKipCWVkZIiIipLL6+nocPnwYGRkZOH36NIDrZ1P8/f2lOmVlZdLZF7VajdraWpSXl+udbSkrK8OQIUOMblelUkGlUhmUK5XKdv+iuHE0Sm2DwqoRcdszdnvsK2sw3rbTUqxyaQcR3XwsuhB31KhROHHiBI4dOyY9IiMj8fjjj+PYsWPo2bMn1Gq13unn2tpa5ObmSglJREQElEqlXp2SkhKcPHnSZNJCREREZNGZFi8vL4SHh+uVeXp6okuXLlJ5QkICkpOTERoaitDQUCQnJ8PDwwNTp04FAPj4+GDmzJlYsGABunTpAl9fXyQlJaFfv34YPXq0jZpFREREHY3NJ0xcuHAhampqMHv2bJSXl2Pw4MHIzs6Gl5eXVGf16tVwcXHBlClTUFNTg1GjRmHTpk1wdna2dThERETUQVidtBw6dEjvuUKhgEajgUajMfkaNzc3pKenIz093drNExER0U2Ccw8RERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLNh8GH+yH2NTx6ucBVLvAcI1+yyekfrnleNsFRoREZHVeKaFiIiIZIFJCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLDBpISKHkJKSgkGDBsHLywvdunXDpEmTcPr0ab06QghoNBoEBATA3d0d0dHROHXqlF4drVaLefPmoWvXrvD09MTEiRNx/vz59mwKEbURJi1E5BByc3MxZ84cHDlyBDk5Oairq0NsbCyuXr0q1UlNTUVaWhoyMjJQUFAAtVqNmJgYVFVVSXUSEhKQlZWFzMxM5OXl4cqVKxg/fjzq6+vt0SwisiEOLkdEDmHv3r16zzdu3Ihu3bqhqKgIw4cPhxACa9aswdKlSzF58mQAwObNm+Hn54dt27Zh1qxZqKiowIYNG7BlyxaMHj0aALB161YEBQVh//79GDNmTLu3i4hsh0kLETmkiooKAICvry8AoLi4GKWlpYiNjZXqqFQqjBgxAvn5+Zg1axaKioqg0+n06gQEBCA8PBz5+fkmkxatVgutVis9r6ysBADodDrodDqbt80UlbMwXu4k9P41ly1jNxVbazXG1p77t62xTeavr7WYtBCRwxFCIDExEcOGDUN4eDgAoLS0FADg5+enV9fPzw9nzpyR6ri6uqJz584GdRpfb0xKSgpWrFhhUJ6dnQ0PDw+r2mKJ1HuaX/5KZINF69uzZ48V0ehrKTZL5eTk6P3bkbBNplVXV1v1eiYtRORw5s6di+PHjyMvL89gmUKhP4eWEMKgrKmW6ixZsgSJiYnS88rKSgQFBSE2Nhbe3t4WRt964Zp9RstVTgKvRDZgWaETtA3mzyF2UmO7n8NMxdZaR5eORE5ODmJiYqBUKm26bnvR6XRsUwsaz2K2FpMWInIo8+bNw65du3D48GEEBgZK5Wq1GsD1syn+/v5SeVlZmXT2Ra1Wo7a2FuXl5XpnW8rKyjBkyBCT21SpVFCpVAblSqWyXb98WprUVNugsGjiU1vGbumEqy1pjK2993F7YJuaX481ePcQETkEIQTmzp2LHTt24MCBAwgJCdFbHhISArVarXeaura2Frm5uVJCEhERAaVSqVenpKQEJ0+ebDZpISJ54JkWInIIc+bMwbZt27Bz5054eXlJ16D4+PjA3d0dCoUCCQkJSE5ORmhoKEJDQ5GcnAwPDw9MnTpVqjtz5kwsWLAAXbp0ga+vL5KSktCvXz/pbiIiki+LzrSsW7cO/fv3h7e3N7y9vREVFYUvv/xSWs6Bn4iotdatW4eKigpER0fD399femzfvl2qs3DhQiQkJGD27NmIjIzEhQsXkJ2dDS8vL6nO6tWrMWnSJEyZMgVDhw6Fh4cHdu/eDWdnZ3s0i4hsyKKkJTAwECtXrkRhYSEKCwsxcuRIPPjgg1JiwoGfiKi1hBBGH9OnT5fqKBQKaDQalJSU4Nq1a8jNzZXuLmrk5uaG9PR0XLp0CdXV1di9ezeCgoLauTVE1BYsSlomTJiABx54AL1790bv3r3x2muvoVOnTjhy5IjBwE/h4eHYvHkzqqursW3bNgCQBn568803MXr0aAwcOBBbt27FiRMnsH///jZpIBEREXUMrb6mpb6+Hp988gmuXr2KqKiom2LgJ+D6AEutHeipKVvHbmzwJ2titccASXIbnElO8ZobqxzaQkQ3J4uTlhMnTiAqKgrXrl1Dp06dkJWVhb59+yI/Px9Axx74CdAfYMnSgZ6asuXAT0Dzgz+1JlZbx2cJuQ3OJKd4W4rV2sGfiIjaisVJS58+fXDs2DH8/vvv+PTTTxEfH4/c3FxpeUce+Am4PsBSawd6asqWAz8Bxgd/siZWW8dnDrkNziSneM2N1drBn4iI2orFSYurqytuv/12AEBkZCQKCgrw1ltvYdGiRQA69sBPgP4AS5YO9NSUrWNvLpbWxGrPL2G5Dc4kp3hbilUu7SCim4/Vg8sJIaDVajnwExEREbUpi860vPDCC4iLi0NQUBCqqqqQmZmJQ4cOYe/evRz4iYiIiNqURUnLL7/8gmnTpqGkpAQ+Pj7o378/9u7di5iYGADXB36qqanB7NmzUV5ejsGDBxsd+MnFxQVTpkxBTU0NRo0ahU2bNnHgJyIiImqWRUnLhg0bml3eOPCTRqMxWadx4Kf09HRLNk1EREQ3OU6YSERERLLApIWIiIhkgUkLERERyQKTFiIiIpIFJi1EREQkC0xaiIiISBaYtBAREZEsMGkhIiIiWWDSQkRERLLApIWIiIhkgUkLERERyYJFcw8RtVaPxV+YVU/lLJB6DxCu2QdtvcJkvZ9XjrNVaEREJBM800JERESywDMtREQdlLlnOInkgmdaiIiISBaYtBAREZEsMGkhIiIiWWDSQkRERLLApIWIiIhkgUkLERERyQKTFiIiIpIFJi1EREQkC0xaiIiISBaYtBAREZEsMGkhIiIiWWDSQkRERLJg0YSJKSkp2LFjB/7973/D3d0dQ4YMwapVq9CnTx+pjhACK1aswPr161FeXo7Bgwfj7bffRlhYmFRHq9UiKSkJH330EWpqajBq1CisXbsWgYGBtmsZERHdNGw5OeTPK8fZbF1kWxadacnNzcWcOXNw5MgR5OTkoK6uDrGxsbh69apUJzU1FWlpacjIyEBBQQHUajViYmJQVVUl1UlISEBWVhYyMzORl5eHK1euYPz48aivr7ddy4iIiKhDsehMy969e/Web9y4Ed26dUNRURGGDx8OIQTWrFmDpUuXYvLkyQCAzZs3w8/PD9u2bcOsWbNQUVGBDRs2YMuWLRg9ejQAYOvWrQgKCsL+/fsxZswYg+1qtVpotVrpeWVlJQBAp9NBp9NZ1mIrqZwFVE7i+v//+29r2Tp2lbNhPNbEasv4jMVmtJ6Z8bb3+25KYxyOEk9zzI1VDm0hopuTRUlLUxUVFQAAX19fAEBxcTFKS0sRGxsr1VGpVBgxYgTy8/Mxa9YsFBUVQafT6dUJCAhAeHg48vPzjSYtKSkpWLFihUF5dnY2PDw8rGmCxVLv+d//X4lssGpde/bssTIafTfG1lRrYrVlfM3FZkxL8dp631krJyfH3iGYraVYq6ur2ykSIiLLtDppEUIgMTERw4YNQ3h4OACgtLQUAODn56dX18/PD2fOnJHquLq6onPnzgZ1Gl/f1JIlS5CYmCg9r6ysRFBQEGJjY+Ht7d3aJrRKuGYfVE4Cr0Q2YFmhE7QNilav66TGMEGzRrhmn0GZNbHaMj5jsRljbry23netpdPpkJOTg5iYGCiVSnuH0yxzY208k0lE5GhanbTMnTsXx48fR15ensEyhUL/y0YIYVDWVHN1VCoVVCqVQblSqWz3Lwpt/f9i1DYo9J5bytaxNxdLa2K1ZXyWbruleB0tQbDHZ7G1WopVLu0goptPq255njdvHnbt2oWDBw/q3fGjVqsBwOCMSVlZmXT2Ra1Wo7a2FuXl5SbrEBERETVlUdIihMDcuXOxY8cOHDhwACEhIXrLQ0JCoFar9X4zr62tRW5uLoYMGQIAiIiIgFKp1KtTUlKCkydPSnWIiIiImrLo56E5c+Zg27Zt2LlzJ7y8vKQzKj4+PnB3d4dCoUBCQgKSk5MRGhqK0NBQJCcnw8PDA1OnTpXqzpw5EwsWLECXLl3g6+uLpKQk9OvXT7qbiIhIDmw5NggRtcyipGXdunUAgOjoaL3yjRs3Yvr06QCAhQsXoqamBrNnz5YGl8vOzoaXl5dUf/Xq1XBxccGUKVOkweU2bdoEZ2dn61pDREREHZZFSYsQLY+1oVAooNFooNFoTNZxc3NDeno60tPTLdk8ERER3cQ49xARERHJApMWIiIikgUmLUTkMA4fPowJEyYgICAACoUCn332md5yIQQ0Gg0CAgLg7u6O6OhonDp1Sq+OVqvFvHnz0LVrV3h6emLixIk4f/58O7aCiNoKkxYichhXr17FgAEDkJGRYXQ5J2QlurlZNfcQEZEtxcXFIS4uzuiytpqQlYjkg0kLEclCW03ICrR+JnlzZy+3lq1mlncktp4h3ZbvRWtjktOs7+aydZusXQ+TFiKShbaakBVo/Uzyls5ebi1rZ5Z3JI2jottqhnRbvhfWziIvp1nfzWWrNlk7izyTFiKSFVtPyAq0fiZ5c2cvt5atZpZ3JEeXjrTpDOm2fC9aO4u8nGZ9N5et22TtLPJMWohIFm6ckNXf318qNzUh641nW8rKypqd26y1M8lbM8t7a1g7s7wjadyvtpoh3Zb7xdp45DTru7ls1SZr18G7h4hIFjghKxHxTAsROYwrV67gxx9/lJ4XFxfj2LFj8PX1RXBwMCdkJbrJMWkhIodRWFiI+++/X3reeJ1JfHw8Nm3axAlZiW5yTFqIyGFER0c3OzErJ2QlurnxmhYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLFg8YeLhw4fx+uuvo6ioCCUlJcjKysKkSZOk5UIIrFixAuvXr5dmYX377bcRFhYm1dFqtUhKSsJHH30kzcK6du1aBAYG2qRRRETk2MI1+5B6z/V/tfUKe4dDMmHxmZarV69iwIAByMjIMLo8NTUVaWlpyMjIQEFBAdRqNWJiYlBVVSXVSUhIQFZWFjIzM5GXl4crV65g/PjxqK+vb31LiIiIqEOz+ExLXFwc4uLijC4TQmDNmjVYunQpJk+eDADYvHkz/Pz8sG3bNsyaNQsVFRXYsGEDtmzZgtGjRwMAtm7diqCgIOzfvx9jxoyxojlERETUUVmctDSnuLgYpaWliI2NlcpUKhVGjBiB/Px8zJo1C0VFRdDpdHp1AgICEB4ejvz8fKNJi1arhVarlZ5XVlYCAHQ6HXQ6nS2b0CKVs4DKSVz//3//bS1bx65yNozHmlhtGZ+x2IzWMzPe9n7fTWmMw1HiaY65scqhLUR0c7Jp0lJaWgoA8PPz0yv38/PDmTNnpDqurq7o3LmzQZ3G1zeVkpKCFStWGJRnZ2fDw8PDFqGbLfWe//3/lcgGq9a1Z88eK6PRd2NsTbUmVlvG11xsxrQUr633nbVycnLsHYLZWoq1urq6nSIhIrKMTZOWRgqF/kVVQgiDsqaaq7NkyRIkJiZKzysrKxEUFITY2Fh4e3tbH7AFwjX7oHISeCWyAcsKnaBtaP0FZCc1tv0pLFyzz6DMmlhtGZ+x2IwxN15b77vW0ul0yMnJQUxMDJRKpb3DaZa5sTaeySQicjQ2TVrUajWA62dT/P39pfKysjLp7ItarUZtbS3Ky8v1zraUlZVhyJAhRterUqmgUqkMypVKZbt/Udx4lbu2QWHVVe+2jr25WFoTqy3js3TbLcXraAmCPT6LrdVSrHJpBxHdfGw6TktISAjUarXe6efa2lrk5uZKCUlERASUSqVenZKSEpw8edJk0kJERERk8ZmWK1eu4Mcff5SeFxcX49ixY/D19UVwcDASEhKQnJyM0NBQhIaGIjk5GR4eHpg6dSoAwMfHBzNnzsSCBQvQpUsX+Pr6IikpCf369ZPuJiIiIrKXHou/aNXrVM7C6NgzP68cZ6vQbnoWJy2FhYW4//77peeN15rEx8dj06ZNWLhwIWpqajB79mxpcLns7Gx4eXlJr1m9ejVcXFwwZcoUaXC5TZs2wdnZ2QZNIiIioo7I4qQlOjoaQpi+HVWhUECj0UCj0Zis4+bmhvT0dKSnp1u6eSIiIrpJce4hIiIikoU2ueWZiIiIrmvtNTLG3OzXx/BMCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLLjYOwAial6PxV/YZD0qZ4HUe2yyKiIiu+CZFiIiIpIFJi1EREQkC3b9eWjt2rV4/fXXUVJSgrCwMKxZswb33XefPUNqV7Y67U/WseZ9aPzJJVyzD9p6BQDg55XjbBUaWeFm71+IOiK7nWnZvn07EhISsHTpUhw9ehT33Xcf4uLicPbsWXuFREQdBPsXoo7Jbmda0tLSMHPmTPzxj38EAKxZswb79u3DunXrkJKSoldXq9VCq9VKzysqKgAAly9fhk6na3Y7g1P+ZtO4XQC4NAhUVzfAReeE+gaFTddva9bEeunSJdvFUXfVvHpmxmuP2Iy+1ki8towNsC4+vfX8N9ZLly5BqVSarFdVVQUAEELYZLv2YEn/ArS+j7HVe9MSOfU55mKbWsfW/UtL35EqJ4EXBzbgrqU7oDWjTV8tGdXscqv7F2EHWq1WODs7ix07duiV//nPfxbDhw83qL98+XIBgA8++GjHx7lz59qrS7ApS/sXIdjH8MFHez9a27/Y5UzLb7/9hvr6evj5+emV+/n5obS01KD+kiVLkJiYKD1vaGjA5cuX0aVLFygU7Z+hV1ZWIigoCOfOnYO3t3e7b98ScooVYLxtydxYhRCoqqpCQEBAO0ZnO5b2L4Dj9TFNyelzZi62SR5s3SZr+xe7XojbtDMQQhjtIFQqFVQqlV7ZLbfc0pahmcXb21s2H0w5xQow3rZkTqw+Pj7tFE3bMbd/ARy3j2lKTp8zc7FN8mDLNlnTv9jlQtyuXbvC2dnZ4K+esrIyg7+OiIgswf6FqOOyS9Li6uqKiIgI5OTk6JXn5ORgyJAh9giJiDoI9i9EHZfdfh5KTEzEtGnTEBkZiaioKKxfvx5nz57Fs88+a6+QzKZSqbB8+XKD08mOSE6xAoy3LckpVmvJuX8xpiO+d2yTPDhamxRC2O++xrVr1yI1NRUlJSUIDw/H6tWrMXz4cHuFQ0QdCPsXoo7HrkkLERERkbk49xARERHJApMWIiIikgUmLURERCQLTFqIiIhIFpi0tFJKSgoUCgUSEhLsHYpJFy5cwBNPPIEuXbrAw8MDd911F4qKiuwdllF1dXV48cUXERISAnd3d/Ts2RMvv/wyGhoa7B0aDh8+jAkTJiAgIAAKhQKfffaZ3nIhBDQaDQICAuDu7o7o6GicOnXKPsGi+Xh1Oh0WLVqEfv36wdPTEwEBAXjyySdx8eJFu8VLpqWkpGDQoEHw8vJCt27dMGnSJJw+fdreYdmMHPpRc8mpvzWHo/bJTFpaoaCgAOvXr0f//v3tHYpJ5eXlGDp0KJRKJb788kt8++23ePPNNx1yaHIAWLVqFd555x1kZGTgu+++Q2pqKl5//XWkp6fbOzRcvXoVAwYMQEZGhtHlqampSEtLQ0ZGBgoKCqBWqxETEyPNZtremou3uroa33zzDZYtW4ZvvvkGO3bswPfff4+JEyfaIVJqSW5uLubMmYMjR44gJycHdXV1iI2NxdWr7TO7dFuSQz9qLrn1t+Zw2D65VdMs3sSqqqpEaGioyMnJESNGjBDz58+3d0hGLVq0SAwbNszeYZht3LhxYsaMGXplkydPFk888YSdIjIOgMjKypKeNzQ0CLVaLVauXCmVXbt2Tfj4+Ih33nnHDhHqaxqvMV9//bUAIM6cOdM+QVGrlZWVCQAiNzfX3qFYRS79qLnk1t+aw1H7ZJ5psdCcOXMwbtw4jB492t6hNGvXrl2IjIzEH/7wB3Tr1g0DBw7Ee++9Z++wTBo2bBj+9re/4fvvvwcA/Otf/0JeXh4eeOABO0fWvOLiYpSWliI2NlYqU6lUGDFiBPLz8+0YmfkqKiqgUChk/VfhzaKiogIA4Ovra+dIrCOXftRccutvzeGofbJdZ3mWm8zMTHzzzTcoKCiwdygt+umnn7Bu3TokJibihRdewNdff40///nPUKlUePLJJ+0dnoFFixahoqICd9xxB5ydnVFfX4/XXnsNjz32mL1Da1bjpHxNJ+Lz8/PDmTNn7BGSRa5du4bFixdj6tSpHW5W2o5GCIHExEQMGzYM4eHh9g6n1eTUj5pLbv2tORy1T2bSYqZz585h/vz5yM7Ohpubm73DaVFDQwMiIyORnJwMABg4cCBOnTqFdevWOeRBtH37dmzduhXbtm1DWFgYjh07hoSEBAQEBCA+Pt7e4bVIoVDoPRdCGJQ5Gp1Oh0cffRQNDQ1Yu3atvcOhFsydOxfHjx9HXl6evUNpNbn1o+aSW39rDoftk+3645SMZGVlCQDC2dlZegAQCoVCODs7i7q6OnuHqCc4OFjMnDlTr2zt2rUiICDAThE1LzAwUGRkZOiVvfLKK6JPnz52isg4NLlG5D//+Y8AIL755hu9ehMnThRPPvlkO0dnqGm8jWpra8WkSZNE//79xW+//db+gZFF5s6dKwIDA8VPP/1k71CsIrd+1Fxy62/N4ah9Ms+0mGnUqFE4ceKEXtlTTz2FO+64A4sWLYKzs7OdIjNu6NChBrdGfv/99+jevbudImpedXU1nJz0L7Fydna2++11LQkJCYFarUZOTg4GDhwIAKitrUVubi5WrVpl5+iM0+l0mDJlCn744QccPHgQXbp0sXdIZIIQAvPmzUNWVhYOHTqEkJAQe4dkFbn1o+aSW39rDkftk5m0mMnLy8vgd2RPT0906dLFIX9ffu655zBkyBAkJydjypQp+Prrr7F+/XqsX7/e3qEZNWHCBLz22msIDg5GWFgYjh49irS0NMyYMcPeoeHKlSv48ccfpefFxcU4duwYfH19ERwcjISEBCQnJyM0NBShoaFITk6Gh4cHpk6d6nDxBgQE4OGHH8Y333yDzz//HPX19dJ1Ob6+vnB1dbVLzGTcnDlzsG3bNuzcuRNeXl7Se+Xj4wN3d3c7R2c5ufWj5pJbf2sOh+2T7XqeR+Yc/Va93bt3i/DwcKFSqcQdd9wh1q9fb++QTKqsrBTz588XwcHBws3NTfTs2VMsXbpUaLVae4cmDh48KAAYPOLj44UQ1297Xr58uVCr1UKlUonhw4eLEydOOGS8xcXFRpcBEAcPHrRbzGScqfdq48aN9g7NZhy9HzWXnPpbczhqn6wQQoj2TJKIiIiIWoPjtBAREZEsMGkhIiIiWWDSQkRERLLApIWIiIhkgUkLERERyQKTFiIiIpIFJi12cvz4cTz11FMICQmBm5sbOnXqhLvvvhupqam4fPmyVE+n02HdunWIioqSBpS68847sXjxYly6dElvnfX19UhLS8PYsWMRGBgIDw8Pqe7vv/+uV/fnn3+GQqEw+dBoNFLd6dOnQ6FQwMvLC1euXDFoy5kzZ+Dk5GTwukOHDkGhUOCvf/2rXv2vvvoKDz30EIKDg6FSqeDn54eoqCgsWLBAr55Op8O7776LQYMGwdfXFx4eHujevTsefPBBZGVlGbTljTfeMIjtu+++w/Tp0xEcHAxXV1d07doVDzzwAL788kuDuo3xKhQK/POf/zRYPn36dHTq1KlVMZLj27Rpk8njISkpCcD1Oabmzp1r9PV//etfoVAocOjQIams8dgx9WjU3Ge4Ka1Wi4yMDAwbNgydO3eGq6srbrvtNkyZMgW5ubkG9R3lGDDVHzSaO3euwXxdPXr0gEKhQHR0tNHXfPDBB1K8N+53jUajt59dXV0REhKC+fPnS31hc+/LjY9Dhw7ZtY8xl7nfKYBl3ysAEB0dDYVCgZ49e8LYKCmHDx+W2rVp0yap3NgxdeuttyI6Ohqff/55q9rJEXHt4L333sPs2bPRp08fPP/88+jbty90Oh0KCwvxzjvv4J///CeysrJQXV2NBx54AHl5eXjmmWewbNkyuLu745///CfeeOMNbNu2DTk5OejTpw8AoKamBhqNBo899hj++Mc/omvXrvjmm2/w6quvYvfu3SgsLDQYRXPevHlGR24NDAzUe65UKlFXV4ft27dj5syZess2btwILy8vVFZWttj2L774AhMnTkR0dDRSU1Ph7++PkpISFBYWIjMzE2+++aZUd9q0adixYwcSEhKwYsUKqFQq/PTTT9i7dy/27duHhx56qNlt7dixA1OnTkXPnj2xbNky9OnTB7/88gs2btyIBx54AM8//zxSU1ONvnbhwoX4+9//3mJ7rI2RHM/GjRtxxx136JUFBAS0en3u7u44cOCAtWEBAH777TeMHTsWx48fx4wZM/D888/D19cXFy5cwM6dOzFq1CgUFRVhwIABADrGMeDl5YXDhw/jP//5D3r16qW37P3334e3t7fJvmfv3r3w8fFBVVUV9uzZg7feegtff/018vPzDZKGV155BQcPHjR4r/r27Wvwpd+oPfavOcz9TgFg8fdKIy8vLxQXF+PAgQMYNWqU3rKW3ofGY0oIgdLSUmRkZGDChAnYtWsXJkyYYFlj7Tq03U0oPz9fODs7i7Fjx4pr164ZLNdqtWLnzp1CCCGeeeYZAUBkZmYa1Dt9+rTw8fERYWFh0iRjdXV1Rie/++STTwQAsWXLFqmscWTU119/vcWY4+Pjhaenp3j00UfFkCFD9JY1NDSI7t27i6effloAEMuXL5eWNY7M+sknn0hlw4cPF7169RI6nc5gO/X19dL/f/rpJwFAvPTSS0ZjurGusbb8+OOPwsPDQ0RGRoorV64YvP7ZZ58VAMRHH31kEO/YsWMFALFr1y6j+6E1MZLj27hxowAgCgoKTNYBIObMmWN0WeNxduPIwk0/M6aYezzGxcUJFxcX8be//c3o8q+//lqcOXNGCOF4x4Cx/uBGc+bMEU2/krp37y7i4uJEYGCgeOGFF/SW/fjjj0KhUEh9z437ffny5QKA+PXXX/VeM23aNAFA5OXlGWy/uffKXn2MOSz5ThHC8u8VIa6PWhwWFibuvfdeMXXqVL3XVFZWCg8PD+l9uHG0ZlPHVHV1tVCpVOKxxx6zqK1CCMGfh9pZcnIyFAoF1q9fD5VKZbDc1dUVEydORGlpKd5//32MGTMGjzzyiEG93r17Y9GiRTh16hQ+++wzANcnszI2+d0999wD4Pq08NaYMWMG8vPz9SYG279/P86cOYOnnnrKrHVcunQJXbt2hYuL4Um+GyfnajxF6e/vb3Q9TSfyamr16tWorq5Geno6PD09DZa/+eabuOWWW/Daa68ZLJs+fTr69u2LJUuWoL6+vtm2WBMjkSWKiorw5ZdfYubMmRg5cqTROoMGDUJwcDCAjnMMODk54cknn8TmzZv1Jut7//33ERQUhNGjR5u9rnvvvRfA9Z+0rdUe+9cc5n6nAGjV98qNZsyYgR07duhdbpCZmQkAePTRR82O2c3NDa6urlAqlWa/phF71XZUX1+PAwcOICIiAkFBQc3WPXjwIOrq6jBp0iSTdRqX5eTkNLuuxtOdYWFhBssaGhpQV1dn8DBm9OjR6N69O95//32pbMOGDRg+fDhCQ0ObjaFRVFQUvvrqK/z5z3/GV199BZ1OZ7TenXfeiVtuuQUrVqzA+vXr8fPPP5u1/kY5OTnw8/OTOqmmPDw8EBsbi5MnT0qT0DVydnZGSkoKTp06hc2bN5vchrUxkmOqr68363iwhLFjzNLZcrOzswGg2T7hRh3pGJgxYwYuXryIffv2Abj+Hm3evBnTp0+3KDFqnEj01ltvtTqm9ti/LbHkOwWw/nvl0UcfhbOzMz766COpbMOGDXj44Yfh7e3dbJx1dXXQ6XQ4f/48EhIScPXq1VZNKsukpR399ttvqK6uNmt6+bNnzwJAs3UblzXWNebChQtYvHgxIiMjMX78eIPlixYtglKpNHjk5eUZ1FUoFJg+fTo++OAD1NXV4fLly/jss88smvVz5cqVGDZsGNLT03HvvffC09MTQ4cOxcqVK/Uu8vX09MSHH36Iuro6zJo1CyEhIejatSumTJmC3bt3t7ids2fPtrifm9t/EydOxLBhw7B8+XJcu3bN6OutjZEc07333mtwPFiTuFy9etXoMRYbG2vReszpE5rW7yjHQK9evTB8+HDpD6Z9+/bh4sWLLZ7hbfyy/P333/Hhhx/inXfeQVBQEO677z6rY2qP/dsSS75Tboyjtd8rXl5eePjhh6X34dtvv8VXX33V4ndA4zHl6uqKoKAgvPvuu8jIyMCYMWPMivtGTFo6gKZX3De6fPkyHnjgAQghsH37dqN/kcyfPx8FBQUGj7vuusvoOp966in88ssv+PLLL/Hhhx/C1dUVf/jDH8yOtUuXLvj73/+OgoICrFy5Eg8++CC+//57LFmyBP369cNvv/0m1X3ggQdw9uxZZGVlISkpCWFhYfjss88wceJEk3dwWEL89yp4U/tv1apVOH/+PN566y2T62jrGKn9ffDBBwbHg7GfM83l7u5u9Bhbu3atDaNuHTkdAzNmzMCuXbtw6dIlbNiwAffffz969OjR7GvUajWUSiU6d+6MJ554AnfffTf27t0LNzc3m8XVHFvsX3sxFfOMGTNQWFiIEydOYMOGDVJC2Zwbj6kvv/wS8fHxmDNnDjIyMiyOi3cPtaOuXbvCw8MDxcXFLdZt/F26ubqNy4ydFiwvL0dMTAwuXLiAAwcOoGfPnkbXERgYiMjISHPCBwB0794do0aNwvvvv4+ff/4Zjz76KDw8PFBdXW32OgAgMjJS2q5Op8OiRYuwevVqpKam6l1t7+7ujkmTJkmnLM+ePYu4uDi8/fbb+NOf/mT0Jy/g+v5raT83nso2dVp1yJAhmDRpElauXIlnnnnG5HpaGyM5pjvvvNPkMeHs7GzyGoTGszFNf6d3cnKy6Bgz5cY+oemdHabqO9Ix0Jj4Nbf/mksOH374YcybNw+rV6/G7t279W6tNWX//v3w8fGBUqlEYGCg0Wv+Wqs9968plnynANZ/rwCQLgd499138fHHHyMhIcFkgtOo6TE1duxYnDlzBgsXLsQTTzyBW265xaz4AZ5paVfOzs7SLYnnz59vtu79998PFxcXoxdDNWpcFhMTo1deXl6O0aNHo7i4GDk5Oejfv7+1oetp/Ivn2LFjFv00ZIpSqcTy5csBACdPnmy2bnBwsHRwnzp1ymS9mJgY/PLLLzhy5IjR5dXV1cjJyUF4eDjUarXJ9aSkpKCqqgrJycktNcPiGEl+/Pz8cOHCBaPLGsv9/PzaZNuNp9Kb6xNu5GjHQON+aW7/NbfvPDw88OijjyIlJQWenp6YPHlyi3EMGDAAkZGRGDBggE0TFsC++7eRJd8pgHXfKzd66qmnsG7dOly+fBnx8fGWhg0A6N+/P2pqavD9999b9DomLe1syZIlEELg6aefRm1trcFynU6H3bt3Q61WY8aMGdi3bx+2b99uUO/777/HqlWrEBYWpndRVWPC8tNPPyE7OxsDBw60eRseeughPPTQQ5gxY4bJi9BMKSkpMVr+3XffAfjfeBhVVVVGB7IzVteY5557Du7u7pg3bx6uXr1qsDwpKQnl5eV48cUXm433jjvuwIwZM5Cenm7wG6+1MZL8jB49GgcPHsSvv/6qVy6EwCeffIIePXrg9ttvb5Nt33333YiLi8OGDRtMjvtSWFgofU4d7RgIDQ1F9+7d8cknnxgMUPbrr7/i4MGDLd4J9Kc//QkTJkzASy+91G4/8ZjSHvvXHOZ+pwBo9fdKU/Hx8ZgwYQKef/553HbbbRbHDADHjh0DYPlF0fx5qJ1FRUVh3bp1mD17NiIiIqRTpzqdDkePHsX69esRHh6OCRMmIC0tDadPn8YTTzyBw4cPY8KECVCpVDhy5AjeeOMNeHl54dNPP4WzszOA64PLjRkzBkePHsWaNWtQV1en91fArbfeajA409mzZ43+pWCsbiM3NzeTo1q2ZMyYMQgMDMSECRNwxx13oKGhAceOHcObb76JTp06Yf78+QCA06dPY8yYMXj00UcxYsQI+Pv7o7y8HF988QXWr1+P6OhoDBkyxOR2evXqhS1btuDxxx/HoEGDkJiYKA389P777+PLL79EUlKS0dv+mtJoNPjwww9x8OBBvVsbrY2R5Oell17C7t27MXjwYCxevBihoaEoLS3Fe++9h4KCAnz88ccGr2loaDD51/jAgQP1blM9ceKE0WNr0KBB6N69Oz744AOMHTsWcXFxmDFjBuLi4tC5c2eUlJRg9+7d+Oijj1BUVITg4GCHPAbeeOMNTJkyBaNGjcLTTz8NtVqNH374AStXroSrqyuWLVvWbBx33XWX2Wea2lp77F9zWPKdAsDi7xVjAgICLHofTp48Kf18eunSJezYsQM5OTl46KGHzL6IWGLxyC5kE8eOHRPx8fEiODhYuLq6Ck9PTzFw4EDx0ksvibKyMqlebW2tePvtt8XgwYNFp06dhEqlEn369BELFy40GEiucQAkU4/4+Hiz6z7++ONSXXMGPPr111/NGlxu+/btYurUqSI0NFR06tRJKJVKERwcLKZNmya+/fZbqV55ebl49dVXxciRI8Vtt90m7aO77rpLvPrqq6K6utqgLcYG5jp16pSIj48XgYGBQqlUCl9fXzF27FjxxRdfGNRtbvCrF154QQDQ2w+WxEiOz5zB5YQQ4ocffhBPPPGE8Pf3Fy4uLuKWW24RsbGxRgd8i4+Pb/Y4++GHH4QQLR+PNw7YVVNTI/7yl7+IqKgo4e3tLVxcXERAQICYPHmy0c+1ox0D+/fvF7GxseKWW24RLi4uwt/fXzzxxBPSvrhR9+7dxbhx44y/Ef9lbFA/U4PLNcfSweUateX+tYS53ylCWPa9IsT/BpdrTkFBgcnB5W58+Pj4iLvuukukpaUZHQyvJQohjEwkQERERORgeE0LERERyQKvaSEiInIwDQ0NLY6abM34QXLFMy1EREQO5uWXXzY6kvKNj5tx6hBe00JERORgLl68iIsXLzZbp3///nB1dW2niBwDkxYiIiKSBf48RERERLIgy6t4GhoacPHiRXh5ebU45wERWUYIgaqqKgQEBBidZPNmwD6GqG1Y27/IMmm5ePGiycmciMg2zp07h8DAQHuHYRfsY4jaVmv7F1kmLV5eXgCuN9rb21sq1+l0yM7ORmxsrMFMq3LUkdrTkdoCdKz2NG1LZWUlgoKCpOPsZmSqjzFFzp8HucYu17gB+cZui7it7V9kmbQ0nq719vY2SFo8PDzg7e0tqw+CKR2pPR2pLUDHao+ptrT3zyLr1q3DunXrpNs4w8LC8NJLLyEuLg7A9dPKK1aswPr161FeXo7Bgwfj7bffRlhYmLQOrVaLpKQkfPTRR6ipqcGoUaOwdu1ai/+iM9XHmCLnz4NcY5dr3IB8Y7dl3K3tX27OH6yJyOEEBgZi5cqVKCwsRGFhIUaOHIkHH3wQp06dAgCkpqYiLS0NGRkZKCgogFqtRkxMDKqqqqR1JCQkICsrC5mZmcjLy8OVK1cwfvx41NfX26tZRGRDTFqIyCFMmDABDzzwAHr37o3evXvjtddeQ6dOnXDkyBEIIbBmzRosXboUkydPRnh4ODZv3ozq6mps27YNAFBRUYENGzbgzTffxOjRozFw4EBs3boVJ06cwP79++3cOiKyBVn+PEREHVt9fT0++eQTXL16FVFRUSguLkZpaSliY2OlOiqVCiNGjEB+fj5mzZqFoqIi6HQ6vToBAQEIDw9Hfn4+xowZY3J7Wq0WWq1Wel5ZWQng+ulwnU7XYryNdcyp62jkGrtc4wbkG7st4ra2zUxaiMhhnDhxAlFRUbh27Ro6deqErKws9O3bF/n5+QAAPz8/vfp+fn44c+YMAKC0tBSurq7o3LmzQZ3S0tJmt5uSkoIVK1YYlGdnZ8PDw8Ps+HNycsyu62jkGrtc4wbkG7s1cVdXV1u1bSYtHUiPxV/YdH0/rxxn0/URtaRPnz44duwYfv/9d3z66aeIj49Hbm6utLzpxXtCiBYv6DOnzpIlS5CYmCg9b7zDITY21uwLcXNychATE+NQF1aGa/a1WEflJPBKZAOWFTpB22B6P53UmD5TZQ+Ous/NIdfYbRF341nM1mLSQkQOw9XVFbfffjsAIDIyEgUFBXjrrbewaNEiANfPpvj7+0v1y8rKpLMvarUatbW1KC8v1zvbUlZWhiFDhjS7XZVKBZVKZVDeODGduSyt39a09ebfoaFtUDRb35HadSNH2+eWkGvs1sRtbXt5IS4ROSwhBLRaLUJCQqBWq/VOS9fW1iI3N1dKSCIiIqBUKvXqlJSU4OTJky0mLUQkDzzTQkQO4YUXXkBcXByCgoJQVVWFzMxMHDp0CHv37oVCoUBCQgKSk5MRGhqK0NBQJCcnw8PDA1OnTgUA+Pj4YObMmViwYAG6dOkCX19fJCUloV+/fhg9erSdW0dEtsCkhYgcwi+//IJp06ahpKQEPj4+6N+/P/bu3YuYmBgAwMKFC1FTU4PZs2dLg8tlZ2frjay5evVquLi4YMqUKdLgcps2bYKzs7O9mkVENsSkhYgcwoYNG5pdrlAooNFooNFoTNZxc3NDeno60tPTbRwdETkCXtNCREREssCkhYiIiGSBPw/ZUUvjqqicBVLvuT7WgiW3LhIREXVEPNNCREREssAzLWSSLUfY/eGV2JYrERERNYNnWoiIiEgWmLQQERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxEREckCkxYiIiKSBYuSlpSUFAwaNAheXl7o1q0bJk2ahNOnT+vVEUJAo9EgICAA7u7uiI6OxqlTp/TqaLVazJs3D127doWnpycmTpyI8+fPW98aIiIi6rAsSlpyc3MxZ84cHDlyBDk5Oairq0NsbCyuXr0q1UlNTUVaWhoyMjJQUFAAtVqNmJgYVFVVSXUSEhKQlZWFzMxM5OXl4cqVKxg/fjzq6+tt1zIiIiLqUFwsqbx371695xs3bkS3bt1QVFSE4cOHQwiBNWvWYOnSpZg8eTIAYPPmzfDz88O2bdswa9YsVFRUYMOGDdiyZQtGjx4NANi6dSuCgoKwf/9+jBkzxmC7Wq0WWq1Wel5ZWQkA0Ol00Ol0Unnj/28sc2QqZ9H8cieh96+cye29aUlHak/TtnSENhFRx2RR0tJURUUFAMDX1xcAUFxcjNLSUsTGxkp1VCoVRowYgfz8fMyaNQtFRUXQ6XR6dQICAhAeHo78/HyjSUtKSgpWrFhhUJ6dnQ0PDw+D8pycHGua1W5S7zGv3iuRDW0bSDtofE/k8t6YqyO1p7Et1dXVdo6EiMi4VictQggkJiZi2LBhCA8PBwCUlpYCAPz8/PTq+vn54cyZM1IdV1dXdO7c2aBO4+ubWrJkCRITE6XnlZWVCAoKQmxsLLy9vaVynU6HnJwcxMTEQKlUtrZp7SZcs6/Z5SongVciG7Cs0AnaBkU7RdU2ji4dKav3piVy+6w1p2lbGs9kEhE5mlYnLXPnzsXx48eRl5dnsEyh0P+CFUIYlDXVXB2VSgWVSmVQrlQqjX5hmCp3NNp68xIRbYPC7LqOqvH9kMt7Y66O1J7GtnSU9hBRx9OqpGXevHnYtWsXDh8+jMDAQKlcrVYDuH42xd/fXyovKyuTzr6o1WrU1taivLxc72xLWVkZhgwZ0qpGEBFR2+qx+Aubru/nleNsuj66OVh095AQAnPnzsWOHTtw4MABhISE6C0PCQmBWq3W+52/trYWubm5UkISEREBpVKpV6ekpAQnT55k0kJEREQmWXSmZc6cOdi2bRt27twJLy8v6RoUHx8fuLu7Q6FQICEhAcnJyQgNDUVoaCiSk5Ph4eGBqVOnSnVnzpyJBQsWoEuXLvD19UVSUhL69esn3U1ERERE1JRFScu6desAANHR0XrlGzduxPTp0wEACxcuRE1NDWbPno3y8nIMHjwY2dnZ8PLykuqvXr0aLi4umDJlCmpqajBq1Chs2rQJzs7O1rWGiIiIOiyLkhYhWh4vRKFQQKPRQKPRmKzj5uaG9PR0pKenW7J5IiIiuolZNU4LERHZjq0vdiXqaDhhIhEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxE5hJSUFAwaNAheXl7o1q0bJk2ahNOnT+vVEUJAo9EgICAA7u7uiI6OxqlTp/TqaLVazJs3D127doWnpycmTpyI8+fPt2dTiKiNMGkhIoeQm5uLOXPm4MiRI8jJyUFdXR1iY2Nx9epVqU5qairS0tKQkZGBgoICqNVqxMTEoKqqSqqTkJCArKwsZGZmIi8vD1euXMH48eNRX19vj2YRkQ1xGH8icgh79+7Ve75x40Z069YNRUVFGD58OIQQWLNmDZYuXYrJkycDADZv3gw/Pz9s27YNs2bNQkVFBTZs2IAtW7ZIs8Zv3boVQUFB2L9/P8aMGdPu7SIi22HSQkQOqaKiAgDg6+sLACguLkZpaSliY2OlOiqVCiNGjEB+fj5mzZqFoqIi6HQ6vToBAQEIDw9Hfn6+yaRFq9VCq9VKzysrKwEAOp0OOp2uxVgb65hTtzkq55YnpbU1lZPQ+7e9WLuvbLXP7UGusdsibmvbzKSFiByOEAKJiYkYNmwYwsPDAQClpaUAAD8/P726fn5+OHPmjFTH1dUVnTt3NqjT+HpjUlJSsGLFCoPy7OxseHh4mB13Tk6O2XWNSb3Hqpdb5ZXIhnbd3p49e2yyHmv3uT3JNXZr4q6urrZq20xaiMjhzJ07F8ePH0deXp7BMoVCofdcCGFQ1lRLdZYsWYLExETpeWVlJYKCghAbGwtvb+8W49XpdMjJyUFMTAyUSmWL9U0J1+xr9WtbS+Uk8EpkA5YVOkHb0Px+tKWTGut+qrPVPrcHucZui7gbz2K2FpMWInIo8+bNw65du3D48GEEBgZK5Wq1GsD1syn+/v5SeVlZmXT2Ra1Wo7a2FuXl5XpnW8rKyjBkyBCT21SpVFCpVAblSqXSos7Z0vpNaevbL2kw2HaDol23b6sva2v3uT3JNXZr4ra2vbx7iIgcghACc+fOxY4dO3DgwAGEhIToLQ8JCYFardY7NV1bW4vc3FwpIYmIiIBSqdSrU1JSgpMnTzabtBCRPPBMCxE5hDlz5mDbtm3YuXMnvLy8pGtQfHx84O7uDoVCgYSEBCQnJyM0NBShoaFITk6Gh4cHpk6dKtWdOXMmFixYgC5dusDX1xdJSUno16+fdDcREckXkxYicgjr1q0DAERHR+uVb9y4EdOnTwcALFy4EDU1NZg9ezbKy8sxePBgZGdnw8vLS6q/evVquLi4YMqUKaipqcGoUaOwadMmODs7t1dTiKiNMGkhIocgRMu33CoUCmg0Gmg0GpN13NzckJ6ejvT0dBtGR0SOgNe0EBERkSwwaSEiIiJZYNJCREREssCkhYiIiGSBSQsRERHJApMWIiIikgUmLURERCQLTFqIiIhIFpi0EBERkSwwaSEiIiJZYNJCREREssCkhYiIiGSBSQsRERHJApMWIiIikgUmLURERCQLTFqIiIhIFpi0EBERkSwwaSEiIiJZYNJCREREssCkhYiIiGSBSQsRERHJApMWIiIikgUmLURERCQLTFqIiIhIFpi0EBERkSwwaSEiIiJZYNJCREREssCkhYiIiGSBSQsRERHJApMWIiIikgWLk5bDhw9jwoQJCAgIgEKhwGeffaa3XAgBjUaDgIAAuLu7Izo6GqdOndKro9VqMW/ePHTt2hWenp6YOHEizp8/b1VDiIiIqGOzOGm5evUqBgwYgIyMDKPLU1NTkZaWhoyMDBQUFECtViMmJgZVVVVSnYSEBGRlZSEzMxN5eXm4cuUKxo8fj/r6+ta3hIiIiDo0F0tfEBcXh7i4OKPLhBBYs2YNli5dismTJwMANm/eDD8/P2zbtg2zZs1CRUUFNmzYgC1btmD06NEAgK1btyIoKAj79+/HmDFjrGgOERERdVQWJy3NKS4uRmlpKWJjY6UylUqFESNGID8/H7NmzUJRURF0Op1enYCAAISHhyM/P99o0qLVaqHVaqXnlZWVAACdTgedTieVN/7/xjJHpnIWzS93Enr/ypnc3puWdKT2NG1LR2gTEXVMNk1aSktLAQB+fn565X5+fjhz5oxUx9XVFZ07dzao0/j6plJSUrBixQqD8uzsbHh4eBiU5+TktCr+9pZ6j3n1XolsaNtA2kHjeyKX98ZcHak9jW2prq62cyRERMbZNGlppFAo9J4LIQzKmmquzpIlS5CYmCg9r6ysRFBQEGJjY+Ht7S2V63Q65OTkICYmBkql0ooWtI9wzb5ml6ucBF6JbMCyQidoG5rff47u6NKRsnpvWiK3z1pzmral8UwmEZGjsWnSolarAVw/m+Lv7y+Vl5WVSWdf1Go1amtrUV5erne2paysDEOGDDG6XpVKBZVKZVCuVCqNfmGYKnc02nrzEhFtg8Lsuo6q8f2Qy3tjro7Unsa2dJT2EFHHY9OkJSQkBGq1Gjk5ORg4cCAAoLa2Frm5uVi1ahUAICIiAkqlEjk5OZgyZQoAoKSkBCdPnkRqaqotw2kTPRZ/Ye8QZClcsw+p91z/1xYJ2M8rx9kgKiKyF2v7UpWz0OtT2CfcHCxOWq5cuYIff/xRel5cXIxjx47B19cXwcHBSEhIQHJyMkJDQxEaGork5GR4eHhg6tSpAAAfHx/MnDkTCxYsQJcuXeDr64ukpCT069dPupuIiIiIqCmLk5bCwkLcf//90vPGa03i4+OxadMmLFy4EDU1NZg9ezbKy8sxePBgZGdnw8vLS3rN6tWr4eLigilTpqCmpgajRo3Cpk2b4OzsbIMmERERUUdkcdISHR0NIUzfgqtQKKDRaKDRaEzWcXNzQ3p6OtLT0y3dPBEREd2kOPcQETkMThNCRM1h0kJEDoPThBBRc9pknBYiotbgNCFE1BwmLSRLtrz1nLdKykNbTRMCmD9ViCm2mgKhpak92oJcpwtpGrecpp+Q65QZtojb2jYzaSEiWWiraUIAy6cKMcXaaR3MndqjLch1upDGuPfs2WPnSCwn12lArInb2mlCmLQQkazYepoQwPypQkyx1bQOLU3t0RbkOl1I07hPauTz059cpwGxRdzWThPCpIWIZKGtpgkBLJ8qxBRrp0Gw53Qdcp0upDFuOX35N5LrtBnWxG1te5m0EJEs3AzThFDr8Tq3mwOTFiJyGJwmhIiaw6SFiBwGpwkhouYwaSEih8FpQoioORwRl4iIiGSBSQsRERHJApMWIiIikgUmLURERCQLTFqIiIhIFpi0EBERkSwwaSEiIiJZYNJCREREssCkhYiIiGSBSQsRERHJApMWIiIikgUmLURERCQLTFqIiIhIFpi0EBERkSwwaSEiIiJZYNJCREREssCkhYiIiGSBSQsRERHJgou9AyCytx6Lv7D4NSpngdR7gHDNPmjrFXrLfl45zlahERHRDXimhYiIiGSBSQsRERHJApMWIiIikgUmLURERCQLTFqIiIhIFpi0EBERkSzwlmciIqIbtGYYhOZwGATb4ZkWIiIikgUmLURERCQLTFqIiIhIFpi0EBERkSzwQlwiolZqvGCzubmoiMh2eKaFiIiIZIFJCxEREclCh/95yNb32xMREZF98EwLERERyUKHP9NC1N44miYR3ahpn2DNhds3e3/AMy1EREQkC0xaiIiISBaYtBAREZEs8JoWIiIimbjZr5mz65mWtWvXIiQkBG5uboiIiMDf//53e4ZDRB0I+xeijsduScv27duRkJCApUuX4ujRo7jvvvsQFxeHs2fP2iskIuog2L8QdUx2+3koLS0NM2fOxB//+EcAwJo1a7Bv3z6sW7cOKSkp9gqLiDoA9i9E5rHk5yZzbtVu65+b7JK01NbWoqioCIsXL9Yrj42NRX5+vkF9rVYLrVYrPa+oqAAAXL58GTqdTirX6XSorq7GpUuXoFQqAQAudVfbogntwqVBoLq6AS46J9Q3yHsSto7UFqB923Pp0qU2XX/T46aqqgoAIIRo0+22FUv7F8D8Pqapxv5Fzp9vucYu17gB+cZuTtwt9VdW9y/CDi5cuCAAiH/84x965a+99pro3bu3Qf3ly5cLAHzwwUc7Ps6dO9deXYJNWdq/CME+hg8+2vvR2v7FrncPKRT6mZoQwqAMAJYsWYLExETpeUNDAy5fvowuXbro1a+srERQUBDOnTsHb2/vtgu8nXSk9nSktgAdqz1N2yKEQFVVFQICAuwdmlXM7V8A8/sYU+T8eZBr7HKNG5Bv7LaI29r+xS5JS9euXeHs7IzS0lK98rKyMvj5+RnUV6lUUKlUemW33HKLyfV7e3vL6oPQko7Uno7UFqBjtefGtvj4+Ng5mtaztH8BLO9jTJHz50Guscs1bkC+sVsbtzX9i13uHnJ1dUVERARycnL0ynNycjBkyBB7hEREHQT7F6KOy24/DyUmJmLatGmIjIxEVFQU1q9fj7Nnz+LZZ5+1V0hE1EGwfyHqmOyWtDzyyCO4dOkSXn75ZZSUlCA8PBx79uxB9+7dW71OlUqF5cuXG5zmlauO1J6O1BagY7WnI7WlUVv0L82R8z6Ua+xyjRuQb+yOELdCCJne10hEREQ3FU6YSERERLLApIWIiIhkgUkLERERyQKTFiIiIpIFJi1EREQkCw6ftBw+fBgTJkxAQEAAFAoFPvvsM73lQghoNBoEBATA3d0d0dHROHXqlF4drVaLefPmoWvXrvD09MTEiRNx/vz5dmzFdSkpKRg0aBC8vLzQrVs3TJo0CadPn9arI6f2rFu3Dv3795dGR4yKisKXX34pLZdTW5pKSUmBQqFAQkKCVCan9mg0GigUCr2HWq2WlsupLY6spf3sKGzRj9pLS7FPnz7d4D2499577RPsDWzV37c3c+K25z53+KTl6tWrGDBgADIyMowuT01NRVpaGjIyMlBQUAC1Wo2YmBhpJkkASEhIQFZWFjIzM5GXl4crV65g/PjxqK+vb69mAAByc3MxZ84cHDlyBDk5Oairq0NsbCyuXv3fTNRyak9gYCBWrlyJwsJCFBYWYuTIkXjwwQelg05ObblRQUEB1q9fj/79++uVy609YWFhKCkpkR4nTpyQbVscWXP72VHYoh+1l5ZiB4CxY8fqvQd79uxpxwiNs1V/74hxA3bc562aZtFOAIisrCzpeUNDg1Cr1WLlypVS2bVr14SPj4945513hBBC/P7770KpVIrMzEypzoULF4STk5PYu3dvu8VuTFlZmQAgcnNzhRDyb48QQnTu3Fn83//9n2zbUlVVJUJDQ0VOTo4YMWKEmD9/vhBCfu/N8uXLxYABA4wuk1tbHFlz+9lRtaYfdRRNYxdCiPj4ePHggw/aJR5LtKa/dwRN4xbCvvvc4c+0NKe4uBilpaWIjY2VylQqFUaMGIH8/HwAQFFREXQ6nV6dgIAAhIeHS3XspaKiAgDg6+sLQN7tqa+vR2ZmJq5evYqoqCjZtmXOnDkYN24cRo8erVcux/b88MMPCAgIQEhICB599FH89NNPAOTZFkdmaj/LhTmfB0d36NAhdOvWDb1798bTTz+NsrIye4dkoDX9vSNoGncje+1zWSctjbO4Np251c/PT1pWWloKV1dXdO7c2WQdexBCIDExEcOGDUN4eDgAebbnxIkT6NSpE1QqFZ599llkZWWhb9++smxLZmYmvvnmG6SkpBgsk1t7Bg8ejA8++AD79u3De++9h9LSUgwZMgSXLl2SXVscWXP7WS7M+Tw4sri4OHz44Yc4cOAA3nzzTRQUFGDkyJHQarX2Dk3S2v7e3ozFDdh3n9tt7iFbUigUes+FEAZlTZlTpy3NnTsXx48fR15ensEyObWnT58+OHbsGH7//Xd8+umniI+PR25urrRcLm05d+4c5s+fj+zsbLi5uZmsJ5f2xMXFSf/v168foqKi0KtXL2zevFm6YE4ubXFkze3nxMREO0ZmudZ8HhzBI488Iv0/PDwckZGR6N69O7744gtMnjzZjpH9j637+/ZiKm577nNZn2lpvEq/aVZaVlYmZa9qtRq1tbUoLy83Wae9zZs3D7t27cLBgwcRGBgolcuxPa6urrj99tsRGRmJlJQUDBgwAG+99Zbs2lJUVISysjJERETAxcUFLi4uyM3NxV/+8he4uLhI8cilPU15enqiX79++OGHH2T33sjJjftZLsz5PMiJv78/unfv7jDvgTX9vT2ZituY9tznsk5aQkJCoFarkZOTI5XV1tYiNzcXQ4YMAQBERERAqVTq1SkpKcHJkyelOu1FCIG5c+dix44dOHDgAEJCQvSWy609xgghoNVqZdeWUaNG4cSJEzh27Jj0iIyMxOOPP45jx46hZ8+esmpPU1qtFt999x38/f1l997IyY37WS7M+TzIyaVLl3Du3Dm7vwe26O/toaW4jWnXfd7OF/5arKqqShw9elQcPXpUABBpaWni6NGj4syZM0IIIVauXCl8fHzEjh07xIkTJ8Rjjz0m/P39RWVlpbSOZ599VgQGBor9+/eLb775RowcOVIMGDBA1NXVtWtb/vSnPwkfHx9x6NAhUVJSIj2qq6ulOnJqz5IlS8Thw4dFcXGxOH78uHjhhReEk5OTyM7Oll1bjLnx7iEh5NWeBQsWiEOHDomffvpJHDlyRIwfP154eXmJn3/+WXZtcWQt7WdHYYt+1F6ai72qqkosWLBA5Ofni+LiYnHw4EERFRUlbrvtNrvHbqv+3tHitvc+d/ik5eDBgwKAwSM+Pl4Icf22seXLlwu1Wi1UKpUYPny4OHHihN46ampqxNy5c4Wvr69wd3cX48ePF2fPnm33thhrBwCxceNGqY6c2jNjxgzRvXt34erqKm699VYxatQoKWERQl5tMaZp0iKn9jzyyCPC399fKJVKERAQICZPnixOnTolLZdTWxxZS/vZUdiiH7WX5mKvrq4WsbGx4tZbbxVKpVIEBweL+Ph4h/ic2qq/b28txW3vfa74b5BEREREDk3W17QQERHRzYNJCxEREckCkxYiIiKSBSYtREREJAtMWoiIiEgWmLQQERGRLDBpISIiIllg0kJERESywKSFiIiIZIFJCxEREckCkxYiIiKShf8Pi9LtKJYTVtUAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "viz = cdf[['CYLINDERS','ENGINESIZE','CO2EMISSIONS','FUELCONSUMPTION_COMB']]\n", + "viz.hist()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, let's plot each of these features against the Emission, to see how linear their relationship is:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(cdf.FUELCONSUMPTION_COMB, cdf.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"FUELCONSUMPTION_COMB\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Practice\n", + "Plot __CYLINDER__ vs the Emission, to see how linear is their relationship is:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(cdf.CYLINDERS, cdf.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Cylinders\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "plt.scatter(cdf.CYLINDERS, cdf.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Cylinders\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Creating train and test dataset\n", + "Train/Test Split involves splitting the dataset into training and testing sets that are mutually exclusive. After which, you train with the training set and test with the testing set. \n", + "This will provide a more accurate evaluation on out-of-sample accuracy because the testing dataset is not part of the dataset that have been used to train the model. Therefore, it gives us a better understanding of how well our model generalizes on new data.\n", + "\n", + "This means that we know the outcome of each data point in the testing dataset, making it great to test with! Since this data has not been used to train the model, the model has no knowledge of the outcome of these data points. So, in essence, it is truly an out-of-sample testing.\n", + "\n", + "Let's split our dataset into train and test sets. 80% of the entire dataset will be used for training and 20% for testing. We create a mask to select random rows using __np.random.rand()__ function: \n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "msk = np.random.rand(len(df)) < 0.8\n", + "train = cdf[msk]\n", + "test = cdf[~msk]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simple Regression Model\n", + "Linear Regression fits a linear model with coefficients B = (B1, ..., Bn) to minimize the 'residual sum of squares' between the actual value y in the dataset, and the predicted value yhat using linear approximation. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Train data distribution\n" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Modeling\n", + "Using sklearn package to model data.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[39.04591701]]\n", + "Intercept: [125.73189084]\n" + ] + } + ], + "source": [ + "from sklearn import linear_model\n", + "regr = linear_model.LinearRegression()\n", + "train_x = np.asanyarray(train[['ENGINESIZE']])\n", + "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n", + "regr.fit(train_x, train_y)\n", + "# The coefficients\n", + "print ('Coefficients: ', regr.coef_)\n", + "print ('Intercept: ',regr.intercept_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As mentioned before, __Coefficient__ and __Intercept__ in the simple linear regression, are the parameters of the fit line. \n", + "Given that it is a simple linear regression, with only 2 parameters, and knowing that the parameters are the intercept and slope of the line, sklearn can estimate them directly from our data. \n", + "Notice that all of the data must be available to traverse and calculate the parameters.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Plot outputs\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can plot the fit line over the data:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Emission')" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS, color='blue')\n", + "plt.plot(train_x, regr.coef_[0][0]*train_x + regr.intercept_[0], '-r')\n", + "plt.xlabel(\"Engine size\")\n", + "plt.ylabel(\"Emission\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Evaluation\n", + "We compare the actual values and predicted values to calculate the accuracy of a regression model. Evaluation metrics provide a key role in the development of a model, as it provides insight to areas that require improvement.\n", + "\n", + "There are different model evaluation metrics, lets use MSE here to calculate the accuracy of our model based on the test set: \n", + "* Mean Absolute Error: It is the mean of the absolute value of the errors. This is the easiest of the metrics to understand since it’s just average error.\n", + "\n", + "* Mean Squared Error (MSE): Mean Squared Error (MSE) is the mean of the squared error. It’s more popular than Mean Absolute Error because the focus is geared more towards large errors. This is due to the squared term exponentially increasing larger errors in comparison to smaller ones.\n", + "\n", + "* Root Mean Squared Error (RMSE). \n", + "\n", + "* R-squared is not an error, but rather a popular metric to measure the performance of your regression model. It represents how close the data points are to the fitted regression line. The higher the R-squared value, the better the model fits your data. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean absolute error: 22.36\n", + "Residual sum of squares (MSE): 835.25\n", + "R2-score: 0.76\n" + ] + } + ], + "source": [ + "from sklearn.metrics import r2_score\n", + "\n", + "test_x = np.asanyarray(test[['ENGINESIZE']])\n", + "test_y = np.asanyarray(test[['CO2EMISSIONS']])\n", + "test_y_ = regr.predict(test_x)\n", + "\n", + "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))\n", + "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y_ - test_y) ** 2))\n", + "print(\"R2-score: %.2f\" % r2_score(test_y , test_y_) )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets see what the evaluation metrics are if we trained a regression model using the `FUELCONSUMPTION_COMB` feature.\n", + "\n", + "Start by selecting `FUELCONSUMPTION_COMB` as the train_x data from the `train` dataframe, then select `FUELCONSUMPTION_COMB` as the test_x data from the `test` dataframe\n" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "msk = np.random.rand(len(df)) < 0.8\n", + "train = cdf[msk]\n", + "test = cdf[~msk]\n", + "\n", + "plt.scatter(train.FUELCONSUMPTION_COMB, train.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"FUELCONSUMPTION_COMB\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show() \n", + "\n", + "from sklearn import linear_model\n", + "regr = linear_model.LinearRegression()\n", + "train_x = np.asanyarray(train[['FUELCONSUMPTION_COMB']])\n", + "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n", + "regr.fit(train_x, train_y)\n", + "# The coefficients\n", + "print ('Coefficients: ', regr.coef_)\n", + "print ('Intercept: ',regr.intercept_)\n", + "\n", + "plt.scatter(train.FUELCONSUMPTION_COMB, train.CO2EMISSIONS, color='blue')\n", + "plt.plot(train_x, regr.coef_[0][0]*train_x + regr.intercept_[0], '-r')\n", + "plt.xlabel(\"FUELCONSUMPTION_COMB\")\n", + "plt.ylabel(\"Emission\")\n", + "\n", + "train_x = train[[\"FUELCONSUMPTION_COMB\"]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "train_x = train[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "test_x = test[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "train_x = train[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "test_x = test[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "train_x = train[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "test_x = test[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "train_x = train[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "test_x = test[[\"FUELCONSUMPTION_COMB\"]]\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now train a Linear Regression Model using the `train_x` you created and the `train_y` created previously\n" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[15.96373638]]\n", + "Intercept: [70.91468093]\n" + ] + } + ], + "source": [ + "regr = linear_model.LinearRegression()\n", + "train_x = np.asanyarray(train[['FUELCONSUMPTION_COMB']])\n", + "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n", + "regr.fit(train_x, train_y)\n", + "# The coefficients\n", + "print ('Coefficients: ', regr.coef_)\n", + "print ('Intercept: ',regr.intercept_)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "regr = linear_model.LinearRegression()\n", + "\n", + "regr.fit(train_x, train_y)\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Find the predictions using the model's `predict` function and the `test_x` data\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[109.22764825]\n", + " [145.94424193]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [153.92611013]\n", + " [118.80589008]\n", + " [118.80589008]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [134.76962647]\n", + " [166.69709923]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [118.80589008]\n", + " [118.80589008]\n", + " [118.80589008]\n", + " [118.80589008]\n", + " [141.15512102]\n", + " [141.15512102]\n", + " [141.15512102]\n", + " [141.15512102]\n", + " [166.69709923]\n", + " [118.80589008]\n", + " [141.15512102]\n", + " [141.15512102]\n", + " [141.15512102]\n", + " [118.80589008]\n", + " [141.15512102]\n", + " [141.15512102]\n", + " [118.80589008]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [109.22764825]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [169.88984651]\n", + " [169.88984651]\n", + " [169.88984651]\n", + " [169.88984651]\n", + " [109.22764825]\n", + " [128.38413191]\n", + " [155.52248376]\n", + " [155.52248376]\n", + " [128.38413191]\n", + " [109.22764825]\n", + " [109.22764825]\n", + " [ 93.26391187]\n", + " [ 93.26391187]\n", + " [155.52248376]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [109.22764825]\n", + " [161.90797832]\n", + " [128.38413191]\n", + " [128.38413191]\n", + " [109.22764825]\n", + " [109.22764825]\n", + " [ 93.26391187]\n", + " [ 93.26391187]\n", + " [ 93.26391187]\n", + " [144.3478683 ]\n", + " [144.3478683 ]\n", + " [102.8421537 ]\n", + " [157.1188574 ]\n", + " [126.78775827]\n", + " [169.88984651]\n", + " [126.78775827]\n", + " [150.73336285]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [126.78775827]\n", + " [110.82402189]\n", + " [155.52248376]\n", + " [155.52248376]\n", + " [155.52248376]\n", + " [139.55874738]\n", + " [139.55874738]\n", + " [155.52248376]\n", + " [109.22764825]\n", + " [128.38413191]\n", + " [155.52248376]\n", + " [102.8421537 ]\n", + " [ 99.64940642]\n", + " [109.22764825]\n", + " [109.22764825]\n", + " [ 94.86028551]\n", + " [102.8421537 ]\n", + " [123.595011 ]\n", + " [102.8421537 ]\n", + " [109.22764825]\n", + " [102.8421537 ]\n", + " [109.22764825]\n", + " [129.98050555]\n", + " [126.78775827]\n", + " [129.98050555]\n", + " [150.73336285]\n", + " [121.99863736]\n", + " [109.22764825]\n", + " [121.99863736]\n", + " [102.8421537 ]\n", + " [109.22764825]\n", + " [ 99.64940642]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [109.22764825]\n", + " [109.22764825]\n", + " [102.8421537 ]\n", + " [109.22764825]\n", + " [153.92611013]\n", + " [118.80589008]\n", + " [102.8421537 ]\n", + " [118.80589008]\n", + " [150.73336285]\n", + " [150.73336285]\n", + " [150.73336285]\n", + " [110.82402189]\n", + " [144.3478683 ]\n", + " [150.73336285]\n", + " [126.78775827]\n", + " [129.98050555]\n", + " [118.80589008]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [129.98050555]\n", + " [ 94.86028551]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [110.82402189]\n", + " [102.8421537 ]\n", + " [110.82402189]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [ 99.64940642]\n", + " [126.78775827]\n", + " [126.78775827]\n", + " [145.94424193]\n", + " [158.71523104]\n", + " [145.94424193]\n", + " [158.71523104]\n", + " [126.78775827]\n", + " [145.94424193]\n", + " [158.71523104]\n", + " [158.71523104]\n", + " [126.78775827]\n", + " [158.71523104]\n", + " [169.88984651]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [102.8421537 ]\n", + " [109.22764825]\n", + " [118.80589008]\n", + " [102.8421537 ]\n", + " [110.82402189]\n", + " [134.76962647]\n", + " [ 96.45665914]\n", + " [ 96.45665914]\n", + " [125.19138464]\n", + " [131.57687919]\n", + " [131.57687919]\n", + " [131.57687919]\n", + " [114.01676917]\n", + " [118.80589008]\n", + " [147.54061557]\n", + " [118.80589008]\n", + " [118.80589008]\n", + " [110.82402189]\n", + " [110.82402189]\n", + " [102.8421537 ]\n", + " [128.38413191]\n", + " [110.82402189]\n", + " [134.76962647]\n", + " [ 99.64940642]\n", + " [134.76962647]\n", + " [114.01676917]\n", + " [126.78775827]\n", + " [134.76962647]\n", + " [161.90797832]\n", + " [126.78775827]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [102.8421537 ]\n", + " [128.38413191]\n", + " [110.82402189]\n", + " [121.99863736]]\n" + ] + } + ], + "source": [ + "predictions = regr.predict(test_x)\n", + "print(predictions)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "predictions = regr.predict(test_x)\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally use the `predictions` and the `test_y` data and find the Mean Absolute Error value using the `np.absolute` and `np.mean` function like done previously\n" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean absolute error: 111.31\n" + ] + } + ], + "source": [ + "print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Click here for the solution\n", + "\n", + "```python \n", + "print(\"Mean Absolute Error: %.2f\" % np.mean(np.absolute(predictions - test_y)))\n", + "\n", + "```\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that the MAE is much worse when we train using `ENGINESIZE` than `FUELCONSUMPTION_COMB`\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Thank you for completing this lab!\n", + "\n", + "\n", + "## Author\n", + "\n", + "Saeed Aghabozorgi\n", + "\n", + "\n", + "### Other Contributors\n", + "\n", + "Joseph Santarcangelo\n", + "\n", + "Azim Hirjani\n", + "\n", + "##

© IBM Corporation. All rights reserved.

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