From 3caee837e3e80e67d7fc009f5e1885b8ec544602 Mon Sep 17 00:00:00 2001 From: 202310715168 RAHMAD SYARIF <202310715168@mhs.ubharajaya.ac.id> Date: Wed, 19 Nov 2025 13:54:57 +0700 Subject: [PATCH] Upload files to "Tugas.Regression" --- ...N-Reg-Mulitple-Linear-Regression-Co2.ipynb | 768 +++++++++ ...A2_ML0101EN-Reg-NoneLinearRegression.ipynb | 890 ++++++++++ ...0101EN-Reg-Polynomial-Regression-Co2.ipynb | 843 ++++++++++ ...1EN-Reg-Simple-Linear-Regression-Co2.ipynb | 1425 +++++++++++++++++ 4 files changed, 3926 insertions(+) create mode 100644 Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb create mode 100644 Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-NoneLinearRegression.ipynb create mode 100644 Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb create mode 100644 Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb diff --git a/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb new file mode 100644 index 0000000..3b2370d --- /dev/null +++ b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Mulitple-Linear-Regression-Co2.ipynb @@ -0,0 +1,768 @@ +{ + "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": 1, + "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": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--2025-10-20 10:23:36-- 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 10:23:36 (45.8 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": [ + "\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": 3, + "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": 3, + "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": 4, + "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
\n", + "
" + ], + "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": 4, + "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": 5, + "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": 6, + "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": 7, + "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": [ + "

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": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[9.81545776 7.85767764 9.73745704]]\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": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean Squared Error (MSE) : 522.80\n", + "Variance score: 0.89\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": 10, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[9.85404898 7.62773683 5.96756017 3.56958505]]\n", + "Residual sum of squares (MSE): 521.52\n", + "Variance score (R^2): 0.89\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" + ] + } + ], + "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/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-NoneLinearRegression.ipynb b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-NoneLinearRegression.ipynb new file mode 100644 index 0000000..41c40b8 --- /dev/null +++ b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-NoneLinearRegression.ipynb @@ -0,0 +1,890 @@ +{ + "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": 1, + "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": 2, + "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": 3, + "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": 4, + "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": 5, + "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": 17, + "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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\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": 7, + "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": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2025-10-20 10:37:17 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": 8, + "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": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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sAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHCvV7g4AAAAkJb9fqq6WfD4pJ0cqLpZcLrt75TiEWQAAgN7m9UqzZ0u7dn3Z5vFICxZIZWX29cuBbF9msGjRIhUWFio9PV2jRo1SdXX1UetbWlp05513Kj8/X2lpaTr55JP11FNP9VJvAQAAesjrla68MjTISlJDQ6Dd67WnXw5l68zssmXLVF5erkWLFun888/X448/rgkTJmjz5s066aSTwr7nqquu0u7du/Xkk0/qlFNO0Z49e9TW1tbLPQcAAOgGvz8wI2tM59eMkSxLKi+XJk1iyUGELGPC/TZ7x5gxYzRy5Eg9+uijwbYRI0Zo8uTJqqio6FS/cuVKff/739f27duVlZXVrc9sbm6W2+1WU1OTMjMzu913AACAqK1eLY0ff+y6VaukkpJ49yZhRZPXbFtm0Nraqk2bNqm0tDSkvbS0VOvXrw/7nr/+9a8aPXq0fvWrX2nYsGEaPny4brvtNn322Wddfk5LS4uam5tDHgAAALbw+WJbB/uWGezdu1d+v1/Z2dkh7dnZ2WpsbAz7nu3bt2vt2rVKT0/XCy+8oL179+rf//3f9fHHH3e5braiokL33ntvzPsPAAAQtZyc2NbB/hvALMsKeW6M6dTWob29XZZl6dlnn9W5556ryy67TA899JD+8Ic/dDk7O3fuXDU1NQUf9fX1Mf8OAAAAESkuDuxa0EXWkWVJeXmBOkTEtjB74oknyuVydZqF3bNnT6fZ2g45OTkaNmyY3G53sG3EiBEyxmjXkXcE/n9paWnKzMwMeQAAANjC5QpsvyV1DrQdz+fP5+avKNgWZvv3769Ro0apqqoqpL2qqkrjxo0L+57zzz9fH374oT799NNg2/vvv6+UlBR5PJ649hcAACAmysqkykpp2LDQdo8n0M4+s1GxdTeDZcuWaerUqXrsscc0duxYPfHEE1q8eLHeeecd5efna+7cuWpoaNAzzzwjSfr00081YsQInXfeebr33nu1d+9e3Xjjjbrwwgu1ePHiiD6T3QwAAEBC4ASwLkWT12zdZ3bKlCnat2+f7rvvPvl8PhUVFWnFihXKz8+XJPl8Pu3cuTNYf/zxx6uqqkq33HKLRo8erUGDBumqq67S/fffb9dXAAAA6B6XK6m334oVW2dm7cDMLAAAQGJzxD6zAAAAQE8RZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjhX1CWAffPCBXnrpJX3xxRe68MILdfrpp8ejXwAAAMAxRRVm16xZo8suu0yHDh0KvDk1VX/84x919dVXx6VzAAAAwNFEtczgP//zPzV+/Hjt2rVL+/bt0/XXX6+f/vSn8eobAAAAcFSWMcZEWpyVlaU1a9aoqKhIknTw4EFlZmZq7969+spXvhK3TsZSNGf9AgAAoPdFk9eimpndv3+/hgwZEnyekZGhAQMGaP/+/d3qKAAAANATUd8AtnnzZjU2NgafG2P07rvv6sCBA8G2M888Mza9AwAAAI4iqmUGKSkpsixL4d7S0W5Zlvx+f0w7GUssMwAAAEhs0eS1qGZm6+rqetQxAAAAIJaiCrP5+fnx6gcAAAAQtajXzErSli1b9Je//EU7duyQZVkqLCzU5MmT9dWvfjXW/QMAAAC6FHWYraio0F133aX29nYNGTJExhh99NFHuuOOO/TAAw/otttui0c/AQAAgE6i2ppr1apVmjdvnu68807t3btXPp9PjY2NwTB7xx13aM2aNfHqKwAAABAiqt0MpkyZooEDB+rxxx8P+/qPfvQjHThwQEuXLo1ZB2ON3QwAAEBc+f1SdbXk80k5OVJxseRy2d0rR4nboQlvvPGGpk6d2uXrU6dO1WuvvRbNJQEAAPoOr1cqKJDGj5euuSbws6Ag0I64iCrM7t69WwUFBV2+XlhYGHKgAgAAQNLweqUrr5R27Qptb2gItBNo4yKqMPv555+rf//+Xb7er18/tba29rhTAAAAjuL3S7NnS+FWb3a0lZcH6hBTUe9m8Pvf/17HH3982NcOP9IWAAAgaVRXd56RPZwxUn19oK6kpNe6lQyiCrMnnXSSFi9efMwaAACApOLzxbYOEYsqzO7YsSNO3QAAAHCwnJzY1iFiUYXZzz//XC+//LIuv/xySdLcuXPV0tLy5cVSU3XfffcpPT09tr0EAABIZMXFkscTuNkr3LpZywq8Xlzc+33r46IKs3/84x/1P//zP8Ewu3DhQp1++uk67rjjJEn/+te/NHToUM2ZMyf2PQUAAEhULpe0YEFg1wLLCg20lhX4OX8++83GQVS7GTz77LO6/vrrQ9qWLFmiVatWadWqVfr1r3+t559/PqYdBAAAcISyMqmyUho2LLTd4wm0l5XZ068+LqqZ2ffff1/Dhw8PPk9PT1dKypd5+Nxzz9XNN98cu94BAAA4SVmZNGkSJ4D1oqjCbFNTk1JTv3zLRx99FPJ6e3t7yBpaAACApONysf1WL4pqmYHH49Hbb7/d5ev//Oc/5fF4etwpAAAAIBJRhdnLLrtMd911lz7//PNOr3322We699579e1vfztmnQMAAACOxjIm3P4R4e3evVtnn322+vfvr5kzZ2r48OGyLEv/+te/tHDhQrW1tammpkbZ2dnx7HOPNDc3y+12q6mpSZmZmXZ3BwAAAEeIJq9FtWY2Oztb69ev149//GPdcccd6sjBlmXpkksu0aJFixI6yAIAAKBviSrMSlJhYaFWrlypjz/+WFu3bpUknXLKKcrKyop55wAAAICjiTrMdsjKytK5554by74AAAAkLr+fLbcSULfDLAAAQNLweqXZs6Vdu75s83gCp35xGIKtotrNAAAAIOl4vYFjag8PspLU0BBo93rt6RckEWYBAAC65vcHZmTDbf7U0VZeHqiDLQizAAAAXamu7jwjezhjpPr6QB1sQZgFAADois8X2zrEHGEWAACgKzk5sa1DzBFmAQAAulJcHNi1wLLCv25ZUl5eoA62IMwCAAB0xeUKbL8ldQ60Hc/nz2e/WRsRZgEAAI6mrEyqrJSGDQtt93gC7ewzaysOTQAAADiWsjJp0iROAEtAhFkAAIBIuFxSSYndvcARWGYAAAAAxyLMAgAAwLEIswAAAHAswiwAAAAcizALAAAAxyLMAgAAwLEIswAAAHAswiwAAAAcy/Ywu2jRIhUWFio9PV2jRo1SdXV1RO9bt26dUlNTdfbZZ8e3gwAAAEhYtobZZcuWqby8XHfeeadqampUXFysCRMmaOfOnUd9X1NTk6ZNm6ZvfvObvdRTAAAAJCLLGGPs+vAxY8Zo5MiRevTRR4NtI0aM0OTJk1VRUdHl+77//e/r1FNPlcvl0osvvqja2tqIP7O5uVlut1tNTU3KzMzsSfcBAAAQB9HkNdtmZltbW7Vp0yaVlpaGtJeWlmr9+vVdvu/pp5/Wtm3bdPfdd0f0OS0tLWpubg55AAAAoG+wLczu3btXfr9f2dnZIe3Z2dlqbGwM+54tW7bojjvu0LPPPqvU1NSIPqeiokJutzv4yMvL63HfAQAAkBhsvwHMsqyQ58aYTm2S5Pf7dc011+jee+/V8OHDI77+3Llz1dTUFHzU19f3uM8AAABIDJFNb8bBiSeeKJfL1WkWds+ePZ1mayXpwIED2rhxo2pqajRz5kxJUnt7u4wxSk1N1UsvvaSLLrqo0/vS0tKUlpYWny8BAAAAW9k2M9u/f3+NGjVKVVVVIe1VVVUaN25cp/rMzEy99dZbqq2tDT5mzJihr33ta6qtrdWYMWN6q+sAAABIELbNzErSnDlzNHXqVI0ePVpjx47VE088oZ07d2rGjBmSAksEGhoa9MwzzyglJUVFRUUh7x8yZIjS09M7tQMAACA52Bpmp0yZon379um+++6Tz+dTUVGRVqxYofz8fEmSz+c75p6zAAAASF627jNrB/aZBQAASGyO2GcWAAAA6CnCLAAAAByLMAsAAADHIswCAADAsWzdzQAAAMBWfr9UXS35fFJOjlRcLLlcdvcKUSDMAgCA5OT1SrNnS7t2fdnm8UgLFkhlZfb1C1FhmQEAAEg+Xq905ZWhQVaSGhoC7V6vPf1C1AizAAAgufj9gRnZcFvtd7SVlwfqkPAIswAAILlUV3eekT2cMVJ9faAOCY8wCwAAkovPF9s62IowCwAAkktOTmzrYCvCLAAASC7FxYFdCywr/OuWJeXlBeqQ8AizAAAgubhcge23pM6BtuP5/PnsN+sQhFkAAJB8ysqkykpp2LDQdo8n0M4+s47BoQkAACA5lZVJkyZxApjDEWYBAEDycrmkkhK7e4EeYJkBAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxUu3uAAAAQMz5/VJ1teTzSTk5UnGx5HLZ3SvEAWEWAAD0LV6vNHu2tGvXl20ej7RggVRWZl+/EBcsMwAAAH2H1ytdeWVokJWkhoZAu9drT78QN4RZAADQN/j9gRlZYzq/1tFWXh6oQ59BmAUAAH1DdXXnGdnDGSPV1wfq0GcQZgEAQN/g88W2Do5AmAUAAH1DTk5s6+AIhFkAANA3FBcHdi2wrPCvW5aUlxeoQ59BmAUAAH2DyxXYfkvqHGg7ns+fz36zfQxhFgAA9B1lZVJlpTRsWGi7xxNoZ5/ZPodDEwAAQN9SViZNmsQJYEmCMAsAAPoel0sqKbG7F+gFLDMAAACAYxFmAQAA4FiEWQAAADgWYRYAAACOxQ1gAADAGfx+dihAJ4RZAACQ+LxeafZsadeuL9s8nsAhCewdm9RYZgAAABKb1ytdeWVokJWkhoZAu9drT7+QEAizAAAgcfn9gRlZYzq/1tFWXh6oQ1IizAIAgMRVXd15RvZwxkj19YE6JCXCLAAASFw+X2zr0OcQZgEAQOLKyYltHfocwiwAAEhcxcWBXQssK/zrliXl5QXqkJQIswAAIHG5XIHtt6TOgbbj+fz57DebxAizAAAgsZWVSZWV0rBhoe0eT6CdfWaTmu1hdtGiRSosLFR6erpGjRql6qPcjej1enXJJZdo8ODByszM1NixY/X3v/+9F3sLAABsUVYm7dghrVolLVkS+FlXR5CFvWF22bJlKi8v15133qmamhoVFxdrwoQJ2rlzZ9j6NWvW6JJLLtGKFSu0adMmjR8/XhMnTlRNTU0v9xwAAMSM3y+tXi0tXRr42dWesS6XVFIiXX114CdLCyDJMibcLsS9Y8yYMRo5cqQeffTRYNuIESM0efJkVVRURHSN008/XVOmTNFdd90VUX1zc7PcbreampqUmZnZrX4DAIAY4ZhahBFNXrNtZra1tVWbNm1SaWlpSHtpaanWr18f0TXa29t14MABZWVldVnT0tKi5ubmkAcAAEgAHFOLGLAtzO7du1d+v1/Z2dkh7dnZ2WpsbIzoGg8++KAOHjyoq666qsuaiooKud3u4CMvL69H/QYAADHAMbWIEdtvALOO2GbDGNOpLZylS5fqnnvu0bJlyzRkyJAu6+bOnaumpqbgo76+vsd9BgAAPcQxtYiRVLs++MQTT5TL5eo0C7tnz55Os7VHWrZsmW644QY9//zzuvjii49am5aWprS0tB73FwAAxBDH1CJGbJuZ7d+/v0aNGqWqqqqQ9qqqKo0bN67L9y1dulTXXnutlixZom9/+9vx7iYAAIgHjqlFjNg2MytJc+bM0dSpUzV69GiNHTtWTzzxhHbu3KkZM2ZICiwRaGho0DPPPCMpEGSnTZumBQsW6LzzzgvO6h533HFyu922fQ8AABCljmNqGxrCr5u1rMDrHFOLY7B1zeyUKVM0f/583XfffTr77LO1Zs0arVixQvn5+ZIkn88Xsufs448/rra2Nt18883KyckJPmbPnm3XVwAAAN3BMbWIEVv3mbUD+8wCAJBAwu0zm5cXCLLsM5u0oslrti4zAAAAfZTfH9iJwOcLrHstLg4/y1pWJk2aFFktEAZhFgAAxFa0p3p1HFMLdIPt+8wCAIA+hFO90MsIswAAIDY41Qs2IMwCAIDY4FQv2IAwCwAAYoNTvWADbgADAACRO9ouBZzqBRswMwsAACLj9UoFBdL48dI11wR+FhR8eVNXx6leRx6C0MGyAnvIcqoXYogwCwAAji2SXQo41Qs2IMwCAICji2aXgrIyqbJSGjYstM7jCbRzqhdijDWzAADg6KLZpaCkhFO90KsIswAA4Og3dnVnlwJO9UIvIcwCAJDsjnX8LLsUIIGxZhYAgGQWyY1d7FKABEaYBQAgWUV6Y5fELgVIWIRZAAD6Kr9fWr1aWro08NPvD309mhu72KUACYo1swAA9EXHWgcrRX9jF7sUIAERZgEA6Gs61sEeuXygYx1sx0xqd27sYpcCJBiWGQAA0JdEc8ABN3ahDyDMAgDgNEdbCxvNOliOn0UfQJgFAMBJvF6poEAaP1665prAz4KCQLvUvXWw3NgFB2PNLAAAieBoJ3B1iGQtbHfWwXJjFxzMMibcopq+q7m5WW63W01NTcrMzLS7OwAARLbzgN8fmIHtagmBZQXes3WrdPLJgYAb7j/xHXV1dYRVJKxo8hrLDAAAiKdj7fUayQlcUuRrYdevZx0skgphFgCAeDnW+tZodh6IZi0s62CRRFgzCwBAPESyvjUrK/KdB6JdC8s6WCQJwiwAALF2rBlXywrMuFZURHY9n0+66qrAzOqx1sIevicsBxwgCbDMAACAaB1rHWyk61s/+iiyz8vJYU9YoAuEWQAAonGsdbBS5OtbBw+O7gQu1sICnRBmAQCIVKQ7D0S6vnXYsOhnW8vKpB07pFWrpCVLAj/r6giySFrsMwsAQCQi3ee1ri7wvKAg8r1ew+0zm5cXCLKEVCShaPIaN4ABANDhaKdwRboOtro6cNPVggWB2VrLCg204WZc2XkA6DbCLAAA0rFP4Ypmn1fpy/Wt4a4ZbsaVnQeAbiHMAgAQyZ6w0e7zKjHjCvQC1swCAJJbpGtht26VTj458nWwALotmrzGbgYAgOQW6VrY9evZ5xVIQIRZAEByi2YtLPu8AgmHNbMAgL7taDsUSNGvhWUdLJBQCLMAgL7rWDsUSIEg6vEcey1sxylcEjsPAAmEZQYAgL4p0tO6XC7WwgIORpgFAPQ9fn9gRjbcTGtHW3l5oE5iLSzgYCwzAAAklmOtcY2kLtrTuiTWwgIORZgFACSOSNa4RlIX7WldHVgLCzgOYRYAEH+RzLZGcgpXWVn8TusC4EicAAYACBXpX/NHWhvJbGu0p3BxWhfQp3ECGAAkKr9fWr1aWro08LPjBqRE+WyvNxAqx4+Xrrkm8LOg4Ms7/6OtjXRHgUjXuC5axGldAEIQZgGgt0QTFGMdemMZPCOtjWZHgUjXuG7bFlkdp3UBSYNlBgDQUz1ZD9oxS3h4uIr0JqhYfvakSZH9NX9dXeB5JLVPPy1dfHH4msOtWhX4OX78sWsffli69dbIrtlxI1c0yyYAJIRo8hphFgC60tvrQevqpL/8JbahN9LPjkfwnDdPuv/+Y9ctWSJddVWgn8da48paWCApsGYWQN8QzV+1R1obaZ0d60FXr478r+Xj8dmR8PkiXxIQqZycyE/h6t+ftbAAQhBmgb4kHjcX2XXNWN+IFG2dHetBV6+OfeiNR/CMdDurkpLALOmRobODZUl5eYEZbynyNa6shQVwOJNkmpqajCTT1NRkd1eQ7NrajFm1ypglSwI/29p6Vrt8uTEejzGBOBN4eDyB9t64ZqTfJ5JrLl9ujGWF1kiBNsvqXm2kdW1tnft3ZH1enjEvv9x1zeGPVasCj0hq582LbV00n/3yy4HvHe53dPj3bmv78ncUSW3H7/3I2nBjGe0/S9H8GQLgKNHkNcIsEAk7g2esw188rhnp94nkmpGGycND1bFqW1oiv2asg+eSJZGHv0gDcjw+O9rgGW3tkb//vLyu/0cLQNIjzB4FYbaH4jFjkujXtDN4xjr8xeOaTpjxfPjhyK+5ZElsA+WqVaG/96OFv1iH3mg++2j/DHcVPKOpZRYVQBQIs0fR62E21kHNzpAYzexbLMOfnde0M3jGI/zF+podfzUdyfeJx4xnpMFz5szIrxmPv5Y/2j9zR4a/WIbeaD+7Qzz+PQMAUSDMHkWvhtlYBzU7Q2Ks1yU64Zp2B894hD87127GY8YzHjOzibAeNFahtzufDQAJgDB7FL0WZmMd1JxwQ0w06xKdcE27g2c8wl+srxmPIB2PG5E6xjzSmcxEWA8aq9ALAA7kqDD7yCOPmIKCApOWlmZGjhxp1qxZc9T61atXm5EjR5q0tDRTWFhoHn300ag+r1fCbKxDld0hMR6zX064pt3BMx7hL9bX7M4SB7tuRIp2JtMp60GZbQXQBzkmzD733HOmX79+ZvHixWbz5s1m9uzZJiMjw3zwwQdh67dv324GDBhgZs+ebTZv3mwWL15s+vXrZyorKyP+zF4Js7EOVXaHxHisS3TCNe0OnvEIf7G+ZrRrN+2+ESnamUyCIgDYwjFh9txzzzUzZswIaTvttNPMHXfcEbb+pz/9qTnttNNC2qZPn27OO++8iD+zV8JsrEOV3SHRCbOo8bim3cHTmPiEv1hfM1FmPNmbFAD6DEeE2ZaWFuNyuYzX6w1pnzVrlvnGN74R9j3FxcVm1qxZIW1er9ekpqaa1tbWsO/5/PPPTVNTU/BRX18f8S+n2/razGw81iU65Zp2B89oa3uyM0VPrsmMJwAghhwRZhsaGowks27dupD2n//852b48OFh33Pqqaean//85yFt69atM5LMhx9+GPY9d999t5HU6dEra2ZjFarsDnTGxGddopOuafe+m/EIf7G+JgEVABAjjgqz69evD2m///77zde+9rWw7zn11FPNAw88ENK2du1aI8n4fL6w77FlZtaY2IcquwNdR32s1yU65Zp2B08AAJKII8Jsby0zOJLt+8z2JFTZHeiMccbhDvG6JgAA6BXR5DXLGGNkkzFjxmjUqFFatGhRsO3rX/+6Jk2apIqKik71t99+u/72t79p8+bNwbYf//jHqq2t1YYNGyL6zObmZrndbjU1NSkzM7PnX+JY/H6pulry+aScHKm4WHK54l8Xr2sCAADEWTR5zdYwu2zZMk2dOlWPPfaYxo4dqyeeeEKLFy/WO++8o/z8fM2dO1cNDQ165plnJEl1dXUqKirS9OnTddNNN2nDhg2aMWOGli5dqiuuuCKiz+z1MAsAAICoRJPXUnupT2FNmTJF+/bt03333Sefz6eioiKtWLFC+fn5kiSfz6edO3cG6wsLC7VixQrdeuuteuSRR5Sbm6vf/va3EQdZAAAA9C22zszagZlZAACAxBZNXkvppT4BAAAAMUeYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4lq0ngNmh44yI5uZmm3sCAACAcDpyWiRneyVdmD1w4IAkKS8vz+aeAAAA4GgOHDggt9t91JqkO862vb1dH374oU444QRZltUrn9nc3Ky8vDzV19dzhG4CYnwSG+OT+BijxMb4JDbGJzxjjA4cOKDc3FylpBx9VWzSzcympKTI4/HY8tmZmZn8g5rAGJ/ExvgkPsYosTE+iY3x6exYM7IduAEMAAAAjkWYBQAAgGMRZntBWlqa7r77bqWlpdndFYTB+CQ2xifxMUaJjfFJbIxPzyXdDWAAAADoO5iZBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYjcCaNWs0ceJE5ebmyrIsvfjiiyGv7969W9dee61yc3M1YMAAXXrppdqyZUun62zYsEEXXXSRMjIyNHDgQJWUlOizzz4Lvv7JJ59o6tSpcrvdcrvdmjp1qvbv3x/nb9c39HSMduzYIcuywj6ef/75YB1j1D2x+DPU2NioqVOnaujQocrIyNDIkSNVWVkZUsP4dF8sxmjbtm367ne/q8GDByszM1NXXXWVdu/eHVLDGEWvoqJC//Zv/6YTTjhBQ4YM0eTJk/Xee++F1BhjdM899yg3N1fHHXecSkpK9M4774TUtLS06JZbbtGJJ56ojIwMfec739GuXbtCahif7onVGD3xxBMqKSlRZmamLMsK+7tnjDojzEbg4MGDOuuss7Rw4cJOrxljNHnyZG3fvl1/+ctfVFNTo/z8fF188cU6ePBgsG7Dhg269NJLVVpaqjfeeENvvvmmZs6cGXJE2zXXXKPa2lqtXLlSK1euVG1traZOndor39HpejpGeXl58vl8IY97771XGRkZmjBhQvBajFH3xOLP0NSpU/Xee+/pr3/9q9566y2VlZVpypQpqqmpCdYwPt3X0zE6ePCgSktLZVmWXnnlFa1bt06tra2aOHGi2tvbg9dijKL36quv6uabb9Zrr72mqqoqtbW1qbS0NOTPx69+9Ss99NBDWrhwod58800NHTpUl1xyiQ4cOBCsKS8v1wsvvKDnnntOa9eu1aeffqrLL79cfr8/WMP4dE+sxujQoUO69NJL9bOf/azLz2KMwjCIiiTzwgsvBJ+/9957RpJ5++23g21tbW0mKyvLLF68ONg2ZswYM2/evC6vu3nzZiPJvPbaa8G2DRs2GEnmX//6V2y/RB/X3TE60tlnn22uv/764HPGKDa6Oz4ZGRnmmWeeCblWVlaW+f3vf2+MYXxiqTtj9Pe//92kpKSYpqamYM3HH39sJJmqqipjDGMUK3v27DGSzKuvvmqMMaa9vd0MHTrU/OIXvwjWfP7558btdpvHHnvMGGPM/v37Tb9+/cxzzz0XrGloaDApKSlm5cqVxhjGJ5a6M0aHW7VqlZFkPvnkk5B2xig8ZmZ7qKWlRZKUnp4ebHO5XOrfv7/Wrl0rSdqzZ49ef/11DRkyROPGjVN2drYuvPDC4OtSYObW7XZrzJgxwbbzzjtPbrdb69ev76Vv0zdFMkZH2rRpk2pra3XDDTcE2xij+Ih0fC644AItW7ZMH3/8sdrb2/Xcc8+ppaVFJSUlkhifeIpkjFpaWmRZVsjG7+np6UpJSQnWMEax0dTUJEnKysqSJNXV1amxsVGlpaXBmrS0NF144YXB3+umTZv0xRdfhNTk5uaqqKgoWMP4xE53xigSjFF4hNkeOu2005Sfn6+5c+fqk08+UWtrq37xi1+osbFRPp9PkrR9+3ZJ0j333KObbrpJK1eu1MiRI/XNb34zuOassbFRQ4YM6XT9IUOGqLGxsfe+UB8UyRgd6cknn9SIESM0bty4YBtjFB+Rjs+yZcvU1tamQYMGKS0tTdOnT9cLL7ygk08+WRLjE0+RjNF5552njIwM3X777Tp06JAOHjyon/zkJ2pvbw/WMEY9Z4zRnDlzdMEFF6ioqEiSgr+77OzskNrs7Ozga42Njerfv7++8pWvHLWG8em57o5RJBij8AizPdSvXz8tX75c77//vrKysjRgwACtXr1aEyZMkMvlkqTgerHp06fruuuu0znnnKOHH35YX/va1/TUU08Fr2VZVqfrG2PCtiNykYzR4T777DMtWbIkZFa2A2MUe5GOz7x58/TJJ5/o5Zdf1saNGzVnzhx973vf01tvvRWsYXziI5IxGjx4sJ5//nn97W9/0/HHHy+3262mpiaNHDkyZBwZo56ZOXOm/vnPf2rp0qWdXjvydxjJ7/XIGsan52I9Rse6Rnev05ek2t2BvmDUqFGqra1VU1OTWltbNXjwYI0ZM0ajR4+WJOXk5EiSvv71r4e8b8SIEdq5c6ckaejQoZ3u+pWkjz76qNP/ySF6xxqjw1VWVurQoUOaNm1aSDtjFD/HGp9t27Zp4cKFevvtt3X66adLks466yxVV1frkUce0WOPPcb4xFkkf4ZKS0u1bds27d27V6mpqRo4cKCGDh2qwsJCSfwZ6qlbbrlFf/3rX7VmzRp5PJ5g+9ChQyUFZu06/nsjBZa4dfxehw4dqtbWVn3yySchs7N79uwJ/g0U49NzPRmjSDBG4TEzG0Nut1uDBw/Wli1btHHjRk2aNEmSVFBQoNzc3E7bdLz//vvKz8+XJI0dO1ZNTU164403gq+//vrrampqCvmrbvRMV2N0uCeffFLf+c53NHjw4JB2xij+uhqfQ4cOSVLI7h9SYN1mx998MD69I5I/QyeeeKIGDhyoV155RXv27NF3vvMdSYxRdxljNHPmTHm9Xr3yyivB/znoUFhYqKFDh6qqqirY1traqldffTX4ex01apT69esXUuPz+fT2228Haxif7ovFGEWCMeqCLbedOcyBAwdMTU2NqampMZLMQw89ZGpqaswHH3xgjDHmz3/+s1m1apXZtm2befHFF01+fr4pKysLucbDDz9sMjMzzfPPP2+2bNli5s2bZ9LT083WrVuDNZdeeqk588wzzYYNG8yGDRvMGWecYS6//PJe/a5OFYsxMsaYLVu2GMuyzP/93/+F/RzGqHt6Oj6tra3mlFNOMcXFxeb11183W7duNb/5zW+MZVnmf//3f4N1jE/3xeLP0FNPPWU2bNhgtm7dav70pz+ZrKwsM2fOnJAaxih6P/7xj43b7TarV682Pp8v+Dh06FCw5he/+IVxu93G6/Wat956y1x99dUmJyfHNDc3B2tmzJhhPB6Pefnll80//vEPc9FFF5mzzjrLtLW1BWsYn+6J1Rj5fD5TU1NjFi9ebCSZNWvWmJqaGrNv375gDWPUGWE2Ah1bZBz5+OEPf2iMMWbBggXG4/GYfv36mZNOOsnMmzfPtLS0dLpORUWF8Xg8ZsCAAWbs2LGmuro65PV9+/aZH/zgB+aEE04wJ5xwgvnBD37QaVsOhBerMZo7d67xeDzG7/eH/RzGqHtiMT7vv/++KSsrM0OGDDEDBgwwZ555Zqetuhif7ovFGN1+++0mOzvb9OvXz5x66qnmwQcfNO3t7SE1jFH0wo2LJPP0008Ha9rb283dd99thg4datLS0sw3vvEN89Zbb4Vc57PPPjMzZ840WVlZ5rjjjjOXX3652blzZ0gN49M9sRqju++++5jXYYw6s4wxJl6zvgAAAEA8sWYWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWABKIMUYXX3yxvvWtb3V6bdGiRXK73dq5c6cNPQOAxESYBYAEYlmWnn76ab3++ut6/PHHg+11dXW6/fbbtWDBAp100kkx/cwvvvgiptcDgN5EmAWABJOXl6cFCxbotttuU11dnYwxuuGGG/TNb35T5557ri677DIdf/zxys7O1tSpU7V3797ge1euXKkLLrhAAwcO1KBBg3T55Zdr27Ztwdd37Nghy7L05z//WSUlJUpPT9d///d/2/E1ASAmLGOMsbsTAIDOJk+erP379+uKK67Qf/3Xf+nNN9/U6NGjddNNN2natGn67LPPdPvtt6utrU2vvPKKJGn58uWyLEtnnHGGDh48qLvuuks7duxQbW2tUlJStGPHDhUWFqqgoEAPPvigzjnnHKWlpSk3N9fmbwsA3UOYBYAEtWfPHhUVFWnfvn2qrKxUTU2NXn/9df39738P1uzatUt5eXl67733NHz48E7X+OijjzRkyBC99dZbKioqCobZ+fPna/bs2b35dQAgLlhmAAAJasiQIfrRj36kESNG6Lvf/a42bdqkVatW6fjjjw8+TjvtNEkKLiXYtm2brrnmGn31q19VZmamCgsLJanTTWOjR4/u3S8DAHGSancHAABdS01NVWpq4F/V7e3tmjhxon75y192qsvJyZEkTZw4UXl5eVq8eLFyc3PV3t6uoqIitba2htRnZGTEv/MA0AsIswDgECNHjtTy5ctVUFAQDLiH27dvn9599109/vjjKi4uliStXbu2t7sJAL2KZQYA4BA333yzPv74Y1199dV64403tH37dr300ku6/vrr5ff79ZWvfEWDBg3SE088oa1bt+qVV17RnDlz7O42AMQVYRYAHCI3N1fr1q2T3+/Xt771LRUVFWn27Nlyu91KSUlRSkqKnnvuOW3atElFRUW69dZb9etf/9rubgNAXLGbAQAAAByLmVkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBY/w99KbzwXu7KKQAAAABJRU5ErkJggg==\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": 10, + "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": 11, + "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": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 12, + "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": 13, + "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": 14, + "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": 15, + "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": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean Absolute Error (MAE): 0.02\n", + "Mean Squared Error (MSE): 0.00\n", + "Root Mean Squared Error (RMSE): 0.02\n", + "R2-score: 0.89\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" + ] + } + ], + "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/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb new file mode 100644 index 0000000..0b33628 --- /dev/null +++ b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Polynomial-Regression-Co2.ipynb @@ -0,0 +1,843 @@ +{ + "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": 1, + "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": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--2025-10-20 10:30:00-- 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 10:30:00 (41.3 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": 3, + "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": 3, + "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": 4, + "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
\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": 4, + "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": 5, + "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": 6, + "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": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1. , 1.5 , 2.25],\n", + " [ 1. , 3.5 , 12.25],\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": 12, + "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": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[ 0. 50.8343626 -1.5636381]]\n", + "Intercept: [106.99883066]\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": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Emission')" + ] + }, + "execution_count": 9, + "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", + "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": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean absolute error: 20.89\n", + "Residual sum of squares (MSE): 790.03\n", + "R2-score: 0.80\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": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# write your code here\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/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb new file mode 100644 index 0000000..705e801 --- /dev/null +++ b/Tugas.Regression/Rahmad Syarif_202310715168_F5A2_ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb @@ -0,0 +1,1425 @@ +{ + "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": 5, + "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": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--2025-10-20 10:20:05-- 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 10:20:05 (43.9 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": 7, + "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": 8, + "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": 8, + "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": 9, + "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": 9, + "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": 10, + "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": 10, + "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": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\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": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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SLCKv5bKwM27cOFRUVKC8vNz4GDx4MGbNmoXy8nL85je/gUqlwoEDB4x1dDodSkpKMGLECADAoEGD4O/vb1JGrVbj9OnTxjJERO7kwQcBM3fuLVJUJM7WIiLruGzMTkhICBISEkyOBQcHIzw83Hg8KysLy5cvR3x8POLj47F8+XIEBQVh5i99v0qlEnPnzkVOTg7Cw8MRFhaG3NxcJCYmthjwTETkSjqdOD1cStCRy4Ht24HHHrN/u4h8gVuvoJyXl4eGhgZkZGSgtrYWQ4cOxf79+xESEmIsU1hYCD8/P8yYMQMNDQ0YN24cNm7cCDlvaBORm8jLE5fJl7r8V1ERgw6RLWSCYM1kR+9UV1cHpVIJrVbL8TtEZFd5ecDKldLqhocDf/sbx+gQtcbSz2+Xr7NDROStdDppGx/6+Ynr7vz8M4MOkT249W0sIiJPNm+etFtXly8DSqX920Pkq9izQ0TkAB98AGzcaH29IUMYdIjsjWGHiMjOpO5cPmQIcOKE/dtD5Ot4G4uIyI62bgX+4z+sq5OcLNbr1MkxbSLvpdcDR44AajUQFQWMHMnVtc1h2CEisoPycmDgQOvrLV4MrFhh9+aQDyguBhYtAi5e/PVYTAywZg0HtjfH21hERDaSyaQFnfR0Bh2SprhYXHupadABgOpq8XhxsWva5a4YdoiIbNDOvsSt6tZNvHVFZC29XuzRMbdKnuFYVpb0RSy9EcMOEZFEtgwmfuMNjq0gaY4cadmj05QgAFVVYjkSMewQEUmQlwcMHWp9Pe5cTrZSq+1bzhdwgDIRkZVs2QKC+1yRraKi7FvOF7Bnh4jIClK3gACALVsYdMh2I0eKs65aGy8mkwGxsWI5EjHsEBFZSKcTZ1BJGfg5eDAwa5b920S+Ry4Xp5cDLQOP4fvVqzkmrCmGHSIiC+TlAUFBwO7d1tcdMgQoLbV7k8iHpaWJK3V362Z6PCZGPM4xYaY4ZoeIqB2LFwOvvy6t7vXrXBmZHCMtDUhJ4QrKlmDYISJqw44d0oLOP/4BPPig/dtD1JRcDowe7epWuD+GHSKiVkjZ5woQe4IYdKg13M/K+Rh2iIjMGDIEOHnSujpyOZCdzS0gqHXcz8o1OECZiKiZwYOtDzqpqcDNmww61DruZ+U6DDtERE1MmQKUlVlXRy4Xx/YEBDimTeT5uJ+VazHsEBH9IjkZ+OQT6+tlZzPoUNu4n5VrMewQEQF49lng44+tr5eby1tX9Kv6euDRR4H+/cWv9fXice5n5VocoExEPm/RInEXcmsVFYkrKhMB4gy8potHVlQAISHiYHdLAzH3s3IMhh0i8mmDB1s/RgcQ97li0CGDtmbvlZaKyxHExIiDkc2N25HJxPPcz8oxeBuLiHzS1atAYKC0oMN9rqipbdvan7138iTw2mvif3M/K+dj2CEin6NSAeHhwK1b1tcdNIj7XNGviostD74ffMD9rFyFt7GIyKeoVMDPP0urO3kysHevfdtDnsswndxS589zPytXYdghIp9x9ar0oDN1KrBnj33bQ56tvenkzfXqJX7lflbOx7BDRD7h3/8GunaVVjcrCygstGtzyIPodMC6dWLPTK9eQEaGuK6StdPEN292TPuofQw7ROT17rkH0Gql1V24kEHHl+XlAQUFpisb5+aKC0k+8ojl1xkyBOjUyf7tI8sw7BCRV1Mqgbo6aXUHDRI3aCTflJcHrFzZ8rheLx6/e7ft6eQGgwcDJ044rp3UPs7GIiKvNX++9KAjZddz8h46ndij05bVq4HXXxf/u/l0coOtWzl7zx0w7BCRV8rNFcdZWCsgALh+nX+J+zK9XrxN1d6mnHq9OG7H3HTy2Fjgww+BmTMd106ynEvDzptvvon+/fsjNDQUoaGhGD58OP7+978bz8+ZMwcymczkMWzYMJNrNDY2IjMzExEREQgODkZycjIuWjM8noi8zvvvA6tWWV8vIABobOTYCl9WXAz06AH87/9aVt4wnfzCBeDQIXGBwUOHgMpKrpvjTlw6ZicmJgavvvoqevfuDQDYtGkTUlJS8NVXX6Ffv34AgIcffhgbNmww1glotrVwVlYWPv74YxQVFSE8PBw5OTmYMmUKysrKIOfCBUQ+p7hY+jYOV67Yty3kWYqLgccea3v8TXOcTu4ZZIJgzdvqeGFhYVi5ciXmzp2LOXPm4Nq1a9i9e7fZslqtFl26dMHmzZuR/sv/3S5duoTY2Fjs27cPEydOtOg56+rqoFQqodVqERoaaq+XQkROpteLtw+k7Bw9ZAhvXfmaplPKe/QQx+hcumR5fbkcuHlT7BEk17D089ttZmPp9Xp88MEHuHHjBoYPH248fvjwYXTt2hX33HMPRo0ahVdeeQVdf1kso6ysDLdv30ZSUpKxfHR0NBISEnDs2LFWw05jYyMaGxuN39dJHcFIRG5DpxNvP92+bX1dBh3fY25KubWysxl0PIXLw05FRQWGDx+OW7duoVOnTti1axfuv/9+AMCkSZMwffp0xMXFobKyEi+88ALGjh2LsrIyKBQKaDQaBAQEoHPnzibXjIyMhEajafU58/Pz8dJLLzn0dRGR87Q2Rbg9HTqI6+9wjI7vuHoV6NPHtluWcrkYdFassF+7yLFcPhvr3nvvRXl5OY4fP44///nPmD17Nr755hsAQHp6OiZPnoyEhARMnToVf//73/H999/jk08+afOagiBA1to8QABLliyBVqs1Pqqqquz6mojIOfR64PHHpQWdjAyxPoOO7zBsAGtL0Jk/X7x1xaDjWVwedgICAtC7d28MHjwY+fn5GDBgANa0sopXVFQU4uLicPbsWQCASqWCTqdDbW2tSbmamhpERka2+pwKhcI4A8zwICLPUlwMdO8O7Nhhfd2cHMtn25B36NpV+r5ogLiOTmysuMgkb115HpeHneYEQTAZT9PUlStXUFVVhaioKADAoEGD4O/vjwMHDhjLqNVqnD59GiNGjHBKe4nI+QyzZqwZTGqwY8evC8GRb8jMFPdGk8pwo2D1au5O7qlcOmZn6dKlmDRpEmJjY3H9+nUUFRXh8OHD+PTTT1FfX49ly5Zh2rRpiIqKwoULF7B06VJERETg0UcfBQAolUrMnTsXOTk5CA8PR1hYGHJzc5GYmIjx48e78qURkYPo9eKtBCnzSLt0AWbMsH+byH3l5QFr19p2jZgYMehw3RzP5dKw8/PPP+PJJ5+EWq2GUqlE//798emnn2LChAloaGhARUUF3nvvPVy7dg1RUVEYM2YMduzYgZCQEOM1CgsL4efnhxkzZqChoQHjxo3Dxo0bucYOkZdSKoEbN6TVPXPGvm0h92bJlg/myOXAvn3i2J6oKGDkSPboeDq3W2fHFbjODpFnCA0Vt3KQQqkErl2za3PIza1eDTz7rPX1Fi/mAGRP4XHr7BARtaa+HmjSoWs1Bh3fdP68deU7dBAHrzPoeB+GHSJyaw8+KH3X6NBQ4Nw5cawO+R7DVg6WCAkBLl/mTCtv5XazsYiIDAYNkhZ05swRN/TUahl0vJ1OJ96uyswUv+p0v57LyLBsrE2XLkBdHYOON2PYISK3NGUKcOqU9fW6dAE2bOAHly/IywOCgsRxOWvXil+DgsTjgPhvIDu77WssWADU1Di+reRaDDtE5HZSU4F2FkpvFWdc+QbDFiHN97bS68XjhsCzYoU44Lh5D49cLh7/n/9xTnvJtTgbC5yNReROGhrEv86l4EBk76bXA0eOAFVV4q3Ku3dbL9t8R/KmO5z36iXe4mLvn+fjbCwi8ki/rBlqtZAQBh1vVlwMLFoEXLxoWXm9Xgw3WVni9wEBv/43+R6GHSJyG9u3A599Zn09uVwcYEreybA9iLX3Iaydek7ei2N2iMilGhrEQaJduwIzZ1pfPyAAuHPH/u0i96DXiz06UgZcWDP1nLwbe3aIyGVSU4GPPpJe/+JFoFs3uzWH3NCRI5bfumpKLhfH5RAB7NkhIhexJehMniz+pc+g4/3Uamn1srM5AJl+xZ4dIi9gmKWiVnvGxoUNDdKDzu9+B+zda9/2kPuKirKuvFwuBh1u+UBNMewQeThzs1RiYoA1a4C0NNe1qy1xcdLqRUcDJSX2bQu5t5EjxX/P1dXmx+3IZOKSAzNnAvHxnFJO5kkOO9euXcOJEydQU1ODu80WO/jDH/5gc8OIqH2tzVKprhaP79zpfoFn8GDg3/+WVvd//se9e6zIOpasfSOXi8H9scfEYNP037pMJn5dv979/p2Te5G0qODHH3+MWbNm4caNGwgJCYHM8C8OgEwmw9WrV+3aSEfjooLkifR6oEeP1gdvymTiX8SVle4REK5eBbp3B27ckFZ/2zbgiSfs2yZyPsMt11WrgH37TBcGbOsWlLkezNhYcT8sBh3fZennt6Sw06dPHzzyyCNYvnw5gqQudepGGHbIEx0+DIwZ0365Q4eA0aMd3Zq2qVTAzz9Lr5+cbNusLXIPli4MuHix+cDjaWPTyPEcuoJydXU1Fi5c6BVBh8hTWTpLRepsFnuxNeikpAC7d9utOeQiH3wAzJhhWdmCAuDll83f0nJ1cCfPJGnq+cSJE3Hy5El7t4WIrGDpLBVrZ7PY09Wr0oKOvz8wf764txGDjufbudO6W5CGrR6I7EVSz87kyZOxePFifPPNN0hMTIS/v7/J+eTkZLs0johaZ8kslZgYsZyrhIdLq3f1KtCpk33bQq5RXAxMn259PW71QPYkKew89dRTAIC//vWvLc7JZDLo9XrbWkVE7bJklsrq1a4b09Bk3oJVhgxh0PEGOh2wdi3w4ovS6nOrB7InSbex7t692+qDQYfIedLSxFsEzVcSjolx7bTz7t2l1Rs0CDhxwr5tIefLywOCgoCcHKC+3vr63OqB7I2LChJ5uLQ0cRCvu8xS6dULqKqyvt4jjwCffGL/9pBz5eUBK1fadg1u9UD2JjnslJSU4PXXX8e3334LmUyGvn37YvHixRjpygECRD7KXWapLFwI/PCD9fU448o76HTiTCqpuNUDOYqk21hbtmzB+PHjERQUhIULF2LBggUIDAzEuHHjsG3bNnu3kYg8wMKF4grH1uKMK++xbp04k8oaMhkwcSJQWCj+W2DQIUeQtKhg37598fTTT+PZZ581OV5QUIC3334b3377rd0a6AxcVJDINr16SevR+eor4IEH7N4ccpHMTHFQsjU++EAcZE8khaWf35J6dn744QdMnTq1xfHk5GRUVlZKuSQReaCffgI6dJAWdAAGHW9jzQyq2Fjgww8ZdMg5JIWd2NhYfP755y2Of/7554iNjbW5UUTk/vz9xd3Lre8bFkmtR+4rI6P9gfEyGbB/v7hnG/e0ImeRNEA5JycHCxcuRHl5OUaMGAGZTIajR49i48aNWLNmjb3bSERupkMH6WElNlbsESLvExAgDjBuazZWbi4wYYLz2kQESAw7f/7zn6FSqbBq1Sq8//77AMRxPDt27EBKSopdG0hE7qVjR+lB5ze/4cq43s4wwLigwHSwMmdakStJGqDsbThAmcgygYHArVvS6mZmAm+8Yd/2kPvS6cTZWefPi2N5MjK4dg7Zn0N3PSci39OjB4MOWS4gAMjKcnUriEQWh52wsDB8//33iIiIQOfOnSFrY+Obq1ev2qVxROQe4uKkj7P5zW8YdIjItSwOO4WFhQgJCTH+d1thh4i8R1AQ0NAgrW6vXsC5c/ZtDxGRtThmBxyzQ9QaW4LOtWuAUmnX5hARmXDoooKnTp1CRUWF8fuPPvoIqampWLp0KXQ6ncXXefPNN9G/f3+EhoYiNDQUw4cPx9///nfjeUEQsGzZMkRHRyMwMBCjR4/GmTNnTK7R2NiIzMxMREREIDg4GMnJybh48aKUl0VETTzwgLSgI5OJs7UYdIjIXUgKO/PmzcP3338PQFxNOT09HUFBQfjggw+Ql5dn8XViYmLw6quv4uTJkzh58iTGjh2LlJQUY6BZsWIFCgoKsHbtWpSWlkKlUmHChAm4fv268RpZWVnYtWsXioqKcPToUdTX12PKlCnQW7tBCxEZJSYC//yn9fUUCuDuXfu3h4jIJoIEoaGhwrlz5wRBEIRXX31VSEpKEgRBEI4ePSrExMRIuaRR586dhXfeeUe4e/euoFKphFdffdV47tatW4JSqRTeeustQRAE4dq1a4K/v79QVFRkLFNdXS106NBB+PTTT1t9jlu3bglardb4qKqqEgAIWq3WprYTeQOZTBDEvhnrHh07urrlRORrtFqtRZ/fknp2BEHA3V/+fDt48CAeeeQRAOI2EpcvX5YUuvR6PYqKinDjxg0MHz4clZWV0Gg0SEpKMpZRKBQYNWoUjh07BgAoKyvD7du3TcpER0cjISHBWMac/Px8KJVK44NbXJAz6PXA4cPA9u3iV3fsfDTcgrJWXJz0sT3kHBoNoFKJi0KqVOL3RL5CUtgZPHgwXn75ZWzevBklJSWYPHkyAKCyshKRkZFWXauiogKdOnWCQqHAM888g127duH++++H5pffxObXi4yMNJ7TaDQICAhA586dWy1jzpIlS6DVao2Pqqoqq9pMZK3iYnGdmjFjgJkzxa89eojH3YXUCZbduwMXLti1KWRnwcFAVBTw889AY6P4NSpKPE7kCySFndWrV+PUqVNYsGABnn/+efTu3RsAsHPnTowYMcKqa917770oLy/H8ePH8ec//xmzZ8/GN998YzzffIq7IAjtTntvr4xCoTAOijY8iByluFjc2bn5uPnqavG4qwPPiRPSg05gIPDjj/ZtD9lXcDBw86b5czdvMvCQb5C0gnL//v1NZmMZrFy5EvL2trxtJiAgwBiWBg8ejNLSUqxZswbPPfccALH3Jioqyli+pqbG2NujUqmg0+lQW1tr0rtTU1NjdegicgS9Hli0yPytIUEQQ0ZWFpCS0v5u0Y5gy3JZgYGtf4iSe9Bo2n+Pbt789RYXkbeS1LNTVVVlMr37xIkTyMrKwnvvvQd/f3+bGiQIAhobG9GzZ0+oVCocOHDAeE6n06GkpMQYZAYNGgR/f3+TMmq1GqdPn2bYIbdw5EjLHp2mBAGoqhLLOZstQWfAAAYdd9V0bNj991tW54EHHNkiIteT1LMzc+ZMPP3003jyySeh0WgwYcIE9OvXD1u2bIFGo8F//dd/WXSdpUuXYtKkSYiNjcX169dRVFSEw4cP49NPP4VMJkNWVhaWL1+O+Ph4xMfHY/ny5QgKCsLMmTMBAEqlEnPnzkVOTg7Cw8MRFhaG3NxcJCYmYvz48VJeGpFdqdX2LWcvtgSdhASgvNxuTSE7Ki4WexKtXWrs2jWHNIfIbUgKO6dPn8aDDz4IAHj//feRkJCA//f//h/279+PZ555xuKw8/PPP+PJJ5+EWq2GUqlE//798emnn2LChAkAgLy8PDQ0NCAjIwO1tbUYOnQo9u/fb9y2AhC3rvDz88OMGTPQ0NCAcePGYePGjVbfTiNyhCZ3YO1Szh5sCToyGWDmDja5gfffB9LTpdW95x67NoXI7UjaLqJTp044ffo0evTogeTkZPzud7/Dc889h59++gn33nsvGjxsDiq3iyBH0evFWVfV1ebH7chkQEwMUFnpnDE73buLt82k4uYy7ik3F1i1Snp9tZpjdsgzWfr5Lalnp1+/fnjrrbcwefJkHDhwAP/93/8NALh06RLCw8OltZjIS+j14hgctVrssSkoEP/ibr6GjaGHZfVq5wSduDgGHW/R0AAsXgycPQvU1Nh2WzEoiEGHvJ+ksPPaa6/h0UcfxcqVKzF79mwMGDAAALBnzx7j7S0iX2RuzERMjPiX9/btLY+vXg2kpTm+XYGBwK1b0usz6LiP1FTgo4/sc62gIODGDftci8idSd71XK/Xo66uzmTK94ULFxAUFISuXbvarYHOwNtYZA+G9XSa/0YZenDefx+IiPi1x2fkSOf06Pj7A3fuSKv71VecqeNObA06nTuLs+juuUfsDWKPDnk6Sz+/JYcdb8KwQ7YyjM1pbRaMs8fmNH1eqfh/BvfS0CD2xEgVG+v8f39Ejmb3MTu//e1v8fnnn6Nz584YOHBgmysUnzp1yrrWEnkonQ5Ytw4oKbF8PZ3Ro53TNgYd77J4sW31nTU2jMgdWRx2UlJSoFAoAACpqamOag+Rx8jLEwcfW7Ohp7PW0+kgablQEYOO+zCE6fPngSZrp1ptxw7njA0jcle8jQXexiLr5eUBK1daX+/QIcf37CgU4oektWJjgZ9+sn97SBopYdqcnBzg9dft0yYid+PQqedN1dfX4+7duybHGBjIm+l04oeQNQxjdkaOdEybDKqrpQWd7t25oac7MEwp37vX9vdDLgeys4EVK+zTNiJPJinsVFZWYsGCBTh8+DBuNZnPathtXG/rnyJEbmzePOv+2nbGejrV1UBiIlBba33djh0ZdNyBPaaUJySIPYe9egEZGUBAgD1aRuT5JIWdWbNmAQDeffddREZGtjlYmcibfPABsHGjdXUcvZ6O1NtWAODnJ/YmkGvZI+ikpAC7d9ujNUTeR1LY+frrr1FWVoZ7773X3u0hcls7dwJPPGF5+f/4D2DuXMeup9Ohg20Dim/ftl9bSJqGBmlBJyEBiI4G4uPF8WOBgfZvG5G3kBR2hgwZgqqqKoYd8hnFxcD06ZaXl8uB9esdexshIMC2oMOpCe5B6pTyuXOBrCy7NoXIa0kKO++88w6eeeYZVFdXIyEhAf7+/ibn+/fvb5fGEbkDvV7cAsIa2dmODToKhfReGZkMaDangJyo6XTyXr2A776z/hpyuTgmh4gsIyns/Pvf/8b58+fxxz/+0XhMJpNxgDJ5pSNH2l4wsLn0dMfOgJE648qAQcd17DWd3NFhmsjbSAo7f/rTnzBw4EBs376dA5TJ61mzEGC3bsDWrY5rCyAOeJbKWYsaUks5OdYvWdDadTidnMg6ksLOjz/+iD179qB37972bg+R24mKsrzsG284dkl+W/6uCArixo+uUF8vbqZ6/rzt19qxA5gxw/brEPkaSYvKjx07Fv/85z/t3RYit6HXA4cPA9u3i/8dE9N20JDLxV3NHTW9/KefbA86N27Yrz3UPr0e6NsXCAmxPejExgIffsigQySVpJ6dqVOn4tlnn0VFRQUSExNbDFBOTk62S+OIXKG4WByQ3HScTni4OHtJJjM/i6moCHjsMce0x98fuHNHWt3ISKC8nD06zlZcDDz+uPWDyOfNE9c++v57IDhYXH8nLs6xyxcQ+QJJe2N1aGOXQU8coMy9sciguFgMLc1/KwwhJzwcuHLl1+OxsY5dMFBq0PH3t20QM0lXXAxMmyatbmEhp5MTWcOhe2M13wuLyBsYppibi/+GXp3AQODgQaCmRhzL48i/uP/zP6X36DDoOF99PTBrFrBvn7T6nE5O5DhWjdl55JFHoNVqjd+/8soruHbtmvH7K1eu4P7777db44icqb0p5oIgnpfLxZWUR492XNDJyxMXJZTi7Fn7toXa9+CD4ticPXukB1ROJydyHKvCzmeffYbGxkbj96+99hquXr1q/P7OnTv417/+Zb/WETmRpdOyHT19W6cTl/+XQiYDOEnSuR58ECgtte0a3J2cyLGsCjvNh/dIGO5D5LYsnWJuzVR0KRQK6XV5h9m56uvtE3RWrbJPe4jIPEljdoi80ciR4hTz6mrz43ZkMvH8yJGOef6KCkDqTiucWu4cDQ3iXlZnz4obcP74o23XW7yYPTpEzmBV2JHJZC1WS+bqyeQt5HJgzRpxNlbzKeaGf+arV9t/nE5ZGTB4sPT6SiXQZOgcOUhqqunu5Pv3S79WbCxw7hzH6BA5i1VhRxAEzJkzB4pf+tlv3bqFZ555BsHBwQBgMp6HyBOlpQE7d7ZcZycmxjFTzG39W6GmBujSxT5todY1DzpS+PkBAwcCX3wBdOpkl2YRkYWsWmen6cafbdmwYYPkBrkC19mh5vR6cXaWWu24Kea2Bp3vvgPuvdc+bSHz9HpxqYGHH7btOnv3itfgwoBE9mXp57ekRQW9DcMOOZutt64A8+OKyH7MraQtxZAhwIkT9mkTEZly6KKCRGQbBh33tmOHuN2DrRh0iNwDww6Rk9l6+4pBx7Fyc6VNBf/P/wQuXxY3/ezVC9i8mWNziNwFww6Rk3zzDdCvn/T6MhnX0XEUnQ5Ytw7YtEncOFWKN94QtxMhIvfDsEPkBLb25pw9y5WR7c2wZs7evbavl5OSwqBD5M4YdogcjLet3I89ppIbpKQAu3fb51pE5BhWbRdhb/n5+RgyZAhCQkLQtWtXpKamtthba86cOcbFDA2PYcOGmZRpbGxEZmYmIiIiEBwcjOTkZFy0dQoFkR188430ul9/zaDjCPYIOgoF8Oc/AzdvMugQeQKXhp2SkhLMnz8fx48fx4EDB3Dnzh0kJSXhRrN17x9++GGo1WrjY9++fSbns7KysGvXLhQVFeHo0aOor6/HlClToNfrnflyiFqQOkbnu++AxET7toXEW1f26NHZtk0c48NbV0SewaW3sT799FOT7zds2ICuXbuirKwMv//9743HFQoFVCqV2WtotVqsX78emzdvxvjx4wEAW7ZsQWxsLA4ePIiJEye2qNPY2Giy2nNdXZ09Xg65AWcsBmgpW7YC4GKBjrF4se3XKCqy/0raRORYLu3ZaU6r1QIAwsLCTI4fPnwYXbt2RZ8+ffDUU0+hpqbGeK6srAy3b99GUlKS8Vh0dDQSEhJw7Ngxs8+Tn58PpVJpfMTGxjrg1ZCzFRcDPXoAY8YAM2eKX3v0EI87m0wG3L4trS5vXTnO2bO21c/JAdLT7dMWInIetwk7giAgOzsbDz30EBISEozHJ02ahK1bt+KLL77AqlWrUFpairFjxxp7ZjQaDQICAtC5c2eT60VGRkKj0Zh9riVLlkCr1RofVVVVjnth5BTFxeIGns2HalVXi8edGXhsGZDMoONY8fHS6snlYq/Q66/btz1E5BxuMxtrwYIF+Prrr3H06FGT4+lN/oxKSEjA4MGDERcXh08++QRpbfQlC4LQ6o7sCoXCuJkpeT69XlzW31xQEAQxfGRlibNmHHVL61//Esfn2DJMjEHH8VauBP73fy0vP3Ag8Ic/ABkZ3KGcyJO5Rc9OZmYm9uzZg0OHDiEmJqbNslFRUYiLi8PZX/qjVSoVdDodamtrTcrV1NQgMjLSYW0m93HkSNv7FwkCUFUllnMEmQy47z7pQYezrpwnMFAMve0x9OScOiUGZQYdIs/m0rAjCAIWLFiA4uJifPHFF+jZs2e7da5cuYKqqipERUUBAAYNGgR/f38cOHDAWEatVuP06dMYMWKEw9pO7kOttm85a9i6ho5azVlXzrZ7d+uBp2dPoLBQnFK+YoVTm0VEDuTS21jz58/Htm3b8NFHHyEkJMQ4xkapVCIwMBD19fVYtmwZpk2bhqioKFy4cAFLly5FREQEHn30UWPZuXPnIicnB+Hh4QgLC0Nubi4SExONs7PIu/2Se+1WzlLNloSyWlAQ0MokQ3Kw3bt/XUH57FlxLM/KlZxKTuStZILgug701sbUbNiwAXPmzEFDQwNSU1Px1Vdf4dq1a4iKisKYMWPw3//93yYzqG7duoXFixdj27ZtaGhowLhx47Bu3TqLZ1lZukU8uSe9Xpx1VV1t/naQTAbExACVlfYds2NLr46/v7gfExERSWfp57dLw467YNjxfIbZWIBp4DEEkp077bs2SocOto2z4W+dbQwbdxp2GOcAYiLfZOnnt1sMUCayVVqaGGi6dTM9HhNj/6AjkzHouFJenngL8NlngbVrxa9BQeJxIiJz3GbqOZGt0tLEgaeOXEGZm3q6Vl6eOLamOb3+1+McWExEzfE2FngbiyzDoONaOp3Yg9PWFH+5XJxJxVtaRL6Bt7GI7Ehq0OnQAThzhkHHHtata38tI71eLEdE1BRvYxG1Q2rQ+fFHoHt3+7bFl50/b99yROQ7GHbIrbl61o3UoOPnx6BjC3Nr4PTqZVldS8sRke/gmB1wzI67yssDCgpMb13I5UB2tnMGoUoNOjIZcPeufdviK3Q6YNAg4PTpluemTgX27eOYHSL6FcfskEczzLpp/sFmmHXj6GnGtgxGZtCRJi8PUCjMBx0A+PhjcfHItmRnM+gQUUsMO+R2dDqxR6ctBQWOW4HYlqDDflJpWptS3tz58+K6Os2XEzBs3Mlp50RkDsMOuZ1581wz66akhEHHFSwJt83L37wpbti5YAE37iSi9nGAMrkNnQ545hlg40bLyttz1g3X0HEevd504cdTp9oPt02dPSveqsrKclgTicjLMOyQW8jLA1atsm68i71m3TDoOE9xMbBoEXDx4q/HOnWy7hrx8fZtExF5P87GAmdjuZql4zWastesG4XCtrE//O2x3PvvA+nptl/n5k0gMND26xCR5+NsLPII1o7XMLDHrBsGHefJzbVP0ElJYdAhIuvxNha5lCVbADSXnm77YFTeunIewy1KW6WkALt3234dIvI9DDvkUtYOMu7WDdi61bbnZNBxHmt77mSylj/fBx4Ajh1jjw4RScewQy5lzSBjmQx4442Wa6xYo7xcel2AQcda1vbcffaZuHGqq7YHISLvxLBDLpWRIY7naO8DMSYGWLMGSEuT/lwVFcDAgdLqfvcdcO+90p/bV1nTcxcbC4wdC0yY4Lj2EJFv4gBlcqmAAHGwcVvS04ELF2wLOjIZ0L+/tLqCwKAjlTU9d6tX29ZrR0TUGoYdcrkVK8Sl/lvbAqCoyLYPQaljdAICeNvKVhkZlr13O3bYFmaJiNrCdXbAdXacpfnKuSNHmn4Q6nTiGA97jtewJeg0Ntr23CRqbx2lnBzg9ded1x4i8h6Wfn5zzA45hbmVc5uPw7H3FgC29AYx6NiPYZmAggLTsVlyuXgLk3taEZGjsWcH7NlxtOJi4LHHWt4SMvS67Nxp/1sY3NDT/Tii546IfJuln98MO2DYcSS9HujRw7RHpymZTOzhqay03+BUudy6PbaaUqsBlco+7SAiIsfidhHkFo4caT3oAGIvSlWVWM4etm6VHnSCghh0iIi8EcfskEOp1fYt15ryculr6ABi0Llxw7Y2EBGRe2LYIYeKirJvOXNs3f6Bt66IiLwbb2ORQ40cKY7JaS2QyGTiyrkjR0q7vj32uWLQISLybgw75FByuTi9HGgZTAzfS105V6mU3q4OHTjriojIVzDskMOlpYnTy7t1Mz0eEyN92rlKBdTVSW+TNZtTEhGRZ+OYHXKKtDQgJaXtFZQtdfUq8PPP0trRoQODDhGRr2HYIaeRy4HRo22/Tni4tHpbtgCzZtn+/ERE5Fl4G4s8ii0Dkhl0iIh8k0vDTn5+PoYMGYKQkBB07doVqamp+Ne//mVSRhAELFu2DNHR0QgMDMTo0aNx5swZkzKNjY3IzMxEREQEgoODkZycjIttrWRHHuebb7gFBBERSePSsFNSUoL58+fj+PHjOHDgAO7cuYOkpCTcaLK624oVK1BQUIC1a9eitLQUKpUKEyZMwPXr141lsrKysGvXLhQVFeHo0aOor6/HlClToOfgDIfR6cRZVJmZ4ledznHPJZMB/fpJq3vkCIMOEZHPE9xITU2NAEAoKSkRBEEQ7t69K6hUKuHVV181lrl165agVCqFt956SxAEQbh27Zrg7+8vFBUVGctUV1cLHTp0ED799FOLnler1QoABK1Wa8dX470WLxYEuVwQxBghPuRy8bi9NX0Oax6hofZvCxERuRdLP7/dasyOVqsFAISFhQEAKisrodFokJSUZCyjUCgwatQoHDt2DABQVlaG27dvm5SJjo5GQkKCsUxzjY2NqKurM3mQZfLygJUrW85o0uvF43l59nsuW25b/fJPyafp9cDhw8D27eJXdnQSka9ym7AjCAKys7Px0EMPISEhAQCg0WgAAJGRkSZlIyMjjec0Gg0CAgLQuXPnVss0l5+fD6VSaXzExsba++V4JZ0OWLWq7TIFBfa5pWVL0PnhB9uf39MVF4u7zY8ZA8ycKX7t0UM8TkTka9wm7CxYsABff/01tm/f3uKcrNknnyAILY4111aZJUuWQKvVGh9VVVXSG+5DHn64/R3F9Xpg3Trbnuf/+/+k1+3QAejZ07bn93TFxcBjj7Xcbb66WjzOwENEvsYtwk5mZib27NmDQ4cOISYmxnhc9cumRc17aGpqaoy9PSqVCjqdDrW1ta2WaU6hUCA0NNTkQW3LyQEOHbKs7Pnztj3XiBHS6/r6rRq9Hli0yPygbMOxrCz+nIjIt7g07AiCgAULFqC4uBhffPEFejb7k7xnz55QqVQ4cOCA8ZhOp0NJSQlG/PKJOGjQIPj7+5uUUavVOH36tLEM2SYnR7w9ZalevaQ9T1kZp5fb6siRlj06TQkCUFUlliMi8hUuXUF5/vz52LZtGz766COEhIQYe3CUSiUCAwMhk8mQlZWF5cuXIz4+HvHx8Vi+fDmCgoIwc+ZMY9m5c+ciJycH4eHhCAsLQ25uLhITEzF+/HhXvjyvkJdnXdCRy4GMDOue49w5ID7eujrNMeiI1Gr7liMi8gYuDTtvvvkmAGB0sz0ENmzYgDlz5gAA8vLy0NDQgIyMDNTW1mLo0KHYv38/QkJCjOULCwvh5+eHGTNmoKGhAePGjcPGjRshl7LxEhnpdNYFHQDIzgYCAiwvb+vu42fOAPffL72+t4mKsm85IiJvIBME/k1cV1cHpVIJrVbL8TtNrF4NPPus5eXHjAG++MLy8rYGHf7LbUmvF2ddVVeb//nIZOJu85WV0jZhJSJyJ5Z+frvFAGVyLw0NwIIF1t+++vRTy8ufO8eg4whyObBmjfjfzcc/Gb5fvZpBh4h8C8MOmUhNBYKCgP/9X3Egq6WsvX1lyxidH3+UXtcXpKUBO3cC3bqZHo+JEY+npbmmXURErsLbWOBtLIOUFGDPHuvrZWe3v9hgUwqF9IUH/fyA27el1fU1er0460qtFsfojBzJHh0i8i6Wfn67dIAyuY/t2x0fdDQa2wbGMuhYRy4Hmo39JyLySbyNRXj/fXFLAWvI5cDixZYHneBg24LOjz8y6BARkTTs2fFxubnW3YKKjRV7czIyLB+jExwM3LwprX0AByMTEZFt2LPjw/LyrAs6AJCcLG43YGnQ0WikB52TJxl0iIjIdhygDN8coKzTibOurN0j6eZNIDDQ8vJSt3+oqQG6dJFWl4iIfAPX2aE2rVtnfdBJSXFO0FEqGXSIiMh+GHZ8lLU7kycnA7t3W15eatAJCACuXZNWl4iIyByGHR9lzc7k27YBH31kWdmffrJt5/LGRul1iYiIzGHY8VEZGZYtMLdjB/DEE+2X0+vFdXDi4qS3iaPHiIjIERh2fFRAgDiFvC05OcCMGe1fq7hYDDrWjgEy+Mc/GHSIiMhxuM6OD1uxQvxaUGAaVORyMQgZzreluBiYNk16G44dAx58UHp9IiKi9nDqOXxz6nlTOp04O+v8eXEsj6ULBur14uwsW1Y29sZ/fdyTiojIObg3FlksIEBcKNBaDz3EoNNccTGwaBFw8eKvx2JigDVruNs4EZGrcMwOSZKUBBw/Lr2+twadxx4zDToAUF0tHi8udk27iIh8HcMOWS0oCDhwQFpdmcw7g45eL/bomHtthmNZWdIHcRMRkXQMO2SVoCCgoUFa3bNngbt37dsed3HkSMsenaYEAaiqEssREZFzccwOWax7d2lBx8/PtrE97qj5oO7wcMvqqdWObRcREbXEsEMW+c1vxJ4Ja02YAOzfb//2uFJeXsvp+h0s7CONinJMm4iIqHUMO9Su3/4WqKy0vt6UKcDHH9u/Pa5gmE6+ahWwd2/L8+3dnpPJxFlZI0c6pn1ERNQ6hh1q029/C3z1lfX1vCnomJtO3pbmg7ANe4WtXs31doiIXIFhh1rVsydw4YL19SZM8K6g89hj1s0gCw0FtNpfv4+JEYMO19khInINhh1qQasFIiOl7UAeGOg9Y3Tamk7ellmzgOnTuYIyEZG7YNghE717izOMpAgMBG7etG97XKm96eStiY8HRo+2e3OIiEgirrNDRr16SQ86sbHeFXQAadPE5XJxbzEiInIfDDsEQLxd88MP0ur27An89JN92+MOpEwTz862bBNVIiJyHoYdQl4e8MYb0uoOHCg9JLm7kSPFwcWG2VRtkcuBxYuBFSsc3y4iIrIOw46P0+nEBfKkGDgQOHXKvu1xJ3K5uFs50DLwGL6fNAkoLBRv4THoEBG5J4YdH6bTAenp0jan7NHDu4OOQVoasHMn0K2b6fGYGODDD4F9+8QNPnnriojIfXE2lo8yt+WBpXr1As6ds3+b3FVaGpCSIs7O4nRyIiLPw7Djg/LygJUrra+nUAA//wwolfZvk7uTyzmdnIjIU7n0NtaXX36JqVOnIjo6GjKZDLt37zY5P2fOHMhkMpPHsGHDTMo0NjYiMzMTERERCA4ORnJyMi5KWRzFR0gdo/Ob3wC3bvlm0CEiIs/m0rBz48YNDBgwAGvXrm21zMMPPwy1Wm187Nu3z+R8VlYWdu3ahaKiIhw9ehT19fWYMmUK9FLuz3i5hgZg7Fjrb10tXCh9/R0iIiJXc+ltrEmTJmHSpEltllEoFFCpVGbPabVarF+/Hps3b8b48eMBAFu2bEFsbCwOHjyIiRMn2r3Nnio1FfjoI+vqyOXiujGcZURERJ7M7WdjHT58GF27dkWfPn3w1FNPoaamxniurKwMt2/fRlJSkvFYdHQ0EhIScOzYsVav2djYiLq6OpOHN5s61fqgk5rK6dREROQd3DrsTJo0CVu3bsUXX3yBVatWobS0FGPHjkXjLztUajQaBAQEoHPnzib1IiMjodFoWr1ufn4+lEql8REbG+vQ1+FKU6cCe/daV0cuB3bs4HRqIiLyDm49Gys9Pd343wkJCRg8eDDi4uLwySefIC0trdV6giBA1sayt0uWLEF2drbx+7q6Oq8MPMnJ1gcdgFseEBGRd3Hrnp3moqKiEBcXh7NnzwIAVCoVdDodamtrTcrV1NQgMjKy1esoFAqEhoaaPLzNs88CH39sXR1ueUBERN7Io8LOlStXUFVVhahfdmgcNGgQ/P39ceDAAWMZtVqN06dPY8SIEa5qpsvl5QGrV1tX53e/4xgdIiLyTi69jVVfX49zTZbiraysRHl5OcLCwhAWFoZly5Zh2rRpiIqKwoULF7B06VJERETg0UcfBQAolUrMnTsXOTk5CA8PR1hYGHJzc5GYmGicneVrpK6jc+AAb10REZF3cmnYOXnyJMaMGWP83jCOZvbs2XjzzTdRUVGB9957D9euXUNUVBTGjBmDHTt2ICQkxFinsLAQfn5+mDFjBhoaGjBu3Dhs3LgRch9by7++HnjySeD4cevX0UlJAQIDHdMuIiIiV5MJgiC4uhGuVldXB6VSCa1W65Hjdx58ECgtlVZ3yhTrx/YQERG5A0s/v916Nha1b8gQ4ORJaXUZdIiIyBd41ABlMrV1q/SgM3Uqgw4REfkGhh0PVVwM/Md/SKublQXs2WPX5hAREbkthh0PpNcDixZZX8+wjk5hof3bRERE5K44ZscDHTkCXLxoefkePcRwlJHB6eVEROR7GHY8jF4PfP65dXUqKoBOnRzTHiIiInfHsOMh9HrglVeANWuAq1ctrzdkCIMOERH5NoYdD1BcDDz9NHDlinX1Bg8GTpxwTJuIiIg8BQcou7niYmDaNOuDzpYt0hcaJCIi8iYMO25MrwcWLrSuTmws8OGHwKxZjmkTERGRp2HYcWOzZgHV1ZaX/8tfgMpKIC3NcW0iIiLyNAw7bkivBx5/HNixw7p648aJa+kQERHRrxh23ExxMRAXZ33QiY0FRo50TJuIiIg8GWdjuZHiYuCxxwBr96GXyYDVq9mrQ0REZA57dtyEYQsIa4NOeDiwcyfH6RAREbWGPTtuwtotIABg4kTgk0/Yo0NERNQW9uy4CbXauvJyubhzOYMOERFR2xh23ERUlHXls7O5qScREZElGHbcxMiRQEyMONi4LR06AIsXAytWOKddREREno5hx03I5eImn0DrgeePfwQaGhh0iIiIrMGw40bS0sSZVd26mR43bAHx7ru8dUVERGQtzsZyM2lpQEqKODtLrRbH8owcyYHIREREUjHsuCG5HBg92tWtICIi8g4MO06g0wHr1gHnzwO9egEZGbwdRURE5CwMOw6WlwcUFIgrJBvk5opTxznQmIiIyPEYdhxErwdmzTK/oadeD6xcKf43Aw8REZFjcTaWA1i6c3lBgXiLi4iIiByHYcfODDuXV1e3X1avF8fyEBERkeMw7NiRlJ3Lz593XHuIiIiIYceupOxc3quXY9pCREREIoYdO5Kyc3lGhmPaQkRERCKGHTvizuVERETuh2HHjrhzORERkftxadj58ssvMXXqVERHR0Mmk2H37t0m5wVBwLJlyxAdHY3AwECMHj0aZ86cMSnT2NiIzMxMREREIDg4GMnJybho7cAZO+HO5URERO7HpWHnxo0bGDBgANauXWv2/IoVK1BQUIC1a9eitLQUKpUKEyZMwPXr141lsrKysGvXLhQVFeHo0aOor6/HlClToG+6ZLETcedyIiIi9yITBGsmSjuOTCbDrl27kJqaCkDs1YmOjkZWVhaee+45AGIvTmRkJF577TXMmzcPWq0WXbp0webNm5Geng4AuHTpEmJjY7Fv3z5MnDjRoueuq6uDUqmEVqtFaGioXV6PXs+dy4mIiBzJ0s9vtx2zU1lZCY1Gg6SkJOMxhUKBUaNG4dixYwCAsrIy3L5926RMdHQ0EhISjGXMaWxsRF1dncnD3gw7lz/xhPiVQYeIiMg13DbsaDQaAEBkZKTJ8cjISOM5jUaDgIAAdO7cudUy5uTn50OpVBofsbGxdm49ERERuQu3DTsGsmYjfQVBaHGsufbKLFmyBFqt1vioqqqyS1uJiIjI/bht2FGpVADQooempqbG2NujUqmg0+lQW1vbahlzFAoFQkNDTR5ERETkndw27PTs2RMqlQoHDhwwHtPpdCgpKcGIESMAAIMGDYK/v79JGbVajdOnTxvLEBERkW/zc+WT19fX49y5c8bvKysrUV5ejrCwMHTv3h1ZWVlYvnw54uPjER8fj+XLlyMoKAgzZ84EACiVSsydOxc5OTkIDw9HWFgYcnNzkZiYiPHjx7vqZREREZEbcWnYOXnyJMaMGWP8Pjs7GwAwe/ZsbNy4EXl5eWhoaEBGRgZqa2sxdOhQ7N+/HyEhIcY6hYWF8PPzw4wZM9DQ0IBx48Zh48aNkHP6ExEREcGN1tlxJUess0NERESO5fHr7BARERHZA8MOEREReTWXjtlxF4Y7eY5YSZmIiIgcw/C53d6IHIYdwLixKFdSJiIi8jzXr1+HUqls9TwHKAO4e/cuLl26hJCQkHZXZ7aXuro6xMbGoqqqioOi3RzfK8/B98oz8H3yHO7+XgmCgOvXryM6OhodOrQ+Moc9OwA6dOiAmJgYlzw3V3D2HHyvPAffK8/A98lzuPN71VaPjgEHKBMREZFXY9ghIiIir8aw4yIKhQIvvvgiFAqFq5tC7eB75Tn4XnkGvk+ew1veKw5QJiIiIq/Gnh0iIiLyagw7RERE5NUYdoiIiMirMewQERGRV2PYcaJly5ZBJpOZPFQqlaubRQC+/PJLTJ06FdHR0ZDJZNi9e7fJeUEQsGzZMkRHRyMwMBCjR4/GmTNnXNNYH9feezVnzpwWv2fDhg1zTWN9XH5+PoYMGYKQkBB07doVqamp+Ne//mVShr9brmfJ++Tpv1cMO07Wr18/qNVq46OiosLVTSIAN27cwIABA7B27Vqz51esWIGCggKsXbsWpaWlUKlUmDBhgnFfNXKe9t4rAHj44YdNfs/27dvnxBaSQUlJCebPn4/jx4/jwIEDuHPnDpKSknDjxg1jGf5uuZ4l7xPg4b9XAjnNiy++KAwYMMDVzaB2ABB27dpl/P7u3buCSqUSXn31VeOxW7duCUqlUnjrrbdc0EIyaP5eCYIgzJ49W0hJSXFJe6htNTU1AgChpKREEAT+brmr5u+TIHj+7xV7dpzs7NmziI6ORs+ePfH444/jhx9+cHWTqB2VlZXQaDRISkoyHlMoFBg1ahSOHTvmwpZRaw4fPoyuXbuiT58+eOqpp1BTU+PqJhEArVYLAAgLCwPA3y131fx9MvDk3yuGHScaOnQo3nvvPXz22Wd4++23odFoMGLECFy5csXVTaM2aDQaAEBkZKTJ8cjISOM5ch+TJk3C1q1b8cUXX2DVqlUoLS3F2LFj0djY6Oqm+TRBEJCdnY2HHnoICQkJAPi75Y7MvU+A5/9ecddzJ5o0aZLxvxMTEzF8+HD06tULmzZtQnZ2tgtbRpaQyWQm3wuC0OIYuV56errxvxMSEjB48GDExcXhk08+QVpamgtb5tsWLFiAr7/+GkePHm1xjr9b7qO198nTf6/Ys+NCwcHBSExMxNmzZ13dFGqDYcZc8780a2pqWvxFSu4nKioKcXFx/D1zoczMTOzZsweHDh1CTEyM8Th/t9xLa++TOZ72e8Ww40KNjY349ttvERUV5eqmUBt69uwJlUqFAwcOGI/pdDqUlJRgxIgRLmwZWeLKlSuoqqri75kLCIKABQsWoLi4GF988QV69uxpcp6/W+6hvffJHE/7veJtLCfKzc3F1KlT0b17d9TU1ODll19GXV0dZs+e7eqm+bz6+nqcO3fO+H1lZSXKy8sRFhaG7t27IysrC8uXL0d8fDzi4+OxfPlyBAUFYebMmS5stW9q670KCwvDsmXLMG3aNERFReHChQtYunQpIiIi8Oijj7qw1b5p/vz52LZtGz766COEhIQYe3CUSiUCAwMhk8n4u+UG2nuf6uvrPf/3ypVTwXxNenq6EBUVJfj7+wvR0dFCWlqacObMGVc3iwRBOHTokACgxWP27NmCIIhTZF988UVBpVIJCoVC+P3vfy9UVFS4ttE+qq336ubNm0JSUpLQpUsXwd/fX+jevbswe/Zs4aeffnJ1s32SufcJgLBhwwZjGf5uuV5775M3/F7JBEEQnBmuiIiIiJyJY3aIiIjIqzHsEBERkVdj2CEiIiKvxrBDREREXo1hh4iIiLwaww4RERF5NYYdIiIi8moMO0REROTVGHaIiIjIqzHsEDnZnDlzIJPJWjzOnTuH0aNHIysrq0Wd3bt3QyaTGb/fuHGj2Wt07NjR5HlSU1PbbMtXX32F6dOnIzIyEh07dkSfPn3w1FNP4fvvvzcpt2nTJjz44IMIDg5GSEgIfv/732Pv3r0mZQ4fPgyZTIaEhATo9XqTc/fccw82btxo8rxTpkxB165d0bFjR/To0QPp6em4fPmyybWuXbvWos0PPPAAli1bZvy+R48ekMlkKCoqalG2X79+kMlkJs9tKC+TyRAUFISEhAT83//7fwEAo0ePNvtzNTx69OhhLNf8fTpz5gxmzJiBLl26QKFQID4+Hi+88AJu3rxpUs7w/MePHzc5npWVhdGjR7d4Da2pq6vD888/j/vuuw8dO3aESqXC+PHjUVxcjKYL41vbLik/R7lcjujoaMydOxe1tbUWvwYiZ2HYIXKBhx9+GGq12uRhyU7DTYWGhra4xo8//mhx/b1792LYsGFobGzE1q1b8e2332Lz5s1QKpV44YUXjOVyc3Mxb948zJgxA//85z9x4sQJjBw5EikpKVi7dm2L654/fx7vvfdeq89bU1OD8ePHIyIiAp999hm+/fZbvPvuu4iKimrxAWyp2NhYbNiwweTY8ePHodFoEBwc3KL8X//6V6jVanz99ddITU3FM888gx07dqC4uNj4szxx4gQA4ODBg8ZjpaWlZp//+PHjGDp0KHQ6HT755BN8//33WL58OTZt2oQJEyZAp9OZlO/YsSOee+45Sa8VAK5du4YRI0bgvffew5IlS3Dq1Cl8+eWXSE9PR15eHrRaraR2Sf05/vTTT9i6dSu+/PJLLFy4UPLrInIU7npO5AIKhQIqlcqma8hkMsnXuHnzJv74xz/ikUcewa5du4zHe/bsiaFDhxp7VI4fP45Vq1bhjTfeQGZmprHcK6+8glu3biE7OxspKSmIjY01nsvMzMSLL76IJ554wqSnyeDYsWOoq6vDO++8Az8/P+Pzjh07VtJrAYBZs2ahsLAQVVVVxra8++67mDVrltngFRISYvzZvfzyy3j//fexe/dupKenG8vcunULABAeHt7mz1kQBMydOxd9+/ZFcXExOnQQ/4aMi4tDnz59MHDgQBQWFpqEm3nz5uHNN9/Evn378Mgjj1j9epcuXYoLFy7g+++/R3R0tPF4nz59jD93Ke2y5efYrVs3/OEPfzDbM0TkauzZIfJBn332GS5fvoy8vDyz5++55x4AwPbt29GpUyfMmzevRZmcnBzcvn0bH374ocnxrKws3Llzx2yvDwCoVCrcuXMHu3btgr32IY6MjMTEiROxadMmAGKY27FjB/70pz9ZVL9jx464ffu2pOcuLy/HN998g+zsbGOgMBgwYADGjx+P7du3mxzv0aMHnnnmGSxZsgR379616vnu3r2LoqIizJo1yyToGHTq1Al+fn6S2mXLz7G6uhp79+7F0KFDrXo9RM7AsEPkAnv37kWnTp2Mj+nTp1t9Da1Wa3KNTp06ISkpyaK6Z8+eBQDcd999bZb7/vvv0atXLwQEBLQ4Fx0dDaVS2WJ8T1BQEF588UXk5+cbb6c0NWzYMCxduhQzZ85EREQEJk2ahJUrV+Lnn3+2qO2t+dOf/oSNGzdCEATs3LkTvXr1wgMPPNBmnTt37mDjxo2oqKjAuHHjJD2v4fX37dvX7Pm+ffu2+BkBwF/+8hdUVlZi69atVj3f5cuXUVtba9F7J6Vd1vwcn3vuOXTq1AmBgYGIiYmBTCZDQUGBVa+HyBkYdohcYMyYMSgvLzc+3njjDauvERISYnKN8vLyFuMtWmOvHhVBEEwGThvMnTsXEREReO2118zWe+WVV6DRaPDWW2/h/vvvx1tvvYX77rsPFRUVktsyefJk1NfX48svv8S7777bZm9E0w/p+fPnY/HixWZ7r+yhtZ9Rly5dkJubi//6r/9qMXamvesBMHtNe7TLmp/j4sWLUV5ejq+//hqff/65sX7zAepErsawQ+QCwcHB6N27t/ERFRUFQBx0bK435Nq1awgNDTU51qFDB5Nr9O7dG926dbPo+fv06QMA+O6779otd/78ebMfxpcuXUJdXR3i4+NbnPPz88PLL7+MNWvW4NKlS2avHR4ejunTp2PVqlX49ttvER0djddffx0AjK+1tZ+FUqk0+5xPPvkkXnzxRfzjH//ArFmzWn1dhg/pH3/8EfX19VixYkWLWz2WMvwsv/nmG7Pnv/vuO7M/IwDIzs5GQ0MD1q1bZ/HzdenSBZ07d8a3337rkHZZ83OMiIhA7969ER8fj7Fjx2L16tU4duwYDh06ZPHrIXIGhh0iN3Lffffh5MmTLY6Xlpbi3nvvtdvzJCUlISIiAitWrDB73jBA+fHHH0d9fb1xanZTr7/+Ovz9/TFt2jSz15g+fTr69euHl156qd32BAQEoFevXrhx4wYAID4+Hh06dGgx+0mtVqO6urrVn8Wf/vQnlJSUICUlBZ07d271+Qwf0tHR0Tb3kDzwwAO47777UFhY2GL8zT//+U8cPHgQTzzxhNm6nTp1wgsvvIBXXnkFdXV1Fj1fhw4dkJ6ejq1bt5oNkjdu3MCdO3dsapelP8fm5HI5AKChocHiOkTOwNlYRG4kIyMDa9euxfz58/H0008jMDAQBw4cwPr167F582aTsoIgQKPRtLhG165djb0UWq0W5eXlJufDwsLQvXt3vPPOO5g+fTqSk5OxcOFC9O7dG5cvX8b777+Pn376CUVFRRg+fDgWLVqExYsXQ6fTITU1Fbdv38aWLVuwZs0arF692mQmVnOvvvoqJk6caHJs7969KCoqwuOPP44+ffpAEAR8/PHH2Ldvn/E2XEhICObNm4ecnBz4+flhwIABuHTpEp5//nn07du31bFJffv2xeXLlxEUFNTuz9peZDIZ3nnnHSQlJWHatGlYsmQJVCoV/vGPfyAnJwfDhw83u3aSwdNPP43CwkJs377d4sG9y5cvx+HDhzF06FC88sorGDx4MPz9/XHkyBHk5+ejtLQU99xzj+R2WfpzvH79OjQaDQRBQFVVFfLy8hAREYERI0ZY9DqInEYgIqeaPXu2kJKS0ur5kydPChMnThS6du0qhIaGCoMHDxa2b99uUmbDhg0CALMPtVptfB5z52fPnm28TmlpqZCWliZ06dJFUCgUQu/evYWnn35aOHv2rMnzrV+/Xhg8eLAQGBgoBAUFCQ899JCwZ88ekzKHDh0SAAi1tbUmx5OSkgQAwoYNGwRBEITz588LTz31lNCnTx8hMDBQuOeee4QhQ4YYzxvcunVL+Otf/yr07dtXCAwMFOLi4oQ5c+YYX59BXFycUFhY2OrPU6lUmly7vfIGlZWVAgDhq6++anFu1KhRwqJFi0yOff3118K0adOE8PBwwd/fX+jVq5fwl7/8Rbhx40a77d22bZsAQBg1alS77TK4du2a8H/+z/8R4uPjhYCAACEyMlIYP368sGvXLuHu3bt2aVdT5n6OTf9ddenSRXjkkUfM/ryIXE0mCHYaqUhERETkhjhmh4iIiLwaww4RkZtpvn5S08eRI0dc3Twij8PbWEREbubcuXOtnuvWrRsCAwOd2Boiz8ewQ0RERF6Nt7GIiIjIqzHsEBERkVdj2CEiIiKvxrBDREREXo1hh4iIiLwaww4RERF5NYYdIiIi8mr/P6f/QGEmLQBcAAAAAElFTkSuQmCC\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": 13, + "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": 14, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df.describe()\n", + "plt.scatter(cdf.CYLINDERS, cdf.CO2EMISSIONS, color='blue')\n", + "plt.xlabel(\"Cylinders\")\n", + "plt.ylabel(\"Emission\")\n", + "plt.show()" + ] + }, + { + "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": 15, + "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": 16, + "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": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[39.58478793]]\n", + "Intercept: [123.87889336]\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": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Emission')" + ] + }, + "execution_count": 18, + "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": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean absolute error: 25.12\n", + "Residual sum of squares (MSE): 1069.33\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": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Rq9xzD9ChA9DQYFu/uDhg2DCnDInIq8kW7IwePRrl5eUoKysz3QYMGIAZM2agrKwMt912GzQaDYqLi0199Ho9Dh48iKFDhwIA+vfvj4CAALM2VVVVOH78uKkNEZE7uecewMKVe6usWiUmJRORbWTL2QkNDUViYqLZsZCQEERERJiOZ2ZmYtmyZUhISEBCQgKWLVuG4OBgTP/P3K9arcbs2bORnZ2NiIgIhIeHIycnB0lJSc0SnomI5FZXJy3QUSqBrVuB9HTHj4nIF7j1Dsq5ubmor6/H3LlzUVNTg0GDBmHv3r0IDQ01tcnPz4e/vz+mTJmC+vp6jB49GgUFBVDyzx8icjOPPiqtX2Eh8PDDjh0LkS9h1XOw6jkRuUa/fkB5ufXtIyKAf/6TMzpELbH289utZ3aIiDxd4zpX1v4t5e8PPPcc8OyzzNEhcgQGO0RETlJUBCxcaHv5h4sXAbXaOWMi8kUMdoiInOC994ApU2zvN3AgAx0iR5O9XAQRkbfZsUPaLscDBwJffeX48RD5Os7sEBE50Pbt1hf0vPdeoLYW6NED2LgRaN/euWMj79M4Jyw6Wtx0knlezTHYISJygB9+APr0sa3PvHmsc0XSWcoJi40FVq/mCr6meBmLiMhOCoXtgQ7AOlckXVGRuPdS0+T38+fF40VF8ozLXTHYISKyQxt1iVvEOlcklcEgzuhY2iXPeCwzU2xHIgY7REQS2bJBYFOsc0VSHTrU+nYGggBUVortSMRgh4hIgtxccUdkWymVYhIzcypIqqoqx7bzBUxQJiKyUW4u8Oqr0vqyzhXZy9pcL+aE/YEzO0RENtDrgZUrpfXdto2BDtlv2DBx1VVL+WIKBXPCmmKwQ0RkJb1e3ENHSuJndra0HZWJmlIqxeXlQPOAx/g9c8LMMdghIrJCbi4QHAzs2mV730WLgNdec/iQyIelp4s7dXfpYn48NlY8zpwwc8zZISJqgz05Og0NQGCgY8dDBIgBTWoqd1C2BoMdIqJWSM3R+fZbICnJ8eMhakypBEaMkHsU7o/BDhFRC+rqgCFDbM/RWbSIgQ61jPWsXI/BDhGRBffcA5SU2NZHqQSysoDly50zJvJ8rGclDyYoExE1MWCA7YFOWhpw7RoDHWoZ61nJh8EOEVEjEyYApaW29VEqxT10mIhMLWE9K3kx2CEi+o/UVOCjj2zvl5XFQIdax3pW8mKwQ0QEYOtWYPdu2/oolWIyMi9dkVFdHfDQQ2LdtIceEr8HWM9KbkxQJiKfV1gITJ9uW5/ERPFyF2d0yKhpUnt5ORAaCgwcaH1AzHpWzsGZHSLyaampwLRptvf7f/+PgQ79YeDAlpPaS0rEGUDWs5IPgx0i8kk6HRAebvulK0D8YGvf3vFjIs+0ZQtw7FjrbY4dA155Rfw361m5HoMdIvI5PXsCHToANTW29+3fH/jqK4cPiTxUUREwY4Z1bd97j/Ws5MKcHSLyKT17AqdPS+v74IPAnj2OHQ95LuNycmudPs16VnJhsENEPkOnkx7opKQAH3zg2PGQZ2trOXlTPXqIX1nPyvUY7BCRT9DpgE6dpPXdskVaEjN5h5ZqWdm6THzjRueMj9rGYIeIvJ49l662bgUeecSx4yHP0VotK1uWiTOpXV5MUCYir3bbbfZdumKg47vaqmX122+tLyc3GjCASe1yY7BDRF5rwQKgokJa39RU5uj4MmtqWWVnA/n54r9bCng2b7a9qCw5HoMdIvJKOTnAf/+37f3CwsTq5bt2OXxI5CEMBvF3x5paVpGRlpeTx8UB779v+87c5ByyBjtvvvkm+vXrh7CwMISFhWHIkCH45JNPTOdnzZoFhUJhdhs8eLDZfTQ0NCAjIwORkZEICQlBSkoKztmSHk9EXmf7dmDFCtv7RUaKicxBQY4fE3mGoiKgWzfg6aeta19VJS4nP3MG2L9fTGbfv1+cUeS+Oe5D1gTl2NhYvPzyy+jZsycAYP369UhNTcU333yDvn37AgDuv/9+rFu3ztQnsMn+7JmZmfjwww9RWFiIiIgIZGdnY8KECSgtLYWSGxcQ+ZyiImDqVNv7+fmJuRjku4w5OpYuXbXEmKTM5eTuTdZgZ+LEiWbfv/TSS3jzzTdx9OhRU7CjUqmg0Wgs9tfpdFi7di02btyIMWPGAAA2bdqEuLg47Nu3D+PGjXPuEyAit2IwAPPnS+ubnc1aV76m8ZLyzp3FHC9rAx2FQkxOZi0rz+A2S88NBgPee+89XL16FUOGDDEdP3DgADp37owOHTpg+PDheOmll9C5c2cAQGlpKW7cuIHk5GRT+5iYGCQmJuLIkSMtBjsNDQ1oaGgwfV9bW+ukZ0VErqLXiyUg6utt77tokfVVqck7WFpSbi3WsvI8sgc75eXlGDJkCK5fv4727dtj586duOOOOwAA48ePx+TJkxEfH4+Kigo899xzGDVqFEpLS6FSqaDVahEYGIiOHTua3WdUVBS0Wm2Lj5mXl4cXXnjBqc+LiFwnNxd49VXb+4WHi3/Vc0bHd+h0wKBBwA8/SL+P2Fgx0GFOjueQfTVW7969UVZWhqNHj+Kvf/0rZs6cie+++w4AMHXqVDz44INITEzExIkT8cknn+DHH3/ERx991Op9CoIARSsbHyxevBg6nc50q6ysdOhzIiLXMBjEfXCkBDoZGcClSwx0fImxAKw9gU5+PpOPPZHswU5gYCB69uyJAQMGIC8vD3feeSdWr15tsW10dDTi4+Nx6tQpAIBGo4Fer0dNk9LF1dXViIqKavExVSqVaQWY8UZEnqWoCOjaFdi2zfa+2dnA6687fkzkvuzZXBIQL13FxYlBMi9deR7Zg52mBEEwy6dp7NKlS6isrET0f9Lf+/fvj4CAABQXF5vaVFVV4fjx4xg6dKhLxktErmdcNXPhgu19t20DXnvN8WMi92XP5pIAc3S8gaw5O0uWLMH48eMRFxeHK1euoLCwEAcOHMCnn36Kuro6LF26FJMmTUJ0dDTOnDmDJUuWIDIyEg899BAAQK1WY/bs2cjOzkZERATCw8ORk5ODpKQk0+osIvIuxhVXtiwPNoqLA6ZMcfyYyH3l5krbXLIx5uh4PlmDnV9//RWPPvooqqqqoFar0a9fP3z66acYO3Ys6uvrUV5ejg0bNuDy5cuIjo7GyJEjsW3bNoSGhpruIz8/H/7+/pgyZQrq6+sxevRoFBQUcI8dIi8VH297tWmjsjKHDoXcnF4PrFxpWx+FQtwNuaAAqK42r3JOnkshCFL+PvIutbW1UKvV0Ol0zN8hcmPdugG//CKtb1QU0MoiTfJCq1ZZvxOykUIhln/gLI5nsPbz2+1ydoiImqqvF3c4ZqBDtrA1ITkmhoGOt2KwQ0RuLS0NCA6WlqMTESEuL2eg45t69LC+bZcuwNmzDHS8FYMdInJbEycCH3xge79Zs4CGBuDiRXHjQPJeer14uSojQ/yq1/9xbu5c63JtuncXd1JmXo73YrBDRG5p4kRgzx7b+/XuDaxbx80CfUFurjjr9/TTwJo14tfgYPE4IP4OZGW1fh8ZGcDPPzt/rCQv2ctFEBE1lZYmLdABgH/9y6FDITfVUokQg+GP48uX/1HzbOVK8ZyRUikGQqyJ5hu4GgtcjUXkTurrxb/OpejRA/jpJ8eOh9yHsUp5ZaV4qfLWrZbbKpXAtWt/zPDp9cAbb4hJyz16iJe4OPvn+az9/ObMDhG5lf/sGWqz+HgGOt7M1irlBoMY3GRmit8HBv7xb/I9DHaIyG1s3Qp89pnt/VQq4MwZhw+H3ISxPIit1yHsqYVF3oUJykQkK+Nqmu7dgenTbe8fHAxcv+7wYZGbMBjEGR0pCRe2LD0n78aZHSKSTW5u88RRaymV4iUNjcbx4yL3ceiQ9ZeuGlMqxbwcIoAzO0QkE+NqGimBzoQJwM2bDHR8gdQ6aFlZTECmP3Bmh8gLGFepVFV5RuFCvR547TVpfe+9F/jwQ8eOh9xXdLRt7bmknCxhsEPk4SytUomNBVavdt+t73v2lJaDERMDHDzo+PGQ+xo2TPx9Pn/e8u+MQgGo1WK+V0ICl5STZZKDncuXL+Orr75CdXU1bjXZ7OAvf/mL3QMjora1tErl/HnxuDsWNRwwQNwnRYr//m/3nrEi21iz941SKQbuDz8sBjaNf9cVCvHr2rXu93tO7kXSpoIffvghZsyYgatXryI0NBQK428cAIVCgd9//92hg3Q2bipInshgALp1azl5U6EQ/yKuqHCPAKG+Hhg0CCgvl9Z/yxZg2jTHjonkYyk5vbVLUJZmMOPixJV8DHR8l7Wf35KCnV69euGBBx7AsmXLECx1q1M3wmCHPNGBA8DIkW23278fGDHC2aNpXVqatIKeRikp9vUn99JSqQejRYssBzyelptGzufUHZTPnz+PBQsWeEWgQ+SprF2lInU1i6PYG+ikpgK7djlqNCSXxqUeVqxove3KlcCLL1q+pCV34E6eSdLS83HjxuHYsWOOHgsR2cDaVSq2rmZxpPp6aYFOUBAwb55Y24iBjucrKhIvuY4cCfzlL63XtAL+KPVA5CiSZnYefPBBLFq0CN999x2SkpIQEBBgdj4lJcUhgyOillmzSiU2VmwnF6mTv9XVQPv2jh0LyYOlHsgdSAp2nnjiCQDAP/7xj2bnFAoFDFJ2CSMim1izSmXVKvlyGhqtW7DJwIEMdLyBXg+sWQM8/zxLPZD8JF3GunXrVos3BjpErpOeLi4v79LF/HhsrLzLzh9/XFq//v2Br75y7FjI9XJzxVm97Gygrs72/iz1QI7GTQWJPFx6upjE6y6rVLKygHXrbO+3cKE4E0Wera2VVtZgqQdyNMnBzsGDB/Haa6/h5MmTUCgUuP3227Fo0SIMkzNBgMhHucsqlexsID/f9n4tLTUmz6LXiyuppGKpB3IWScHOpk2b8NhjjyE9PR0LFiyAIAg4cuQIRo8ejYKCAkyfPt3R4yQiN7dwIfD667b3a2jgX/He4o03bC/sqlYDM2aw1AM5l6RNBW+//XY8+eSTePrpp82Or1y5Em+//TZOnjzpsAG6AjcVJLLPwIGAlN0oTpwA7rjD8eMheWRkiEnJ1jAmsLtjSRPyHNZ+fktKUP75558xceLEZsdTUlJQUVEh5S6JyAPpdEBoqLRAB2Cg421sWUEldxI9+RZJwU5cXBw+//zzZsc///xzxMXF2T0oInJ/PXsCHTpIW20DSFuOTO5t7ty2E+MVCmDvXrFmGwMdchVJOTvZ2dlYsGABysrKMHToUCgUChw+fBgFBQVYvXq1o8dIRG4mPh44e1Za38ceA95917HjIfcQGCgmGLe2GisnBxg71nVjIgIkBjt//etfodFosGLFCmzfvh2AmMezbds2pKamOnSARORegoKA69el9X36aftW65D7M66ksqWiOZGzSUpQ9jZMUCayjj2BTlZW2wUgyXvo9eLqrNOnxVwerrQiZ3Bq1XMi8j39+kkPdBYsYKDjawIDgcxMuUdBJLI62AkPD8ePP/6IyMhIdOzYEYpWCt/8/vvvDhkcEbmHu+8Gysul9R0wQKzhRUQkF6uDnfz8fISGhpr+3VqwQ0TeIypKrEIuxcCBrHVFRPJjzg6Ys0PUEo0G+PVX2/sFB4v9WL2ciJzJqZsKfv311yhvNKf9wQcfIC0tDUuWLIFer7f6ft58803069cPYWFhCAsLw5AhQ/DJJ5+YzguCgKVLlyImJgZBQUEYMWIETpw4YXYfDQ0NyMjIQGRkJEJCQpCSkoJz585JeVpE1MgDD0gLdLp2Ba5eZaBDRO5DUrAzZ84c/PjjjwDE3ZSnTp2K4OBgvPfee8jNzbX6fmJjY/Hyyy/j2LFjOHbsGEaNGoXU1FRTQLN8+XKsXLkSa9asQUlJCTQaDcaOHYsrV66Y7iMzMxM7d+5EYWEhDh8+jLq6OkyYMAEGWwu0EJHJ2LFAo787rNauHfDLL44fDxGRXQQJwsLChJ9++kkQBEF4+eWXheTkZEEQBOHw4cNCbGyslLs06dixo/DOO+8It27dEjQajfDyyy+bzl2/fl1Qq9XCW2+9JQiCIFy+fFkICAgQCgsLTW3Onz8v+Pn5CZ9++mmLj3H9+nVBp9OZbpWVlQIAQafT2TV2Im/g5ycI4v7Gtt3atZN75ETka3Q6nVWf35JmdgRBwK1btwAA+/btwwMPPABALCNx8eJFSUGXwWBAYWEhrl69iiFDhqCiogJarRbJycmmNiqVCsOHD8eRI0cAAKWlpbhx44ZZm5iYGCQmJpraWJKXlwe1Wm26scQFuYLBABw4AGzdKn51x8lHhQL4z1vbJklJQH2948dDjqPVijlY7dqJX7VauUdE5DqSgp0BAwbgxRdfxMaNG3Hw4EE8+OCDAICKigpERUXZdF/l5eVo3749VCoVnnrqKezcuRN33HEHtP95Jza9v6ioKNM5rVaLwMBAdOzYscU2lixevBg6nc50q6ystGnMRLYqKgK6dQNGjgSmTxe/dusmHncXUhdY3nUX8O23Dh0KOVhICBAdLeZgNTSIX6OjxeNEvkDSpoKrVq3CjBkzsGvXLjz77LPo2bMnAGDHjh0YOnSoTffVu3dvlJWV4fLly3j//fcxc+ZMHDx40HS+6RJ3QRDaXPbeVhuVSgWVSmXTOImkKioCHn64eeHL8+fF43JXfv7hB6BPH2l9O3cGvvnGseMhxwoJAa5ds3zu2jXx/NWrrh0TkatJCnb69etnthrL6NVXX4WyrZK3TQQGBpqCpQEDBqCkpASrV6/GM888A0CcvYmOjja1r66uNs32aDQa6PV61NTUmM3uVFdX2xx0ETmDwQAsXGi5wrcgiLMpmZlAamrb1aKdwZ7tsqKieCnE3Wm1LQc6Rteu/XGJi8hbSbqMVVlZaba8+6uvvkJmZiY2bNiAgIAAuwYkCAIaGhrQvXt3aDQaFBcXm87p9XocPHjQFMj0798fAQEBZm2qqqpw/PhxBjvkFg4dAlrbCUEQgMpKsZ2r2RPojB/PQMddNc4Nu+MO6/rcdZczR0QkP0kzO9OnT8eTTz6JRx99FFqtFmPHjkXfvn2xadMmaLVa/P3vf7fqfpYsWYLx48cjLi4OV65cQWFhIQ4cOIBPP/0UCoUCmZmZWLZsGRISEpCQkIBly5YhODgY06dPBwCo1WrMnj0b2dnZiIiIQHh4OHJycpCUlIQxY8ZIeWpEDlVV5dh2jmJPoDNmDPDxx44bCzlOUZE4k2jrVmOXLztlOERuQ1Kwc/z4cdxzzz0AgO3btyMxMRH/9//+X+zduxdPPfWU1cHOr7/+ikcffRRVVVVQq9Xo168fPv30U4wdOxYAkJubi/r6esydOxc1NTUYNGgQ9u7daypbAYilK/z9/TFlyhTU19dj9OjRKCgosPlyGpEzNLoC65B2jmBPoOPnBzSaSCU3sn07MHWqtL4dOjh0KERuR1K5iPbt2+P48ePo1q0bUlJScO+99+KZZ57B2bNn0bt3b9R72BpUlosgZzEYxFVX589bzttRKIDYWKCiwjU5O127ipfNpGJxGfeUk2NfVfmqKubskGey9vNb0sxO37598dZbb+HBBx9EcXEx/uu//gsAcOHCBUREREgbMZGXMBjEHJyqKnHGZuVK8S9uhcI8WDDOsKxa5ZpAp3t3BjreovHv2AcfANu2Sb+v4GAGOuT9JAU7r7zyCh566CG8+uqrmDlzJu68804AwO7du02Xt4h8kaWcidhY8S/vrVubH1+1yjXLzjt1AiTu9wmAgY47kZqXY0lwMJedk2+QXPXcYDCgtrbWbMn3mTNnEBwcjM6dOztsgK7Ay1jkCC3tp2Ocwdm+HYiM/GPGZ9gw18zodOgA6HTS+p44Yf2KHnK+ln7HrNWxo7jUvEMHoKyMMzrk+az9/JYc7HgTBjtkL2NuTkt/bbs6N8fIz0/6ByP/Z3Avbf2OtSUuzvW/f0TO5vCcnT/96U/4/PPP0bFjR9x9992t7lD89ddf2zZaIg9lzJ34/HPr99MZMcI1Y7Nn1RUDHffT1p5NbXFVbhiRO7I62ElNTTWVWEhLS3PWeIg8hpTcCVftpxMYKL0vAx33odcDb7wBnD5t314427bJW5KESG68jAVexiLbSc2d2L/f+TM7rdVCak1cHHD2rOPHQ9Lk5oor+QwG++4nOxt47TXHjInI3Th16XljdXV1uHXrltkxBgzkzVqrd9USY87OsGHOGxdgXS0kS7p1E/M5SF719cCiRcCePcAvv9h3X0olkJUFLF/umLEReTJJwU5FRQXmz5+PAwcO4Pr166bjxmrjBnv/FCFyYy+9ZNulK1fsp3P+PJCUBNTU2N43MpKBjjtISxP3zJHC+Ds2a5Y4s9ejBzB3rn2XM4m8iaRgZ8aMGQCAd999F1FRUa0mKxN5k6Ii4Pnnbevj7P10VCoxt0MKtRr47TfHjodsZ0+gA7h2zyYiTyS5XERpaSl69+7tjDG5HHN2yBq2Lv3929+A0aOdu5+Ov7/0nA6FAmhyBZpkUF8vbu5nq7Q0YMoU1+7ZRORunJqzM3DgQFRWVnpNsENkDVuW/sbFAUuXOvcDKCzMvuRVBjruYdEiaf2GDwemTXPsWIi8laRg55133sFTTz2F8+fPIzExEQEBAWbn+/Xr55DBEbkTW5aNO3tPkw4dgCtXpPUNCJB+2Yvs13g5eY8ewPff234fSqWYk0NE1pEU7Pz22284ffo0HnvsMdMxhULBBGXyatHR1rV74QXn5k789pv08g8KBQMdOTlqOXlWFpOPiWwhKdh5/PHHcffdd2Pr1q1MUCafMWyYmAh6/nzLy85jY4Fnn3XuOOwpPSdltRY5Rna2GOjYg8vJiaSRFOz88ssv2L17N3r27Ono8RC5LaUSWL1a3ExQoTAPeIzx/urVzr185ecnvW+PHuLqK3Kt+npgyBDg3/+Wfh/duwMLFnA5OZFUkv7rHDVqFP5tzzuXyM0ZDMCBA8DWreJX42WH9HRgxw6gSxfz9rGx4nFnXb767bfmAZYtevQAfvrJsWOi1hkMwH33iSut7PnvMjUV+PlnIDOTgQ6RVJJmdiZOnIinn34a5eXlSEpKapagnJKS4pDBEcnBUs2r2Fhx1iY9Xbylpoqrs6qqnL/0t0MH6Tk6994LfPQRZ3RcragImDEDaLTnqlXmzBG3Ezh1CkhIAF59FQgKcs4YiXyJpH12/FqZS/fEBGXus0NGLdW8Ml6mcubsjSVSA53QUKC21uHDISsUFQGTJknrm58vzuAQkXWs/fxmIVAw2CFRW5sGGutbVVS4ZgO3336TnozMd7Xr1deLScjvvgs0NNjeX6kU65rxUhWR9az9/LYpZ+eBBx6ArtGfmS+99BIuX75s+v7SpUu44447bB8tkRtoa9NAQQAqK8V2riA10Pn5Z8eOg9qWlibm5rz5prRAB+ByciJnsinY+eyzz9DQ6J38yiuv4Pfffzd9f/PmTfzwww+OGx2RC1m7aaAtmwtKJXXVlZ+fuHKHXMfeulYAl5MTOZtNCcpNr3jxChh5E2s3DbS2nVRSt61SKOzfrI5sU1/vmEBnxQrHjIeILJO0GovIG7W1aaAxZ2fYMOc8fkUFcNtt0vqGhwOXLjl2PNScI0o9NLZoEWd0iFzBpmBHoVA02y2ZuyeTt7Bm00Bn1Lz67jugb1/p/aOiAK3WceMhyxxV6gEAEhOB0lLm6BC5is2XsWbNmgWVSgUAuH79Op566imEhIQAgFk+D5EnMm4aaGmfnVWrHL/s3N6/FS5dEmd1yLlyc8U9b+yhUgEjRgA7d3LvHCJXs2npeePCn61Zt26d5AHJgUvPqSmDwfmbBtob6Pz8M5ORnc1gAL74Ahg3zr7l/J98Aowd65otC4h8CffZsQGDHXI1ey9d+fkxGdnZLO2kLUVqKrBrl0OGRERNWPv5zQRlIhnYE+hw1ZXz7dgBTJ5s//0w0CFyDwx2iFzM3stXt245Zhxk2XvvAdOm2d7vlVeAs2dZ14rIHTHYIXKRH34A+vSR3l+hYKDjLMYl5Z99Bnz6qe39lUpWJSdyZwx2iFzA3tmcU6eAnj0dMxYSGQOcDRuAsjL7EpBZ6oHIvTHYIXIyewIdJiI7h6P2zFEqWeqByBNIrMDjGHl5eRg4cCBCQ0PRuXNnpKWlNautNWvWLNNmhsbb4MGDzdo0NDQgIyMDkZGRCAkJQUpKCs7Zu4SCyAHsKRX3888MdJzBuGeOPT/b9u3FEg/XrjHQIfIEsgY7Bw8exLx583D06FEUFxfj5s2bSE5OxtWrV83a3X///aiqqjLdPv74Y7PzmZmZ2LlzJwoLC3H48GHU1dVhwoQJMPCTgmQmNUfnl1+4h44z6PXijI691q/npSsiTyLrZaxPm2QCrlu3Dp07d0ZpaSn+/Oc/m46rVCpoNBqL96HT6bB27Vps3LgRY8aMAQBs2rQJcXFx2LdvH8aNG9esT0NDg9luz7W1tY54OkRmIiKk9fP3B7p2dexYSPTGG/bN6CiVQGGh43fSJiLnknVmpymdTgcACG+y//2BAwfQuXNn9OrVC0888QSqq6tN50pLS3Hjxg0kJyebjsXExCAxMRFHjhyx+Dh5eXlQq9WmW1xcnBOeDfkypRL4/XdpfW/ccOxY6A+nT9vXf+tWsXYaEXkWtwl2BEFAVlYW7rvvPiQmJpqOjx8/Hps3b8YXX3yBFStWoKSkBKNGjTLNzGi1WgQGBqJjx45m9xcVFQVtC9URFy9eDJ1OZ7pVVlY674mRz1EqpS8R537mztWjh7R+cXHA++87ZqNBInI9t1mNNX/+fHz77bc4fPiw2fGpU6ea/p2YmIgBAwYgPj4eH330EdJbmUsWBKHFiuwqlcpUzJTIEc6eFXdFrquTfh8MdJxv7lwgJ8f6S1kTJgDZ2c6pjUZEruMWMzsZGRnYvXs39u/fj9jY2FbbRkdHIz4+HqdOnQIAaDQa6PV61NTUmLWrrq5GVFSU08ZMZBQQAMTHSw90vv+egY6rBAaKicVtUSqBRYuADz8UK5Uz0CHybLIGO4IgYP78+SgqKsIXX3yB7lYsP7l06RIqKysRHR0NAOjfvz8CAgJQXFxsalNVVYXjx49j6NChThs7ESAGOjdvSu9/6RLQu7fjxkNtW75cDGSaBjAKBXDXXUB+PpeUE3kbWauez507F1u2bMEHH3yA3o3+x1er1QgKCkJdXR2WLl2KSZMmITo6GmfOnMGSJUtw9uxZnDx5EqGhoQCAv/71r9izZw8KCgoQHh6OnJwcXLp0CaWlpVBa8ScZq56TFGfPijM6UkVFAS2klZELGHdQPn1azOWZO5dLyYk8jbWf37IGOy3l1Kxbtw6zZs1CfX090tLS8M033+Dy5cuIjo7GyJEj8V//9V9mK6iuX7+ORYsWYcuWLaivr8fo0aPxxhtvWL3KisEOSWHPzsjh4eKsDhERSecRwY67YLBDtrLn8hVLQNiPszJEBFj/+e02q7GIPAVrXcnLUl2rnBzWqCKiljHYIbKBvdXLGejYx1jXqimD4Y/jDHiIqClexgIvY5F1OKMjL70eCA5u/eeoVIorqXhJi8g3WPv57Rb77BC5O6mBTrt2rF7uKNbUtTIYxHZERI3xMhZRG6QGOufOAV26OHYsvszaulb21r8iIu/DYIfcmtyrbqQGOoGBDHTsYel1t7auldT6V0TkvZizA+bsuCtLq26UStetupEa6Pj7s3K5VHo9cP/9wP795seVSmDBAuD115mzQ0R/YM4OeTTjqpumH2zGVTe5uc59fHuSkRnoSJObK+Y4NQ10APF1z88H/vSn1u8jK4uBDhE1x2CH3I5eL87otGblSrGdM9gT6HCeVBpjcNvWz+/rr8WApmkVGGPhTi47JyJLmLNDbmfOHOtX3WRmOu5xS0uBAQOk92egI401wa2RwQDExYmXqriDMhFZi8EOuQ29HnjqKaCgwLr2jlx1Y+9mgQx0pLNmSXljp0+LgY0jA10i8m68jEVuITcXCAoC1q2zvo+jVt0w0JGXrUErV1sRka04s0Oya6kEQGuUSvHShb3at7evPwMd67W0jYAtwYujXnci8i2c2SFZ2ZKv0ZgjVt2EhgJXr0rvz0DHerm5YqmHp58G1qwRvwYHi8fnzm2ecNwSrrYiIik4s0OysjVfAwCmTrV/1Q0vXbmONcU7s7Jan91TKMTK5lxtRURSMNghWdmar9GlC7B5s32PyUDHdazdRuDatT/+3Tj4VSiAESOATz/ljA4RScdgh2RlS76GQiHuoGvtJQ9LfvhBel+AgY6tbCneuXw58OKLXFJORI7HYIdkNXeueHmirQ/E2Fhg9WogPV36Y/30E9Cnj7S+338P9O4t/bF9la3FO7mknIicgQnKJKvAQDFfozVTpwJnztgX6Pj5AQkJ0voKAgMdqVi8k4jcAYMdkt3y5eJW/y2VACgstO/SlUIh7fJTSAgvW9nLmpVWXE5ORM7GYIdcxmAADhwAtm4Vvza+dLV8uZikmp8PzJ8vfr12zf7VN1KDpPbtgbo6+x6brJu543JyInI25uyQSxQVAQsXAufO/XGsaR6Oo/M1/P2BW7ek9b1yxXHj8HXGgLXpSiulUgx0uJyciJxNIQicqK+trYVarYZOp0NYWJjcw/E6RUXAww83vyRkXAK+Y4d9+TiWKJXSAx2+I5yjpR2UiYiksvbzm8EOGOw4k8EAdOtmPqPTmEIhzvBUVNiXl9NYQABw86a0vtXVQKdOjhkHERE5l7Wf38zZIac6dKjlQAcQZ1EqK8V2jrBjh/RAR61moENE5I2Ys0NOVVXl2HYtKS8H+vWT3l+tBi5ftm8MRETknhjskFNFRzu2nSX2ln/gpSsiIu/Gy1jkVMOGiTk5LQUkCgUQFye2k8KeQMfPT7yMxkCHiMi7Mdghp1IqxeXlQPPAxPj9qlXSkpP79rVvXLZWWyciIs/EYIecLj1dTBzu0sX8eGys9GXn99wDfPedtPH4+UlPYiYiIs/Dpefg0nNXMRjEVVdVVWKOzrBh0mZ06uqA0FBpY/D3B27ckNaXiIjci7Wf30xQJpdRKoERI+y/H6nx6HvviZsbEhGRb+FlLPIoxqRiKRjoEBH5JlmDnby8PAwcOBChoaHo3Lkz0tLS8MMPP5i1EQQBS5cuRUxMDIKCgjBixAicOHHCrE1DQwMyMjIQGRmJkJAQpKSk4FxrO9mRx6mokF69HGAJCCIiXyZrsHPw4EHMmzcPR48eRXFxMW7evInk5GRcvXrV1Gb58uVYuXIl1qxZg5KSEmg0GowdOxZXGlVqzMzMxM6dO1FYWIjDhw+jrq4OEyZMgIHLbZymtQrmjqZUArfdJq3vv/7FQIeIyOcJbqS6uloAIBw8eFAQBEG4deuWoNFohJdfftnU5vr164JarRbeeustQRAE4fLly0JAQIBQWFhoanP+/HnBz89P+PTTT616XJ1OJwAQdDqdA5+N93r/fUGIjRUEMYwQb7Gx4nFHa/wYttzuuMPxYyEiIvdi7ee3W+Xs6HQ6AEB4eDgAoKKiAlqtFsnJyaY2KpUKw4cPx5EjRwAApaWluHHjhlmbmJgYJCYmmto01dDQgNraWrMbWcdYwbzpVcLz58XjRUWOeyypGwb6+QFNrnT6JFfOvhERuTO3CXYEQUBWVhbuu+8+JCYmAgC0Wi0AICoqyqxtVFSU6ZxWq0VgYCA6duzYYpum8vLyoFarTbe4uDhHPx2vZDAACxZYvixkPJaZ6ZgPVXt2Rj571v7H93RFRWK1+ZEjgenTxa/dujk2GCUi8hRuE+zMnz8f3377LbZu3drsnKLJJ58gCM2ONdVam8WLF0On05lulZWV0gfuQ2bMEGdwWuKoCuZlZdL7BgY237zQ17hy9o2IyBO4RbCTkZGB3bt3Y//+/YiNjTUd12g0ANBshqa6uto026PRaKDX61FTU9Nim6ZUKhXCwsLMbtS6nBxg2zbr2tpbwfzuu6X1UyiAhgb7HtvTGQzAwoWumX0jIvIUsgY7giBg/vz5KCoqwhdffIHu3bubne/evTs0Gg2Ki4tNx/R6PQ4ePIihQ4cCAPr374+AgACzNlVVVTh+/LipDdln+3ZgxQrr20utYP7DD/Zdvrp1S3pfb3HoUPMZncYcNftGRORJZN1Bed68ediyZQs++OADhIaGmmZw1Go1goKCoFAokJmZiWXLliEhIQEJCQlYtmwZgoODMX36dFPb2bNnIzs7GxEREQgPD0dOTg6SkpIwZswYOZ+eVygqAqZOtb69lArmWq30AMmIy8tF1s6q2Tv7RkTkSWQNdt58800AwIgmNQTWrVuHWbNmAQByc3NRX1+PuXPnoqamBoMGDcLevXsR2qg4Un5+Pvz9/TFlyhTU19dj9OjRKCgogFJK4SUyMV4SsYWtFcxDQoBr12x7jMa+/x7o3Vt6f29jbdBob3BJRORJWAgULATakgMHxFU81po1C1i3zvr29gY6/M1tzmAQV12dP2/556NQiNXmKyqkFWElInIn1n5+u0WCMrmX+npg/nxxmbm1lErgf//X+vZaLQMdZ1AqgdWrxX83zX8yfm/r7BsRkadjsENm0tKA4GDgf/4HKC+3vl9Wlrjs21qNFt3ZjPkmrUtPB3bsaL4EPzZWPJ6eLs+4iIjkImvODrmX1FRg927b+2VnA8uXW9++Tx/pS5+Dg4H/7EhArUhPF1/PQ4fE4DA6Wkwc54wOEfkiBjsEQCwpICXQ2bYNmDLFura//w5ERNj+GEbBwUCjGrHUBqUSaJL7T0Tkk3gZi7B9u1hSwBZxccD771sf6Gg09gU6VVUMdIiISBrO7Pi4nBzbNgxMSgJef922SyIaDfDrr9LGBzAZmYiI7MOZHR+Wm2tboAMAf/6zeGnE2kDn99+lBzrff89Ah4iI7Md9duCb++zo9WIOjK2JwteuAUFB1reXWv7hyhWgfXtpfYmIyDdwnx1q1Rtv2B7opKa6JtAZOJCBDhEROQ6DHR91+rRt7VNSgF27rG8vNdDp3Rv46itpfYmIiCxhsOOjevSwvu2WLcAHH1jX9uxZ+yqXf/+99L5ERESWMNjxUXPnWpdkvG0bMG1a2+0MBsDfH4iPlz4mZo8REZEzMNjxUYGBYomH1mRnW7ePTlGRGOhI3RX5228Z6BARkfNwnx0fZizxsHKleaCiVIqBkDUlIIqKgEmTpI/hxAngjjuk9yciImoLl57DN5eeN6bXi6uzTp8Wc3nmzrWuqKfBIK7OunFD+mN742+fwcCaVERErmDt5zdndgiBgUBmpu397ruPgU5TRUXAwoXAuXN/HIuNBVavZrVxIiK5MGeHJHngAeDoUen9vTXQefhh80AHAM6fF48XFckzLiIiX8dgh2zWowfwySfS+vr5eWegYzCIMzqWnpvxWGam9CRuIiKSjsEO2eS224Cff5bW9+efvffD/tCh5jM6jQkCUFkptiMiItdizg5Z7U9/AioqbO/n729fbo87apqEfP68df2qqpw7LiIiao7BDlmlf3/gm29s7zd2LLB3r+PHIydLSciRkdb1jY52zpiIiKhlDHaoTf37A19/bXu/CROADz90/HjkYJzJ+eADYNWq5ucvXmy9v0IhrsoaNswpwyMiolYw2KFWMdCxPJPTGoXCPFHZWCts1Srut0NEJAcmKFOLpAY648d7V6BjaTl5a5pe0oqNBXbs4D47RERy4cwONVNXJ35A63S2973tNuDjjx0/Jjm0tpy8Nfn5QJcu3EGZiMhdMNghM/fcA5SUSOvbvbtYcsJbtLWcvCVdugAjRjh8OEREJBEvY5HJgAHSA52775a+/467snWZuEIBxMUxCZmIyN0w2CEAwNNPA6Wl0vr+6U/ScnvcnS3LxJmETETkvhjsEHJzLS+ntsaf/iQ9SHJ3w4aJuUvGQKY1TEImInJfDHZ8nF4PrFwpra83BzqAOEOzerX476YBj/H7zExg/35xZ2kGOkRE7onBjg/T64GpU6XVq/L2QMcoPV2csenSxfx4bCzw/vviyqsRI3jpiojInXE1lo/KzRVndKQEOgMHAl995fgxuav0dCA11bwWFpeTExF5DgY7Pig3F3j1Vdv7qdXiUuz27R0/JnenVHI5ORGRp5L1MtaXX36JiRMnIiYmBgqFArt27TI7P2vWLCgUCrPb4MGDzdo0NDQgIyMDkZGRCAkJQUpKCs5J2RzFR0jN0enfH7h82TcDHSIi8myyBjtXr17FnXfeiTVr1rTY5v7770dVVZXp9nGT7XkzMzOxc+dOFBYW4vDhw6irq8OECRNgkHJ9xsvV1wOjRtl+6SozEzh2zClDIiIicjpZL2ONHz8e48ePb7WNSqWCRqOxeE6n02Ht2rXYuHEjxowZAwDYtGkT4uLisG/fPowbN87hY/ZUaWlixW5bKJVAVhawfLlThkREROQSbr8a68CBA+jcuTN69eqFJ554AtXV1aZzpaWluHHjBpKTk03HYmJikJiYiCNHjrR4nw0NDaitrTW7ebOJE20PdNLSgGvXGOgQEZHnc+tgZ/z48di8eTO++OILrFixAiUlJRg1ahQaGhoAAFqtFoGBgejYsaNZv6ioKGi12hbvNy8vD2q12nSLi4tz6vOQ08SJwJ49tvVRKoFt24DAQOeMiYiIyJXcejXW1KlTTf9OTEzEgAEDEB8fj48++gjprezgJggCFK1se7t48WJkZWWZvq+trfXKgCclxfZABxAvXTHQISIib+HWMztNRUdHIz4+HqdOnQIAaDQa6PV61NTUmLWrrq5GVFRUi/ejUqkQFhZmdvM2Tz8NfPihbX2USmDRIl66IiIi7+JRwc6lS5dQWVmJ6P9UaOzfvz8CAgJQXFxsalNVVYXjx49j6NChcg1TdlJqXd17L3N0iIjIO8l6Gauurg4//fST6fuKigqUlZUhPDwc4eHhWLp0KSZNmoTo6GicOXMGS5YsQWRkJB566CEAgFqtxuzZs5GdnY2IiAiEh4cjJycHSUlJptVZvkbqPjrFxbx0RURE3knWYOfYsWMYOXKk6XtjHs3MmTPx5ptvory8HBs2bMDly5cRHR2NkSNHYtu2bQgNDTX1yc/Ph7+/P6ZMmYL6+nqMHj0aBQUFUPrYXv719eIlqOJi2/fRSU0FgoKcMy4iIiK5KQRBEOQehNxqa2uhVquh0+k8Mn9Hyh46RhMm2J7bQ0RE5A6s/fx269VY1LbUVGD3bml9GegQEZEv8KgEZTK3dav0QGfiRAY6RETkGxjseKiiImD6dGl9MzOlB0lERESehsGOBzIYgIULbe9n3EcnP9/xYyIiInJXzNnxQIcOAefOWd8+MRGYPRuYO5fLy4mIyPcw2PFAVVW2tf/qKy4tJyIi38XLWB7oPxtIW4V76BARka9jsOOBhg0DYmOBVmqdAhALge7a5ZIhERERuS0GOx5IqQRWrxb/3VLAs2WL9I0GiYiIvAmDHTen14tFPTMyxK96vXg8PR3YsQPo0sW8fVwc8P77wLRprh4pERGRe2K5CLhvuYjcXLGoZ+NaV0olkJX1R3Vyg0FcnVVVJebyDBsmtiEiIvJ2LBfhwQwGYMYMYNs2y+defVX89/LlYmAzYoRLh0dERORReBnLzRQVAfHxlgOdxlau/OOSFhEREbWMwY4bKSoCHn4YOH++7bYGA/DGG84fExERkadjsOMmjCUgbMmgOn3aeeMhIiLyFgx23IStJSAAoEcP54yFiIjImzDYcRO2loBQKsVaV0RERNQ6BjtuwpYSEIC4/JxFPYmIiNrGYMdNWFsCws8PWLToj312iIiIqHUMdtyENSUgHnsMqK9noENERGQLBjtupK0SEO++y0tXREREtuIOym4mPR1ITWUJCCIiIkdhsOOGWAKCiIjIcRjsuACLdRIREcmHwY6TFRWJOyM33jAwNlZMRk5Pl29cREREvoIJyk5iMAD/+AcwaVLznZHPnxdrYBUVyTM2IiIiX8JgxwmKioBu3YDnn7d83lj/KjNTDIqIiIjIeRjsOJixcnlbda4EAaisFHN5iIiIyHkY7DiQlMrlttbEIiIiItsw2HEgKZXLba2JRURERLbhaiwHsmWWRqEQV2UNG+a88RARERFndhzK1lmaVau43w4REZGzMdhxIGsrl8fGijWwuM8OERGR88ka7Hz55ZeYOHEiYmJioFAosGvXLrPzgiBg6dKliImJQVBQEEaMGIETJ06YtWloaEBGRgYiIyMREhKClJQUnLM1ccZBrKlc/sILwJkzDHSIiIhcRdZg5+rVq7jzzjuxZs0ai+eXL1+OlStXYs2aNSgpKYFGo8HYsWNx5coVU5vMzEzs3LkThYWFOHz4MOrq6jBhwgQYZNrApq3K5X//Oy9dERERuZJCEGxZKO08CoUCO3fuRFpaGgBxVicmJgaZmZl45plnAIizOFFRUXjllVcwZ84c6HQ6dOrUCRs3bsTUqVMBABcuXEBcXBw+/vhjjBs3zqrHrq2thVqthk6nQ1hYmEOeD+thEREROZe1n99um7NTUVEBrVaL5ORk0zGVSoXhw4fjyJEjAIDS0lLcuHHDrE1MTAwSExNNbSxpaGhAbW2t2c3RjJXLp00TvzLQISIikofbBjtarRYAEBUVZXY8KirKdE6r1SIwMBAdO3ZssY0leXl5UKvVpltcXJyDR09ERETuwm2DHSNFk0xfQRCaHWuqrTaLFy+GTqcz3SorKx0yViIiInI/bhvsaDQaAGg2Q1NdXW2a7dFoNNDr9aipqWmxjSUqlQphYWFmNyIiIvJObhvsdO/eHRqNBsXFxaZjer0eBw8exNChQwEA/fv3R0BAgFmbqqoqHD9+3NSGiIiIfJus5SLq6urw008/mb6vqKhAWVkZwsPD0bVrV2RmZmLZsmVISEhAQkICli1bhuDgYEyfPh0AoFarMXv2bGRnZyMiIgLh4eHIyclBUlISxowZI9fTIiIiIjcia7Bz7NgxjBw50vR9VlYWAGDmzJkoKChAbm4u6uvrMXfuXNTU1GDQoEHYu3cvQkNDTX3y8/Ph7++PKVOmoL6+HqNHj0ZBQQGUXP5EREREcKN9duTkjH12iIiIyLk8fp8dIiIiIkdgsENEREReTdacHXdhvJLnjJ2UiYiIyDmMn9ttZeQw2AFMhUW5kzIREZHnuXLlCtRqdYvnmaAM4NatW7hw4QJCQ0Pb3J3ZUWpraxEXF4fKykomRbs5vlaeg6+VZ+Dr5Dnc/bUSBAFXrlxBTEwM/PxazszhzA4APz8/xMbGyvLY3MHZc/C18hx8rTwDXyfP4c6vVWszOkZMUCYiIiKvxmCHiIiIvBqDHZmoVCo8//zzUKlUcg+F2sDXynPwtfIMfJ08h7e8VkxQJiIiIq/GmR0iIiLyagx2iIiIyKsx2CEiIiKvxmCHiIiIvBqDHRdaunQpFAqF2U2j0cg9LALw5ZdfYuLEiYiJiYFCocCuXbvMzguCgKVLlyImJgZBQUEYMWIETpw4Ic9gfVxbr9WsWbOavc8GDx4sz2B9XF5eHgYOHIjQ0FB07twZaWlp+OGHH8za8L0lP2teJ09/XzHYcbG+ffuiqqrKdCsvL5d7SATg6tWruPPOO7FmzRqL55cvX46VK1dizZo1KCkpgUajwdixY0111ch12nqtAOD+++83e599/PHHLhwhGR08eBDz5s3D0aNHUVxcjJs3byI5ORlXr141teF7S37WvE6Ah7+vBHKZ559/XrjzzjvlHga1AYCwc+dO0/e3bt0SNBqN8PLLL5uOXb9+XVCr1cJbb70lwwjJqOlrJQiCMHPmTCE1NVWW8VDrqqurBQDCwYMHBUHge8tdNX2dBMHz31ec2XGxU6dOISYmBt27d8cjjzyCn3/+We4hURsqKiqg1WqRnJxsOqZSqTB8+HAcOXJExpFRSw4cOIDOnTujV69eeOKJJ1BdXS33kAiATqcDAISHhwPge8tdNX2djDz5fcVgx4UGDRqEDRs24LPPPsPbb78NrVaLoUOH4tKlS3IPjVqh1WoBAFFRUWbHo6KiTOfIfYwfPx6bN2/GF198gRUrVqCkpASjRo1CQ0OD3EPzaYIgICsrC/fddx8SExMB8L3ljiy9ToDnv69Y9dyFxo8fb/p3UlIShgwZgh49emD9+vXIysqScWRkDYVCYfa9IAjNjpH8pk6davp3YmIiBgwYgPj4eHz00UdIT0+XcWS+bf78+fj2229x+PDhZuf43nIfLb1Onv6+4syOjEJCQpCUlIRTp07JPRRqhXHFXNO/NKurq5v9RUruJzo6GvHx8XyfySgjIwO7d+/G/v37ERsbazrO95Z7ael1ssTT3lcMdmTU0NCAkydPIjo6Wu6hUCu6d+8OjUaD4uJi0zG9Xo+DBw9i6NChMo6MrHHp0iVUVlbyfSYDQRAwf/58FBUV4YsvvkD37t3NzvO95R7aep0s8bT3FS9juVBOTg4mTpyIrl27orq6Gi+++CJqa2sxc+ZMuYfm8+rq6vDTTz+Zvq+oqEBZWRnCw8PRtWtXZGZmYtmyZUhISEBCQgKWLVuG4OBgTJ8+XcZR+6bWXqvw8HAsXboUkyZNQnR0NM6cOYMlS5YgMjISDz30kIyj9k3z5s3Dli1b8MEHHyA0NNQ0g6NWqxEUFASFQsH3lhto63Wqq6vz/PeVnEvBfM3UqVOF6OhoISAgQIiJiRHS09OFEydOyD0sEgRh//79AoBmt5kzZwqCIC6Rff755wWNRiOoVCrhz3/+s1BeXi7voH1Ua6/VtWvXhOTkZKFTp05CQECA0LVrV2HmzJnC2bNn5R62T7L0OgEQ1q1bZ2rD95b82nqdvOF9pRAEQXBlcEVERETkSszZISIiIq/GYIeIiIi8GoMdIiIi8moMdoiIiMirMdghIiIir8Zgh4iIiLwagx0iIiLyagx2iIiIyKsx2CEiIiKvxmCHyMVmzZoFhULR7PbTTz9hxIgRyMzMbNZn165dUCgUpu8LCgos3ke7du3MHictLa3VsXzzzTeYPHkyoqKi0K5dO/Tq1QtPPPEEfvzxR7N269evxz333IOQkBCEhobiz3/+M/bs2WPW5sCBA1AoFEhMTITBYDA716FDBxQUFJg97oQJE9C5c2e0a9cO3bp1w9SpU3Hx4kWz+7p8+XKzMd91111YunSp6ftu3bpBoVCgsLCwWdu+fftCoVCYPbaxvUKhQHBwMBITE/G///u/AIARI0ZY/Lkab926dTO1a/o6nThxAlOmTEGnTp2gUqmQkJCA5557DteuXTNrZ3z8o0ePmh3PzMzEiBEjmj2HltTW1uLZZ59Fnz590K5dO2g0GowZMwZFRUVovDG+reOS8nNUKpWIiYnB7NmzUVNTY/VzIHIVBjtEMrj//vtRVVVldrOm0nBjYWFhze7jl19+sbr/nj17MHjwYDQ0NGDz5s04efIkNm7cCLVajeeee87ULicnB3PmzMGUKVPw73//G1999RWGDRuG1NRUrFmzptn9nj59Ghs2bGjxcaurqzFmzBhERkbis88+w8mTJ/Huu+8iOjq62QewteLi4rBu3TqzY0ePHoVWq0VISEiz9v/4xz9QVVWFb7/9FmlpaXjqqaewbds2FBUVmX6WX331FQBg3759pmMlJSUWH//o0aMYNGgQ9Ho9PvroI/z4449YtmwZ1q9fj7Fjx0Kv15u1b9euHZ555hlJzxUALl++jKFDh2LDhg1YvHgxvv76a3z55ZeYOnUqcnNzodPpJI1L6s/x7Nmz2Lx5M7788kssWLBA8vMichZWPSeSgUqlgkajses+FAqF5Pu4du0aHnvsMTzwwAPYuXOn6Xj37t0xaNAg04zK0aNHsWLFCrz++uvIyMgwtXvppZdw/fp1ZGVlITU1FXFxcaZzGRkZeP755zFt2jSzmSajI0eOoLa2Fu+88w78/f1Njztq1ChJzwUAZsyYgfz8fFRWVprG8u6772LGjBkWA6/Q0FDTz+7FF1/E9u3bsWvXLkydOtXU5vr16wCAiIiIVn/OgiBg9uzZuP3221FUVAQ/P/FvyPj4ePTq1Qt333038vPzzYKbOXPm4M0338THH3+MBx54wObnu2TJEpw5cwY//vgjYmJiTMd79epl+rlLGZc9P8cuXbrgL3/5i8WZISK5cWaHyAd99tlnuHjxInJzcy2e79ChAwBg69ataN++PebMmdOsTXZ2Nm7cuIH333/f7HhmZiZu3rxpcdYHADQaDW7evImdO3fCUXWIo6KiMG7cOKxfvx6AGMxt27YNjz/+uFX927Vrhxs3bkh67LKyMnz33XfIysoyBRRGd955J8aMGYOtW7eaHe/WrRueeuopLF68GLdu3bLp8W7duoXCwkLMmDHDLNAxat++Pfz9/SWNy56f4/nz57Fnzx4MGjTIpudD5AoMdohksGfPHrRv3950mzx5ss33odPpzO6jffv2SE5OtqrvqVOnAAB9+vRptd2PP/6IHj16IDAwsNm5mJgYqNXqZvk9wcHBeP7555GXl2e6nNLY4MGDsWTJEkyfPh2RkZEYP348Xn31Vfz6669Wjb0ljz/+OAoKCiAIAnbs2IEePXrgrrvuarXPzZs3UVBQgPLycowePVrS4xqf/+23327x/O23397sZwQAf/vb31BRUYHNmzfb9HgXL15ETU2NVa+dlHHZ8nN85pln0L59ewQFBSE2NhYKhQIrV6606fkQuQKDHSIZjBw5EmVlZabb66+/bvN9hIaGmt1HWVlZs3yLljhqRkUQBLPEaaPZs2cjMjISr7zyisV+L730ErRaLd566y3ccccdeOutt9CnTx+Ul5dLHsuDDz6Iuro6fPnll3j33XdbnY1o/CE9b948LFq0yOLslSO09DPq1KkTcnJy8Pe//71Z7kxb9wfA4n06Yly2/BwXLVqEsrIyfPvtt/j8889N/ZsmqBPJjcEOkQxCQkLQs2dP0y06OhqAmHRsaTbk8uXLCAsLMzvm5+dndh89e/ZEly5drHr8Xr16AQC+//77NtudPn3a4ofxhQsXUFtbi4SEhGbn/P398eKLL2L16tW4cOGCxfuOiIjA5MmTsWLFCpw8eRIxMTF47bXXAMD0XFv6WajVaouP+eijj+L555/Hv/71L8yYMaPF52X8kP7ll19QV1eH5cuXN7vUYy3jz/K7776zeP7777+3+DMCgKysLNTX1+ONN96w+vE6deqEjh074uTJk04Zly0/x8jISPTs2RMJCQkYNWoUVq1ahSNHjmD//v1WPx8iV2CwQ+RG+vTpg2PHjjU7XlJSgt69ezvscZKTkxEZGYnly5dbPG9MUH7kkUdQV1dnWprd2GuvvYaAgABMmjTJ4n1MnjwZffv2xQsvvNDmeAIDA9GjRw9cvXoVAJCQkAA/P79mq5+qqqpw/vz5Fn8Wjz/+OA4ePIjU1FR07NixxcczfkjHxMTYPUNy1113oU+fPsjPz2+Wf/Pvf/8b+/btw7Rp0yz2bd++PZ577jm89NJLqK2tterx/Pz8MHXqVGzevNliIHn16lXcvHnTrnFZ+3NsSqlUAgDq6+ut7kPkClyNReRG5s6dizVr1mDevHl48sknERQUhOLiYqxduxYbN240aysIArRabbP76Ny5s2mWQqfToayszOx8eHg4unbtinfeeQeTJ09GSkoKFixYgJ49e+LixYvYvn07zp49i8LCQgwZMgQLFy7EokWLoNfrkZaWhhs3bmDTpk1YvXo1Vq1aZbYSq6mXX34Z48aNMzu2Z88eFBYW4pFHHkGvXr0gCAI+/PBDfPzxx6bLcKGhoZgzZw6ys7Ph7++PO++8ExcuXMCzzz6L22+/vcXcpNtvvx0XL15EcHBwmz9rR1EoFHjnnXeQnJyMSZMmYfHixdBoNPjXv/6F7OxsDBkyxOLeSUZPPvkk8vPzsXXrVquTe5ctW4YDBw5g0KBBeOmllzBgwAAEBATg0KFDyMvLQ0lJCTp06CB5XNb+HK9cuQKtVgtBEFBZWYnc3FxERkZi6NChVj0PIpcRiMilZs6cKaSmprZ4/tixY8K4ceOEzp07C2FhYcKAAQOErVu3mrVZt26dAMDiraqqyvQ4ls7PnDnTdD8lJSVCenq60KlTJ0GlUgk9e/YUnnzySeHUqVNmj7d27VphwIABQlBQkBAcHCzcd999wu7du83a7N+/XwAg1NTUmB1PTk4WAAjr1q0TBEEQTp8+LTzxxBNCr169hKCgIKFDhw7CwIEDTeeNrl+/LvzjH/8Qbr/9diEoKEiIj48XZs2aZXp+RvHx8UJ+fn6LP0+1Wm123221N6qoqBAACN98802zc8OHDxcWLlxoduzbb78VJk2aJERERAgBAQFCjx49hL/97W/C1atX2xzvli1bBADC8OHD2xyX0eXLl4X/83/+j5CQkCAEBgYKUVFRwpgxY4SdO3cKt27dcsi4GrP0c2z8e9WpUyfhgQcesPjzIpKbQhAclKlIRERE5IaYs0NERERejcEOEZGbabp/UuPboUOH5B4ekcfhZSwiIjfz008/tXiuS5cuCAoKcuFoiDwfgx0iIiLyaryMRURERF6NwQ4RERF5NQY7RERE5NUY7BAREZFXY7BDREREXo3BDhEREXk1BjtERETk1f4/RoVza0zrZ6sAAAAASUVORK5CYII=\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": [ + "Now train a Linear Regression Model using the `train_x` you created and the `train_y` created previously\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coefficients: [[15.96526128]]\n", + "Intercept: [70.90496725]\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_)" + ] + }, + { + "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": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[165.10000882]\n", + " [145.94169528]\n", + " [145.94169528]\n", + " [102.83548981]\n", + " [102.83548981]\n", + " [118.8007511 ]\n", + " [134.76601238]\n", + " [102.83548981]\n", + " [118.8007511 ]\n", + " [118.8007511 ]\n", + " [153.92432592]\n", + " [118.8007511 ]\n", + " [118.8007511 ]\n", + " [118.8007511 ]\n", + " [102.83548981]\n", + " [134.76601238]\n", + " [102.83548981]\n", + " [118.8007511 ]\n", + " [118.8007511 ]\n", + " [102.83548981]\n", + " [118.8007511 ]\n", + " [118.8007511 ]\n", + " [118.8007511 ]\n", + " [141.1521169 ]\n", + " [141.1521169 ]\n", + " [166.69653495]\n", + " [118.8007511 ]\n", + " [118.8007511 ]\n", + " [141.1521169 ]\n", + " [141.1521169 ]\n", + " [141.1521169 ]\n", + " [141.1521169 ]\n", + " [102.83548981]\n", + " [109.22159433]\n", + " [118.8007511 ]\n", + " [128.37990787]\n", + " [169.88958721]\n", + " [169.88958721]\n", + " [169.88958721]\n", + " [169.88958721]\n", + " [128.37990787]\n", + " [128.37990787]\n", + " [169.88958721]\n", + " [ 93.25633304]\n", + " [155.52085205]\n", + " [155.52085205]\n", + " [155.52085205]\n", + " [155.52085205]\n", + " [166.69653495]\n", + " [166.69653495]\n", + " [147.53822141]\n", + " [128.37990787]\n", + " [109.22159433]\n", + " [155.52085205]\n", + " [155.52085205]\n", + " [139.55559077]\n", + " [169.88958721]\n", + " [ 99.64243756]\n", + " [155.52085205]\n", + " [155.52085205]\n", + " [155.52085205]\n", + " [128.37990787]\n", + " [128.37990787]\n", + " [128.37990787]\n", + " [173.08263946]\n", + " [128.37990787]\n", + " [161.90695656]\n", + " [173.08263946]\n", + " [161.90695656]\n", + " [109.22159433]\n", + " [ 93.25633304]\n", + " [ 93.25633304]\n", + " [161.90695656]\n", + " [128.37990787]\n", + " [ 93.25633304]\n", + " [ 93.25633304]\n", + " [ 93.25633304]\n", + " [157.11737818]\n", + " [129.976434 ]\n", + " [129.976434 ]\n", + " [150.73127367]\n", + " [150.73127367]\n", + " [150.73127367]\n", + " [169.88958721]\n", + " [126.78338174]\n", + " [ 96.4493853 ]\n", + " [102.83548981]\n", + " [126.78338174]\n", + " [128.37990787]\n", + " [155.52085205]\n", + " [155.52085205]\n", + " [147.53822141]\n", + " [139.55559077]\n", + " [155.52085205]\n", + " [169.88958721]\n", + " [139.55559077]\n", + " [109.22159433]\n", + " [128.37990787]\n", + " [169.88958721]\n", + " [126.78338174]\n", + " [ 96.4493853 ]\n", + " [102.83548981]\n", + " [109.22159433]\n", + " [ 96.4493853 ]\n", + " [126.78338174]\n", + " [129.976434 ]\n", + " [126.78338174]\n", + " [110.81812046]\n", + " [118.8007511 ]\n", + " [150.73127367]\n", + " [150.73127367]\n", + " [150.73127367]\n", + " [150.73127367]\n", + " [109.22159433]\n", + " [121.99380336]\n", + " [102.83548981]\n", + " [109.22159433]\n", + " [109.22159433]\n", + " [128.37990787]\n", + " [128.37990787]\n", + " [ 96.4493853 ]\n", + " [ 96.4493853 ]\n", + " [102.83548981]\n", + " [123.59032948]\n", + " [109.22159433]\n", + " [109.22159433]\n", + " [118.8007511 ]\n", + " [150.73127367]\n", + " [150.73127367]\n", + " [118.8007511 ]\n", + " [150.73127367]\n", + " [150.73127367]\n", + " [118.8007511 ]\n", + " [150.73127367]\n", + " [126.78338174]\n", + " [126.78338174]\n", + " [126.78338174]\n", + " [150.73127367]\n", + " [144.34516915]\n", + " [126.78338174]\n", + " [129.976434 ]\n", + " [157.11737818]\n", + " [131.57296013]\n", + " [110.81812046]\n", + " [129.976434 ]\n", + " [110.81812046]\n", + " [102.83548981]\n", + " [110.81812046]\n", + " [102.83548981]\n", + " [110.81812046]\n", + " [102.83548981]\n", + " [126.78338174]\n", + " [169.88958721]\n", + " [158.71390431]\n", + " [126.78338174]\n", + " [126.78338174]\n", + " [145.94169528]\n", + " [145.94169528]\n", + " [158.71390431]\n", + " [158.71390431]\n", + " [126.78338174]\n", + " [126.78338174]\n", + " [145.94169528]\n", + " [145.94169528]\n", + " [ 96.4493853 ]\n", + " [ 96.4493853 ]\n", + " [ 96.4493853 ]\n", + " [ 96.4493853 ]\n", + " [ 96.4493853 ]\n", + " [ 96.4493853 ]\n", + " [ 96.4493853 ]\n", + " [ 90.06328079]\n", + " [129.976434 ]\n", + " [126.78338174]\n", + " [110.81812046]\n", + " [ 96.4493853 ]\n", + " [126.78338174]\n", + " [ 96.4493853 ]\n", + " [134.76601238]\n", + " [125.18685561]\n", + " [131.57296013]\n", + " [131.57296013]\n", + " [131.57296013]\n", + " [114.01117271]\n", + " [114.01117271]\n", + " [128.37990787]\n", + " [118.8007511 ]\n", + " [147.53822141]\n", + " [161.90695656]\n", + " [161.90695656]\n", + " [128.37990787]\n", + " [118.8007511 ]\n", + " [176.27569172]\n", + " [177.87221785]\n", + " [177.87221785]\n", + " [ 86.87022853]\n", + " [ 86.87022853]\n", + " [102.83548981]\n", + " [110.81812046]\n", + " [102.83548981]\n", + " [102.83548981]\n", + " [134.76601238]\n", + " [ 99.64243756]\n", + " [126.78338174]\n", + " [ 99.64243756]\n", + " [126.78338174]\n", + " [134.76601238]\n", + " [161.90695656]\n", + " [ 94.85285917]\n", + " [110.81812046]\n", + " [110.81812046]\n", + " [102.83548981]\n", + " [ 99.64243756]\n", + " [102.83548981]\n", + " [110.81812046]]\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": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean Absolute Error: 136.71\n" + ] + } + ], + "source": [ + "print(\"Mean Absolute Error: %.2f\" % np.mean(np.absolute(predictions - 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.

\n", + "\n", + "\n", + "\n", + "\n" + ] + } + ], + "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": "20d6dc1d9e74df451be22381c972d7921c93657bea402a00c749dca52bb85996" + }, + "nbformat": 4, + "nbformat_minor": 4 +}