diff --git a/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-Mulitple-Linear-Regression-Co2.ipynb b/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-Mulitple-Linear-Regression-Co2.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<p style=\"text-align:center\">\n",
+    "    <a href=\"https://skills.network\" target=\"_blank\">\n",
+    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
+    "    </a>\n",
+    "</p>\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": [
+    "<h1>Table of contents</h1>\n",
+    "\n",
+    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
+    "    <ol>\n",
+    "        <li><a href=\"#understanding-data\">Understanding the Data</a></li>\n",
+    "        <li><a href=\"#reading_data\">Reading the Data in</a></li>\n",
+    "        <li><a href=\"#multiple_regression_model\">Multiple Regression Model</a></li>\n",
+    "        <li><a href=\"#prediction\">Prediction</a></li>\n",
+    "        <li><a href=\"#practice\">Practice</a></li>\n",
+    "    </ol>\n",
+    "</div>\n",
+    "<br>\n",
+    "<hr>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Importing Needed packages\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "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": null,
+   "metadata": {},
+   "outputs": [],
+   "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",
+    "<h2 id=\"understanding_data\">Understanding the Data</h2>\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": [
+    "<h2 id=\"reading_data\">Reading the data in</h2>\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "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": null,
+   "metadata": {},
+   "outputs": [],
+   "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": null,
+   "metadata": {},
+   "outputs": [],
+   "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": null,
+   "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": null,
+   "metadata": {},
+   "outputs": [],
+   "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": [
+    "<h2 id=\"multiple_regression_model\">Multiple Regression Model</h2>\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": null,
+   "metadata": {},
+   "outputs": [],
+   "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": [
+    "<h2 id=\"prediction\">Prediction</h2>\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "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": [
+    "<h2 id=\"practice\">Practice</h2>\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": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "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))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<details><summary>Click here for the solution</summary>\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",
+    "</details>\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",
+    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
+    "\n",
+    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
+    "    \n",
+    "<!--\n",
+    "\n",
+    "## Change Log\n",
+    "\n",
+    "\n",
+    "|  Date (YYYY-MM-DD) |  Version | Changed By  |  Change Description |\n",
+    "|---|---|---|---|\n",
+    "| 2020-11-03  | 2.1  | Lakshmi  | Made changes in URL |\n",
+    "| 2020-08-27  | 2.0  | Lavanya  |  Moved lab to course repo in GitLab |\n",
+    "|   |   |   |   |\n",
+    "|   |   |   |   |\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": "c1170d4cb1c9bbce7dbbef74b645fc6b265a5aaf4ce89c4ac861feed8769ed99"
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-NoneLinearRegression.ipynb b/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-NoneLinearRegression.ipynb
new file mode 100644
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--- /dev/null
+++ b/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-NoneLinearRegression.ipynb	
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<p style=\"text-align:center\">\n",
+    "    <a href=\"https://skills.network\" target=\"_blank\">\n",
+    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
+    "    </a>\n",
+    "</p>\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": [
+    "<h2 id=\"importing_libraries\">Importing required libraries</h2>\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "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": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": 22,
+   "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": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": [
+    "<a id=\"ref2\"></a>\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": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2025-10-20 16:22:45 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": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Year</th>\n",
+       "      <th>Value</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1960</td>\n",
+       "      <td>5.918412e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>1961</td>\n",
+       "      <td>4.955705e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>1962</td>\n",
+       "      <td>4.668518e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>1963</td>\n",
+       "      <td>5.009730e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>1964</td>\n",
+       "      <td>5.906225e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>1965</td>\n",
+       "      <td>6.970915e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>1966</td>\n",
+       "      <td>7.587943e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>1967</td>\n",
+       "      <td>7.205703e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>8</th>\n",
+       "      <td>1968</td>\n",
+       "      <td>6.999350e+10</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>9</th>\n",
+       "      <td>1969</td>\n",
+       "      <td>7.871882e+10</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "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": 24,
+     "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": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 800x500 with 1 Axes>"
+      ]
+     },
+     "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": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": 27,
+   "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": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7485709d92d0>]"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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oBII8GmDx813RMYAz6JbMbPcZISIiuldeUSne/uEU/ndKBQB4rIMP/u/ZULg5OUhcGdUXhhEiIpLMhfQcvPztCSRm5sPeToa3h7TF5L7B3EnVxjCMEBGRJLbGpeK97adRWKKFr5sTlozpgrCgqnfnJuvFMEJERPWqsESDeT+exeZY3YaW4a08sXBUZ3jwKrs2i2GEiIjqTUp2AaZ9E4dzqhzIZMDsR1pjxsCWkHO1jE1jGCEionpx6EomXvnuBG4XlMDDxRGLnuuCvq08pS6LzADDCBER1SkhBNYevIaPdp6HRivQsYkSK8aGwb+Rs9SlkZlgGCEiojpTWKLBO9tOI/pEGgDg6S5NEBXZkdeWoXIYRoiIqE7cuHMX07+Nw6lUNeR2MrzzeDtMeqgZl+1SBQwjRERkcseSsvHyhjhk5hWjcQMHLB7dFQ+15PkhVDmGESIiMhkhBL49mowFO86iVCvQzs8NK8eGIdC9gdSlkRljGCEiIpMo1Wix4Kdz+ObIdQDAk5388MmITmjgyI8aqh6/Q4iIqNZyCkvwyoYTiLmcCZkM+MdjbTG9X3OeH0IGYRghIqJaSc4qwOSvj+NyRh6cHeRY+FxnPNbBV+qyyIIwjBARUY3FXsvGi9/EITu/GD5uCqwe3x0hTZRSl0UWhmGEiIhqZHt8Gv6x9RSKNVqENHHDV+O6w1fpJHVZZIEYRoiIyCharcDC3y/hiz1XAACPdfDB56M680RVqjF+5xARkcEKSzR4fctJ/HxKBQCY3q8F/vFYG9jxQndUCwwjRERkkNv5xZj89XGcSL4DB7kMHz3dESO7BUpdFlkBhhEiInqglOwCjF9zDImZ+XBzsseKsd3Qu4WH1GWRlWAYISKiap1OVWPiuuPIzCtCk0bO+HpSd7T0dpW6LLIiDCNERFSlPy9m4JUNJ1BQrEE7Pzesm9gdPm5cMUOmxTBCRESV+v54CuZuOw2NViC8lSeWjukKVycHqcsiK8QwQkRE5QghsOiPy1j4+2UAQGTXJvg4shMc7e0kroysFcMIERHplWq0eG/7GWw6ngIAmDGgJV6PaM1rzFCdYhghIiIAwN1iDV757gT2XMiAnQz41/AQjOkZJHVZZAMYRoiICOq7JZi87jhir9+Gk4Mdvny+Kwa195G6LLIRDCNERDYuI6cQ49Ycw4X0XLg52WPtxO4IC3KXuiyyIQwjREQ2LDmrAC+sPork7AJ4uSqwflIPtPNzk7ossjEMI0RENuq8Kgfj1hzDrdwiNHVvgG8n90RTjwZSl0X1SaMBYmIAlQrw8wPCwwG5vN7LYBghIrJBsdeyMWndceQUlqKtryvWT+4Bb1duZmZToqOBWbOA1NS/2wICgEWLgMjIei2Fi8aJiGzMnxcz8MLqo8gpLEW3oMbYPK03g4itiY4GRowoH0QAIC1N1x4dXa/lMIwQEdmQHxPSMPXrWBSWaDGgjRe+mdwTSmfuqmpTNBrdjIgQFe8ra5s9W9evnjCMEBHZiA1Hr2P25gSUagWGdfbHynHd4OxY/+cHkMRiYirOiNxLCCAlRdevnvCcESIiG/BVTCI+/Pk8AGBc7yDMH9oBdnbcVdUmqVSm7WcCDCNERFZu8Z7L+O9vlwAA0/u1wFuD23B7d1vm52fafibAwzRERFZKCIH/+/WCPojMGdSaQYR0y3cDAoCqvg9kMiAwUNevnjCMEBFZISEEPvjfOSz58yoA4J3H22LmI60YREi3j8iiRbr/vv/7oezrhQvrdb8Ro8PI/v37MXToUPj7+0Mmk2H79u0PfMy+ffsQFhYGJycnNG/eHMuXL69JrUREZACtVuCdbWew9uA1AMC/hnXAiw+3kLYoMi+RkcDWrUCTJuXbAwJ07ea+z0h+fj5CQ0OxePFig/onJSXh8ccfR3h4OOLj4/HOO+9g5syZ+OGHH4wuloiIqleq0eL1LSex8Vgy7GTAJyM6YWzvZlKXReYoMhK4dg3480/gu+90/yYl1XsQAQCZEJUtNDbwwTIZtm3bhuHDh1fZ56233sKOHTtw/vx5fdv06dNx8uRJHD582KDXycnJgVKphFqthpsbr5lARFSZ4lItZm2Kxy9n0iG3k+HzUZ3xVKi/1GWRDTP087vOzxk5fPgwIiIiyrU99thjiI2NRUlJSaWPKSoqQk5OTrkbERFVrahUg5c3xOGXM+lwlNth2ZiuDCJkMeo8jKSnp8PHx6dcm4+PD0pLS5GZmVnpY6KioqBUKvW3wMDAui6TiMhiFZVq8NK3J/D7+Qwo7O2wclwYIjr4Sl0WkcHqZTXN/Wdvlx0Zquqs7rlz50KtVutvKSkpdV4jEZElKizRYPo3cdhzQRdEVo/vjv5tvKUui8godb7pma+vL9LT08u1ZWRkwN7eHh4eHpU+RqFQQKFQ1HVpREQWrbBEg2nfxGHfpVtwctAFkYdaekpdFpHR6nxmpHfv3ti9e3e5tt9++w3dunWDgwMvzkREVBOFJRpMXR+rDyJrJjCIkOUyOozk5eUhISEBCQkJAHRLdxMSEpCcnAxAd4hl3Lhx+v7Tp0/H9evXMWfOHJw/fx5r1qzB6tWr8cYbb5jmHRAR2ZiyIBJzORPODnKsndADfVowiJDlMvowTWxsLAYMGKD/es6cOQCA8ePHY926dVCpVPpgAgDBwcHYuXMnXnvtNSxZsgT+/v744osv8Mwzz5igfCIi23K3WIMp64/j4JUsNHCUY+2E7ujZvPJD3kSWolb7jNQX7jNCRAQUFJdi8rpYHE7MgoujHGsn9kCPYHepyyKqkqGf37xqLxGRBbhbrCkXRL6e1APdmjGIkHVgGCEiMnNl54gcTsxCQ4U9vp7UHWFBDCJkAI0GiIkBVCrAz093Jd56vACeoRhGiIjMWNny3QNXMtHAUY51ExlEyEDR0cCsWUBq6t9tAQG6K/ZKcP2Z6tTLpmdERGS84lItXtlwQr98d+2E7jw0Q4aJjgZGjCgfRAAgLU3XHh0tTV1VYBghIjJDJRotXt14An/8tbPqmvFcNUMG0mh0MyKVrU8pa5s9W9fPTDCMEBGZmVKNFrM3JeDXszfhaG+HVeO6oQ83NCNDxcRUnBG5lxBASoqun5lgGCEiMiMarcCc70/i59MqOMhlWPFCGB5u7SV1WWRJVCrT9qsHDCNERGZCoxV4c+tJ7Dh5A/Z2MiwdE4YBbXnROzKSn59p+9UDhhEiIjOg1Qq8E30a0SfSILeT4cvnu2BQex+pyyJLFB6uWzUjk1V+v0wGBAbq+pkJhhEiIokJITBvx1lsjk2BnQxYOKozhnQ0n79aycLI5brlu0DFQFL29cKFZrXfCMMIEZGEhBD4+JcL+ObIdchkwH+fDcXQUH+pyyJLFxkJbN0KNGlSvj0gQNduZvuMcNMzIiIJffHHFazYnwgA+Gh4R0R2DZC4IrIakZHAsGHcgZWIiKq2an8iPv/9EgDgn0+2x+ieTSWuiKyOXA707y91FQ/EwzRERBL49sh1fLTzPADg9UGtMblvsMQVEUmHYYSIqJ79EJeK97afAQC81L8FZgxsKXFFRNJiGCEiqkc7T6vw5taTAIAJfZrhH4+1gayqJZhENoJhhIionuy5cBMzN8ZDK4CR3QLw/pPtGUSIwDBCRFQvDl3NxPRvT6BUKzA01B9RkZ1gZ8cgQgQwjBAR1bn45NuY8nUsiku1GNTeB5+NDIWcQYRIj2GEiKgOXUzPxYS1x1FQrEHflp5YPLoLHOT81Ut0L/5EEBHVketZ+Xhh9VGo75agS9NGWDE2DAp789twikhqDCNERHUgXV2IMV8dxa3cIrT1dcW6CT3gouA+k0SVYRghIjKx7PxivLD6KFJv30UzjwZYP7kHlA0cpC6LyGwxjBARmVBuYQnGrzmGKxl58HVzwjeTe8Lb1UnqsojMGsMIEZGJFJZoMPnrWJxOU8PdxRHfTumBQPcGUpdFZPYYRoiITKBEo8XLG07gWFI2XBX2WD+pB1p6u0pdFpFF4NlURES1pNEKvP79Sey5kAGFvR2+Gt8NIU2UUpdFtkCjAWJiAJUK8PMDwsN1V+q1MAwjRES1IITA/B1nsePkDdjbybD8hTD0bO4hdVlkC6KjgVmzgNTUv9sCAoBFi4DISOnqqgEepiEiqoXPf7+Mb45ch0wGfDaqMwa09Za6JLIF0dHAiBHlgwgApKXp2qOjpamrhhhGiIhqaO3BJHzxx2UAwAfDQvBUqL/EFZFN0Gh0MyJCVLyvrG32bF0/C8EwQkRUA9vj07Dgp3MAgDmDWmNsryCJKyKbERNTcUbkXkIAKSm6fhaCYYSIyEh7LtzE61tOAgAm9GmGVwe2lLgisikqlWn7mQGGESIiIxxLysZL356ARiswvLM/3n+yPWQyXoGX6pGfn2n7mQGGESIiA527kYPJXx9HUakWA9t64/+eDYWdHYMI1bPwcN2qmapCsEwGBAbq+lkIhhEiIgNcz8rHuDXHkFtYiu7NGmPJ6K5wkPNXKElALtct3wUqBpKyrxcutKj9RviTRET0ABk5hXhh9VFk5umuwPvV+O5wdrScX/RkhSIjga1bgSZNyrcHBOjaLWyfEW56RkRUDfXdEoxbcwwp2XcRVHYFXmdegZfMQGQkMGwYd2AlIrJmhSUaTP06FhfSc+HlqsA3k3gFXjIzcjnQv7/UVdRajQ7TLF26FMHBwXByckJYWBhiHrCWecOGDQgNDUWDBg3g5+eHiRMnIisrq0YFExHVh1KNFjO+i8exa7oL3309sQeaevAKvER1wegwsnnzZsyePRvvvvsu4uPjER4ejiFDhiA5ObnS/gcOHMC4ceMwefJknD17Flu2bMHx48cxZcqUWhdPRFQXhBCYG30av5+/Cce/LnzX3t9N6rKIrJbRYeSzzz7D5MmTMWXKFLRr1w4LFy5EYGAgli1bVmn/I0eOoFmzZpg5cyaCg4PRt29fTJs2DbGxsbUunoioLvxn10VsiUuFnQxY/HwXXviOqI4ZFUaKi4sRFxeHiIiIcu0RERE4dOhQpY/p06cPUlNTsXPnTgghcPPmTWzduhVPPPFEla9TVFSEnJyccjciovqwan8ilu+7CgD4OLITIjr4SlwRkfUzKoxkZmZCo9HAx8enXLuPjw/S09MrfUyfPn2wYcMGjBo1Co6OjvD19UWjRo3w5ZdfVvk6UVFRUCqV+ltgYKAxZRIR1cgPcan4aOd5AMBbg9tiZHf+7iGqDzU6gfX+rY+FEFVuh3zu3DnMnDkT77//PuLi4rBr1y4kJSVh+vTpVT7/3LlzoVar9beUlJSalElEZLA9F27iHz+cAgBM6RuM6f2aS1wRke0wammvp6cn5HJ5hVmQjIyMCrMlZaKiovDQQw/hzTffBAB06tQJLi4uCA8Px4cffgi/SvbOVygUUCgUxpRGRFRjsdey8fIG3fVmIrs0wTuPt+P1ZojqkVEzI46OjggLC8Pu3bvLte/evRt9+vSp9DEFBQWwsyv/MvK/NmQRQhjz8kREJnfpZi4mrTuOwhItBrTxwn9GdOL1ZojqmdGHaebMmYOvvvoKa9aswfnz5/Haa68hOTlZf9hl7ty5GDdunL7/0KFDER0djWXLliExMREHDx7EzJkz0aNHD/j7+5vunRARGSntzl2MW30MOYWl6Nq0EZaM4fVmiKRg9A6so0aNQlZWFj744AOoVCqEhIRg586dCAoKAgCoVKpye45MmDABubm5WLx4MV5//XU0atQIAwcOxH/+8x/TvQsiIiNl5xdj7OqjSM8pRCvvhlgzoTsaOHJTaiIpyIQFHCvJycmBUqmEWq2Gmxs3HiKi2skvKsXor47iZMod+Cud8MPLfeCndJa6LCKrY+jnN+cjicimlGi0eGnDCZxMuYNGDRywfnIPBhEiiXFOkohshlYr8OaWk9h/6RacHeRYM6E7Wnq7Sl0WUeU0Gqu4Iq8hGEaIyCYIIfDRzvPYnnAD9nYyLH2hK7o2bSx1WUSVi44GZs0CUlP/bgsIABYtAiIjpaurjvAwDRHZhOX7ErH6QBIA4P+e7YQBbbwlroioCtHRwIgR5YMIAKSl6dqjo6Wpqw4xjBCR1dsSm4L/7LoAAHjviXZ4ukuAxBURVUGj0c2IVLa2pKxt9mxdPyvCMEJEVu33czfxdvRpAMC0fs0xJZzbvJMZi4mpOCNyLyGAlBRdPyvCMEJEViv2WjZe+U63zfszXQPw9uC2UpdEVD2VyrT9LATDCBFZpbJt3otKtRjY1hsfP9OR15sh81fJ9dpq1c9CMIwQkdW5d5v3sKDGWDKa27yThQgP162aqSo4y2RAYKCunxXhTycRWZX7t3lfPb4bnB2tc28GskJyuW75LlAxkJR9vXCh1e03wjBCRFajoLgUE9cdR+KtfPgrnbB+cg80auAodVlExomMBLZuBZo0Kd8eEKBrt8J9RrjpGRFZhRKNFi99y23eyUpERgLDhnEHViIiS1G2zfu+v7Z5X8tt3skayOVA//5SV1EveJiGiCxaZdu8d+E270QWhWGEiCzaiv3c5p3I0jGMEJHF+v54Cj7+hdu8E1k6hhEiski7z93E29GnAHCbdyJLxzBCRBbnWFI2Znx3AloBPBvGbd6JLB3DCBFZlPOqHEz+WrfN+6PtfBAVyW3eiSwdwwgRWYyU7AKMW3MMuYWl6N6sMRaP7gJ7bvNOZPH4U0xEFuFWbhHGrj6KW7lFaOvriq/Gd4eTg3VuAEVkaxhGiMjs5RaWYMLaY7iWVYCAxs5YP6kHlM4OUpdFRCbCMEJEZq2wRIMX18fh7I0ceLg44pvJPeHt5iR1WURkQgwjRGS2NFqB2ZsScDgxCw0V9vh6Ug8Ee7pIXRYRmRjDCBGZJSEE3t12GrvOpsNRboeVY8MQ0kQpdVlEVAcYRojILP1n10VsOp4COxnwxfOd0aelp9QlEVEdYRghIrOzYt9VLN93FQAQFdkRg0P8JK6IiOoSwwgRmZXvj6cg6q/rzbw9pC1GdW8qcUVEVNcYRojIbPx6Nv3v68083BzT+7WQuCIiqg8MI0RkFg5dzcSrG+OhFcCoboF4ewivN0NkKxhGiEhyp1PVeHF9HIpLtXisgw8+ejqE15shsiEMI0Qkqau38jB+7THkFZWiTwsPLHqO15shsjX8iSciydy4cxfjVh9Ddn4xOgUosXJcN15vhsgGMYwQkSQy84rwwuqjSLtzF829XLB2Qnc0VNhLXRYRSYBhhIjqnfpuCcatPobEW/lo0sgZ307uCY+GCqnLIiKJMIwQUb26W6zBlK+P45wqB54NHfHtlJ7wb+QsdVlEJCGGESKqN8WlWkz/Ng7Hr92Gq5M91k/qyQvfERF4gJaI6oVGK/Da5gTsu3QLzg5yrJvYHe393aQui0g6Gg0QEwOoVICfHxAeDsht8wRuhhEiqnNCCLwTfRo/n1bBQS7DirFhCAtyl7osIulERwOzZgGpqX+3BQQAixYBkZHS1SWRGh2mWbp0KYKDg+Hk5ISwsDDExMRU27+oqAjvvvsugoKCoFAo0KJFC6xZs6ZGBRORZRFC4N87z2Nz7F9X4H2uCx5u7SV1WUTSiY4GRowoH0QAIC1N1x4dLU1dEjJ6ZmTz5s2YPXs2li5dioceeggrVqzAkCFDcO7cOTRtWvkFrUaOHImbN29i9erVaNmyJTIyMlBaWlrr4onI/C358wpWxSQBAD5+phOGdOQVeMmGaTS6GREhKt4nBCCTAbNnA8OG2dQhG5kQlY1I1Xr27ImuXbti2bJl+rZ27dph+PDhiIqKqtB/165deO6555CYmAh395pNy+bk5ECpVEKtVsPNjceYiSzFuoNJmP/TOQDAP59sj8l9gyWuiEhie/cCAwY8uN+ffwL9+9d1NXXO0M9vow7TFBcXIy4uDhEREeXaIyIicOjQoUofs2PHDnTr1g2ffPIJmjRpgtatW+ONN97A3bt3q3ydoqIi5OTklLsRkWX5/niKPojMfKQVgwgRoDtZ1ZT9rIRRh2kyMzOh0Wjg4+NTrt3Hxwfp6emVPiYxMREHDhyAk5MTtm3bhszMTLz88svIzs6u8ryRqKgoLFiwwJjSiMiM7Dh5A29FnwIATOkbjNcebSVxRURmws/Aw5SG9rMSNTqB9f6raQohqrzCplarhUwmw4YNG9CjRw88/vjj+Oyzz7Bu3boqZ0fmzp0LtVqtv6WkpNSkTCKSwG9n0/Ha5gQIAYzp2RTvPtGOV+AlKhMerls1U9XPhEwGBAbq+tkQo8KIp6cn5HJ5hVmQjIyMCrMlZfz8/NCkSRMolUp9W7t27SCEQOr9ZxL/RaFQwM3NrdyNiMzf/ku3MOO7eGi0ApFdmuBfw0IYRIjuJZfrlu8CFQNJ2dcLF9rUyauAkWHE0dERYWFh2L17d7n23bt3o0+fPpU+5qGHHsKNGzeQl5enb7t06RLs7OwQEBBQg5KJyBwdTczCi9/EolijxeMdffHJiE6ws2MQIaogMhLYuhVo0qR8e0CArt0G9xkxejXN5s2bMXbsWCxfvhy9e/fGypUrsWrVKpw9exZBQUGYO3cu0tLSsH79egBAXl4e2rVrh169emHBggXIzMzElClT0K9fP6xatcqg1+RqGiLzlpByBy98dRR5RaUY0MYLK8Z2g6M9rzZBVC0b2IHV0M9vo/cZGTVqFLKysvDBBx9ApVIhJCQEO3fuRFBQEABApVIhOTlZ379hw4bYvXs3Xn31VXTr1g0eHh4YOXIkPvzwwxq8LSIyN+dVORi/5hjyikrRp4UHlr0QxiBCZAi53CqW75qC0TMjUuDMCJF5upKRh1ErDiMrvxhhQY2xflIPuCh4lQki0qmTfUaIiMpcz8rHC18dRVZ+MUKauGHNhO4MIkRUIwwjRGS0lOwCPL/yCNJzCtHapyHWT+oJpbOD1GURkYViGCEio6TduYvnVx3BDXUhWni5YMOUXnB3cZS6LCKyYAwjRGSwdHUhnl95BKm37yLY0wUbp/aCl6tC6rKIyMIxjBCRQTJyCvH8qiNIzi5AU/cG+G5qT3i7OUldFhFZAYYRInqgW7lFeH7VESRl5qNJI2d8N7Un/JTOUpdFRFaCYYSIqpWdX4wXvjqKq7fy4ad0wqYXeyGgcQOpyyIiK8IwQkRVulNQjDFfHcXFm7nwcVNg49ReCHRnECEi02IYIaJKqQtK8MLqozivyoFnQwW+m9oLzTxdpC6LiKwQwwgRVXCnoBhjVh/BmbQceLg4YuPUnmjh1VDqsojISnG7RCIqp+zQzNkbuiDy3dReaOXjKnVZRGTFGEaISO92vi6InFPlwLOhLoi0ZhAhqhkbuCqvqTCMEBEA3aqZ0auO4EJ6LjwbKrBxak/OiBDVVHQ0MGsWkJr6d1tAALBoERAZKV1dZornjBARsvKKygWRTS8yiBDVWHQ0MGJE+SACAGlpuvboaGnqMmMMI0Q2LjOvCKNXHcWF9Fx4uSqw6cVeaOnNIEJUIxqNbkZEiIr3lbXNnq3rR3oMI0Q27FZuEZ5feQQXb+bCWx9EuGqGqMZiYirOiNxLCCAlRdeP9HjOCJGNupWrOzRzOSNPv6FZcy7fJaodlcq0/WwEwwiRDVKp72LMqqNIzMyHr5sTNr7YC8Hc0Iyo9vz8TNvPRvAwDZGNSckuwMgVh5H410XvNjGIEJlOeLhu1YxMVvn9MhkQGKjrR3oMI0Q2JPFWHp5dfhgp2XcR5NEAm6dxi3cik5LLdct3gYqBpOzrhQu538h9GEaIbMTF9FyMXHEE6TmFaOndEN9P682r7xLVhchIYOtWoEmT8u0BAbp27jNSAc8ZIbIBp1PVGLvmKO4UlKC9nxu+mdwDHg0VUpdFZL0iI4Fhw7gDq4EYRoisXNz1bExYcxy5RaUIDWyE9RN7QNnAQeqyiKyfXA707y91FRaBYYTIih26mokpX8eioFiDHs3csXpCN7g6MYgQ1RqvO2NSDCNEVmrvxQxM+yYORaVahLfyxMqx3eDsyF+WRLXG686YHE9gJbJCP528ganrY1FUqsWj7byxahyDCJFJ8LozdYJhhMjKfHPkOmZuikeJRmBoqD+WvRAGJwcGEaJa43Vn6gzDCJGVEELgyz8u45/bz0AIYGyvICwa1RkOcv6YE5kErztTZ3jOCJEV0GoFPvz5PNYcTAIAzHykFV57tBVkVe0CSUTG43Vn6gzDCJGFK9Fo8dYPpxB9Ig0AMG9oe0x8KFjiqoisEK87U2cYRogsWGGJBjO+O4Hfz2dAbifDf5/thKe7BEhdFpF1KrvuTFpa5eeNyGS6+3ndGaPxYDKRhcopLMG41cfw+/kMKOztsHJsGIMIUV3idWfqDMMIkQXKyC3EcyuO4Ni1bLgq7LF+Ug880s5H6rKIrB+vO1MneJiGyMJcvZWH8WuOIfX2XXg2dMTXk3qgg79S6rKIbAevO2NyDCNEFiTuejYmfx2LOwUlaObRAOsm9kAzTxepyyKyPbzujEkxjBBZiF1n0jFrUzyKSrUIDWyENeO78cq7RGQVGEaILMD6w9cwb8dZCAE80tYbX47uggaO/PElIuvA32ZEZkyrFfjk14tYvu8qAGB0z6b44KkOsOeuqkRkRWr0G23p0qUIDg6Gk5MTwsLCEGPg1rcHDx6Evb09OnfuXJOXJbIpxaVazPk+QR9E3ohojY+GhzCIEJHVMfq32ubNmzF79my8++67iI+PR3h4OIYMGYLk5ORqH6dWqzFu3Dg88sgjNS6WyFbkFJZgwtpj2J5wA/Z2Mvz32VDMGMjt3YnIOsmEqGwbuar17NkTXbt2xbJly/Rt7dq1w/DhwxEVFVXl45577jm0atUKcrkc27dvR0JCgsGvmZOTA6VSCbVaDTc3N2PKJbI4KdkFmPz1cVy6mQcXRzmWvRCGh1t7SV0WEZHRDP38NmpmpLi4GHFxcYiIiCjXHhERgUOHDlX5uLVr1+Lq1auYN2+eQa9TVFSEnJyccjciWxB3PRvDlxzEpZt58HFTYPO03gwiRGT1jAojmZmZ0Gg08PEpv9Ojj48P0tPTK33M5cuX8fbbb2PDhg2wtzfsfNmoqCgolUr9LTAw0JgyiSzSjwlpeH7VUWTlF6ODvxt+fKUvQppwMzMisn41OhPu/uPWQohKj2VrNBqMHj0aCxYsQOvWrQ1+/rlz50KtVutvKSkpNSmTyCIIIfDZ7kuYtSkBxaVaRLT3wZbpveGrdJK6NCKiemHU0l5PT0/I5fIKsyAZGRkVZksAIDc3F7GxsYiPj8eMGTMAAFqtFkII2Nvb47fffsPAgQMrPE6hUECh4GZOZP0KSzR4Y8tJ/O+UCgAwrV9zvPVYW9jZ8URVIrIdRoURR0dHhIWFYffu3Xj66af17bt378awYcMq9Hdzc8Pp06fLtS1duhR79uzB1q1bERwcXMOyiSxfRm4hXlwfh4SUO7C3k+HfT3fEyO48JElEtsfoTc/mzJmDsWPHolu3bujduzdWrlyJ5ORkTJ8+HYDuEEtaWhrWr18POzs7hISElHu8t7c3nJycKrQT2ZIL6TmYvC4WaXfuQunsgOUvhKF3Cw+pyyIikoTRYWTUqFHIysrCBx98AJVKhZCQEOzcuRNBQUEAAJVK9cA9R4hs2a4zKsz5/iQKijUI9nTBmgndEcyL3RGRDTN6nxEpcJ8RsgZarcDC3y/hiz1XAAB9Wnhg6ZiuaNTAUeLKiKgCjQaIiQFUKsDPDwgP112pl4xi6Oc3r01DVA9yCkvw2qYE/HEhAwAw6aFgvPN4W27tTmSOoqOBWbOA1NS/2wICgEWLgMhI6eqyYgwjRHXs6q08TF0fi8Rb+XC0t8PHkR0R2TVA6rKIqDLR0cCIEcD9Bw3S0nTtW7cykNQB/llGVIf+OH8TwxcfROKtfPgpnbB1em8GESJzpdHoZkQqO3uhrG32bF0/MimGEaI6oNUKfPnHZUxZH4vcolL0aOaOHTP6olNAI6lLI6KqxMSUPzRzPyGAlBRdPzIpHqYhMrG8olK8ueUkfjmj2xxwXO8gvPdEezjaM/sTmTWVyrT9yGAMI0QmdCE9By9/ewKJmflwlNvhX8M7YFT3plKXRUSG8PMzbT8yGMMIkYlsiU3BP388g8ISLfyUTlgypiu6Nm0sdVlEZKjwcN2qmbS0ys8bkcl094eH139tVo7zxkS1VFiiwT+2nsSbW0+hsESLfq298PPMcAYRIksjl+uW7wK64HGvsq8XLuR+I3WAYYSoFpIy8/H00kP4PjYVdjLgjYjWWDuhO9xduJEZkUWKjNQt323SpHx7QACX9dYhHqYhqqFfTqvw5tZTyCsqhWdDR3zxXBf0aekpdVlEVFuRkcCwYdyBtR4xjBAZqbhUi6hfzmPtwWsAgB7N3PHl6C7wcXOStjAiMh25HOjfX+oqbAbDCJERrmXmY9ameJxMVQMApvdrgTciWnNbdyKiWmAYITKAEAI/nEjDvB/PIL9YA6WzAz59NhSPtveRujQiIovHMEL0ADmFJXh32xn8dPIGAKBnsDsWPtcZfkpniSsjIrIODCNE1Yi7no1ZmxKQevsu5HYyzBnUGtP7tYDcTvbgBxMRkUEYRogqodEKLN5zBV/suQyNViDQ3RlfPNcFXbh3CBGRyTGMEN0n7c5dvLYpAceuZQMAhnf2x7+Gh8DVyUHiyoiIrBPDCNFfhBCIPpGG+T+dRW5hKRoq7PGv4R3wdJcAqUsjIrJqDCNEADJyC/FO9Bn8fv4mAKBzYCMseq4zgjxcJK6MiMj6MYyQzfvfqRv45/YzuF1QAge5DLMfbY1pDzfn3iFE1kyj4Q6rZoRhhGzW7fxi/PPHM/jfKRUAoL2fGz4dGYp2fm4SV0ZEdSo6Gpg1C0hN/bstIEB3kTxee0YSDCNkk3afu4m50aeRmVcEuZ0Mr/RvgRkDW8HRnrMhRFYtOhoYMQIQonx7WpqunRfDk4RMiPv/j5ifnJwcKJVKqNVquLnxr1aqOXVBCT743zn8cEL3F1FL74b4bGQoOgU0krYwIqp7Gg3QrFn5GZF7yWS6GZKkJB6yMRFDP785M0I2QQiBn0+rMH/HOWTmFUEmA14Mb47XBrWGkwN/6RDZhJiYqoMIoJstSUnR9eNF8uoVwwhZvRt37uKf28/gjwsZAIAWXi74zzOd0K2Zu8SVEVG9UqlM249MhmGErJZGK/DN4Wv4v18vIr9YAwe5DC/3b4mXB7SAwp6zIUQ2x8/PtP3IZBhGyCpdSM/B2z+cRkLKHQBAWFBjfBzZEa18XKUtjIikEx6uOyckLa3iCazA3+eMhIfXf202jmGErEphiQaL91zB8n1XUaoVcFXY4x9D2mJMj6aw48XtiGybXK5bvjtihC543BtIZH/9fli4kCevSoBhhKzGH+dvYsFP55CcXQAAeKyDDxY8FQJfpZPElRGR2YiM1C3frWyfkYULuaxXIgwjZPGuZ+Xjg5/O6U9Q9XFTYMFTIRgc4itxZURkliIjgWHDuAOrGWEYIYt1t1iDZXuvYPn+RBSXauEgl2FS32DMHNgKLgp+axPZLEO2epfLuXzXjPA3NlkcIQR+PZuOf/3vPNLu3AUAhLfyxLyhHdDSu6HE1RGRpLjVu0ViGCGLcvVWHubvOIuYy5kAgCaNnPHPJ9vjsQ4+kMl4giqRTeNW7xaL28GTRcjOL8YXf1zGt0euo1Qr4Ghvh+kPN8dL/VvC2ZHHeYlsHrd6N0vcDp6sQmGJBusOXcOSPVeQW1QKAHikrTfeH9oeQR4uEldHRGaDW71bNIYRMktarcBPp27gk10X9eeFtPdzw7tPtMNDLT0lro6IzA63erdoDCNkdo4lZeOjn8/hZKoaAODr5oQ3H2uDp7s04cZlRFQ5bvVu0RhGyGxcycjF//16Eb+evQkAcHGU46X+LTC5b3OeF0JE1eNW7xbNriYPWrp0KYKDg+Hk5ISwsDDExMRU2Tc6OhqDBg2Cl5cX3Nzc0Lt3b/z66681Lpisz/WsfMzZnICIz/fj17M3YScDxvRsir1vDsCMga0YRIioPI0G2LsX2LhR969G8/dW78DfW7uX4VbvZs/oMLJ582bMnj0b7777LuLj4xEeHo4hQ4YgOTm50v779+/HoEGDsHPnTsTFxWHAgAEYOnQo4uPja108WbYbd+5ibvRpPPLpPkTHp0ErdFu4/zr7YXz0dEd4uSqkLpGIzE10tG7VzIABwOjRun+bNdO1l2313qRJ+ccEBHBZr5kzemlvz5490bVrVyxbtkzf1q5dOwwfPhxRUVEGPUeHDh0watQovP/++wb159Je65KRW4ilf17Fd0eTUazRAgD6tfbC6xGt0SmgkbTFEZH5qmofkbKZj7LAYcgOrFQv6mRpb3FxMeLi4vD222+Xa4+IiMChQ4cMeg6tVovc3Fy4u7tX2aeoqAhFRUX6r3Nycowpk8zU7fxirNifiK8PXcPdEg0AoGewO954rA26N6v6+4GICBqNbmfVyv5+FkIXSGbP1l1zhlu9WxyjwkhmZiY0Gg18fHzKtfv4+CA9Pd2g5/j000+Rn5+PkSNHVtknKioKCxYsMKY0MmMZOYX46kASvj1yHQXFuhASGtgIb0a0wUMtPbhzKhE9GPcRsWo1Wk1z/4eHEMKgD5SNGzdi/vz5+PHHH+Ht7V1lv7lz52LOnDn6r3NychAYGFiTUklCqbcLsGJfIjbHpqC4VHc4pr2fG+YMao1H2nkzhBCR4biPiFUzKox4enpCLpdXmAXJyMioMFtyv82bN2Py5MnYsmULHn300Wr7KhQKKBQ8edFSXb2Vh2V7r2J7fBpKtbop1bCgxpgxoCX6t/FiCCEi43EfEatmVBhxdHREWFgYdu/ejaefflrfvnv3bgwbNqzKx23cuBGTJk3Cxo0b8cQTT9S8WjJr527kYMneK9h5WqU/rNu3pSdeGdASvZq7M4QQ0YNVdfIp9xGxakYfppkzZw7Gjh2Lbt26oXfv3li5ciWSk5Mxffp0ALpDLGlpaVi/fj0AXRAZN24cFi1ahF69eulnVZydnaFUKk34VkgKWq3Avku38NWBRBy8kqVvf7SdD14Z0AJdmjaWsDoisijR0bqTVO89NyQgQLd/SGSk7t8RI3TB495Awn1ELJ7RYWTUqFHIysrCBx98AJVKhZCQEOzcuRNBQUEAAJVKVW7PkRUrVqC0tBSvvPIKXnnlFX37+PHjsW7dutq/A5JEYYkG0SfSsPpAIq7eygcAyO1keLyjH17u3wLt/LgEm4iMUNWy3bQ0XXvZst2tWysPLAsXch8RC2b0PiNS4D4j5iMjtxDfHr6Ob48mIzu/GADgqrDHcz0CMb5PMwQ0biBxhURkcTQa3cZlVa2WKTsEk5Skm/ngPiIWo072GSHbdSZNjXWHrmFHwg39RmUBjZ0x8aFgjOwWAFcnB4krJCKLZeyyXe4jYnUYRqhKhSUa/O+UCt8cuY6TKXf07WFBjTGlbzAGtfeBvbxGlzciIltV2awGl+3aPIYRqiApMx8bjlzHlrhUqO+WAAAc5DIMCfHDhIeaoStPSiWimqjqBNWpUw17PJftWi2eM0IAgFKNFn9cyMC3R64j5nKmvr1JI2eM6dUUI7sFwrMh934hohqq7royQgAeHkB2dvXLdsvOGSGLwXNGyCBXb+VhS2wqok+kIiNXdz0gmQzo39oLY3sHoV9rb8jtuD8IERmossMwwIOvK1OGy3ZtEsOIDcotLMHPp1T4PjYFJ5Lv6NvdXRwxqnsgRvdoikB3roohIiNVdxjmQSeoZmUBCxYAq1Zx2a4NYhixEVqtwNGkbGyJTcHOMyoUluhWxMjtZOjf2gvPdgvAwLY+cLTnCalEVAPV7RMyb55hz9GqFXDtGpft2iCGESt3MT0XO06m4ceEG0i9fVff3tK7IZ4NC8DTXZrA281JwgqJyGJUtb+HRlP9YRhD+flx2a6NYhixQinZBdhx8gZ+OnkDF9Jz9e2uCns8GeqPZ7sFoEtgI14rhogMV91W7e7u1R+GeRBeV8bmMYxYicy8Ivx8SoUdJ28g7vptfbuj3A792nhhWGd/PNLWB86OnO4kIiM9aKv2WbMMfy6eoEqVYBixYOnqQvx2Lh27zqTjaFI2NFrdD7hMBvRp4YGnQv0xuIMflA24OyoRGaCmK2E2bDDs+XmCKlWBYcTCJGcVYNdZFXadSS+3EgYAQgMbYVioP57s5MfzQIioouqu6VKblTC3bgFeXkBmZvX7hLz7ru7GE1TpPgwjZk4IgUs38/DrWd0MyDlVTrn7w4IaY3AHXwwO8eVyXCKqWnXnfAC1XwkzZozuuQw5DMMTVOk+DCNmqLBEg8OJWdhzPgN7LmQg7c7fq2DkdjL0DHbHkBBfRHTwhQ9nQIgIePCsR1Vh45lndLuf1nYlzLBhutesLPDwMAw9ALeDNxPp6kLsuZCBPRdu4uCVLNwt0ejvU9jb4aGWnhjcwRePtveBu4ujhJUSkdmpbtZj2DCgWbParXapzv1btVcXisjmcDt4M1dYokHc9dvYf/kWYi5lVjj84uvmhIHtvPFIW2/0aeHJVTBEVLkHrXSZP990QcSQQzDcJ4RqgGGkngghcPFmLmIuZSLmSiaOJWXpd0EFdD/TnQMb4ZG23hjY1gft/Fy5DwgR/a2mK13KzgmpLa6EoTrEMFJHhBBIvX0XhxOzcORqFmKuZOLWXxeiK+PtqkB4Ky+Et/JE31aevCouEVWuNitdsrNr99pcCUP1gGHERIQQSMm+iyOJWTiSmIWjSdnlTjwFACcHO/Rq7oG+LT3xcGsvtPJuyNkPIqqeKa754u4O3L5d9bJbd/e/QwtXwpAEGEZqSKsVuHIrD3HXb+NYUjaOJGZBpS4s18feToZOAUpdAGnlibCgxlDY868IIqpETQ7DGGrWLN25I1Wd87Fy5d/9eBiGJMAwYqD8olKcTLmDuOu3EZd8Gyeu30ZOYWm5Pg5yGUIDGqFXcw/0bO6OsKDGaODIISaiB6jpYZgHufcQS0jIg8PGsGE8DEOS4NLeSmi1AomZ+TiZcgenUu8gLvk2zqty9dutl3F2kKNzYCN0a9YYvZp7oGvTxlz1QkTGqeowzP2zGA9S1azH1q1/hw0uu6V6xqW9BhJC4Ia6EKdS7uBkqhonU+7gTJoauUWlFfr6K53QNagxugU1RliQO9r6ucJBbidB1URkFTQa0xyGMXSlC5fdkpmy6TDywU/nsOPkDWTmFVW4z8nBDiH+SnQKaISuQY3QtWlj+DdylqBKIrJ4Vc1IxMSY7jAMV7qQBbPpMJJfVIrMvCLI7WRo6+uKTgGNEBqgRGhgI7Tybgh7znoQUW1VtztqUcU/hKrEa76QFbPpMDKpbzBGdg9EB383ODnwLwgiMjFDdkc1BDccIyvHE1iJiB7kQSd+VrUst7prwshkQJMmuv9OS6t6D5Cy674APAxDFocnsBIRGeJBQaO6wyyRkbXbHTU1VTfrUd0eIDwMQzaAMyNEZNlqMmtRdr8hQaOqZbcA8MYbwH//W7tlud99BygUFesIDORhGLJ4hn5+M4wQUc3UJgSY6jVqOmtRdvG46oLG5s3AnDnVz27I5boaa+PPP3UzHtwDhKwQwwgR1U5tZxSqu99Ur1GbWQsPDyArq/L3LpMBnp7ArVuGj5ex7j0fhKGDrBTDCBFVrTYzDkDNQwDw946gljBrYSqG7I5KZIUYRojqQn0cejDkNaQ6T+JBMwpA9SGgbDbgs8+AkSPNd9bClCpblsvzQchGGPz5LSyAWq0WAIRarZa6FJJSaakQf/4pxHff6f4tLTXu/to+xw8/CBEQIITu41J3CwjQtZvqOQx5jdo8xw8/CCGTlb8P0LXJZEJ8/33Fx9bFzcur7l/DVHVWNl5lN7m86vtlMiECA3X//w353iSyQoZ+fjOMkGnUdVAw9w9xUzzHm28++DVq8xyAEB4eVX+wymSWExLq+lYWJLZs+Xtsqxvvqu6/P6gS2RiGkQep67+irek1HtSnroOCJXyI3/vBVZPnAHR/ZVf3GgEBD561qO45rO1W21kLDw/DgkRl35uBgYbfT2TDGEaqU9d/RVvTazyoT10HBcByPsQ5q/D3WFYXAmo7TqactTA0SJgi0BPZIIaRqhgy3V7bD9i6/ku9vl7DXIICb/V7q27GwZAZhQeFgLLzUsxl1oJBgqjO1GkYWbJkiWjWrJlQKBSia9euYv/+/dX237t3r+jatatQKBQiODhYLFu2zKjXM1kYKS2t/oPPVH9F18df6nX9GgwKtnczdMbBkBkFQ+7nrAWR1auzMLJp0ybh4OAgVq1aJc6dOydmzZolXFxcxPXr1yvtn5iYKBo0aCBmzZolzp07J1atWiUcHBzE1q1bDX5Nk4WRP/+U/hc+b9Z3M9WJnw86vFEWDs3hPAkhah8COGtBZPXqLIz06NFDTJ8+vVxb27Ztxdtvv11p/3/84x+ibdu25dqmTZsmevXqZfBrmiyMfPed9B9cvJn+Zg4f4qY49GDoOQ7mcp6EKTBsEFm1OgkjRUVFQi6Xi+jo6HLtM2fOFA8//HCljwkPDxczZ84s1xYdHS3s7e1FcXFxpY8pLCwUarVaf0tJSTHozTwQZ0bq/1bboGBJH+KmOPRgSFDgeRJEZCHqJIykpaUJAOLgwYPl2j/66CPRunXrSh/TqlUr8dFHH5VrO3jwoAAgbty4Uelj5s2bJwBUuJnsnJG6/CvaFB/A5vAa5hQULOlDvD4Ob5jqOYiI6lidhpFDhw6Va//www9FmzZtKn1Mq1atxL///e9ybQcOHBAAhEqlqvQxdTYzIoThH3y1+YCtj7/U63M2wByCghCW8yHOIEBEJISw8MM096uXfUZM/Ve0tbyGoX3qIygQEZFFMfTzWyaEEMZc9KZnz54ICwvD0qVL9W3t27fHsGHDEBUVVaH/W2+9hZ9++gnnzp3Tt7300ktISEjA4cOHDXrNOrlQXl1fjMyaXsPQPkRERPeos6v2bt68GWPHjsXy5cvRu3dvrFy5EqtWrcLZs2cRFBSEuXPnIi0tDevXrwcAJCUlISQkBNOmTcPUqVNx+PBhTJ8+HRs3bsQzzzxj0jdDRERE5sPQz297Y5941KhRyMrKwgcffACVSoWQkBDs3LkTQUFBAACVSoXk5GR9/+DgYOzcuROvvfYalixZAn9/f3zxxRcGBxEiIiKybkbPjEiBMyNERESWx9DPb7t6rImIiIioAoYRIiIikhTDCBEREUmKYYSIiIgkxTBCREREkmIYISIiIkkxjBAREZGkjN70TAplW6Hk5ORIXAkREREZquxz+0FbmllEGMnNzQUABAYGSlwJERERGSs3NxdKpbLK+y1iB1atVosbN27A1dUVMpnMZM+bk5ODwMBApKSkcGdXE+B4mg7H0rQ4nqbDsTQtax9PIQRyc3Ph7+8PO7uqzwyxiJkROzs7BAQE1Nnzu7m5WeU3gVQ4nqbDsTQtjqfpcCxNy5rHs7oZkTI8gZWIiIgkxTBCREREkrLpMKJQKDBv3jwoFAqpS7EKHE/T4ViaFsfTdDiWpsXx1LGIE1iJiIjIetn0zAgRERFJj2GEiIiIJMUwQkRERJJiGCEiIiJJWXwY2b9/P4YOHQp/f3/IZDJs37693P03b97EhAkT4O/vjwYNGmDw4MG4fPlyhec5fPgwBg4cCBcXFzRq1Aj9+/fH3bt39fffvn0bY8eOhVKphFKpxNixY3Hnzp06fnf1r7bjee3aNchkskpvW7Zs0fezhfE0xfdmeno6xo4dC19fX7i4uKBr167YunVruT62MJaAacbz6tWrePrpp+Hl5QU3NzeMHDkSN2/eLNfHFsYzKioK3bt3h6urK7y9vTF8+HBcvHixXB8hBObPnw9/f384Ozujf//+OHv2bLk+RUVFePXVV+Hp6QkXFxc89dRTSE1NLdfH2sfTVGO5cuVK9O/fH25ubpDJZJWOkTWPpcWHkfz8fISGhmLx4sUV7hNCYPjw4UhMTMSPP/6I+Ph4BAUF4dFHH0V+fr6+3+HDhzF48GBERETg2LFjOH78OGbMmFFu69rRo0cjISEBu3btwq5du5CQkICxY8fWy3usT7Udz8DAQKhUqnK3BQsWwMXFBUOGDNE/ly2Mpym+N8eOHYuLFy9ix44dOH36NCIjIzFq1CjEx8fr+9jCWAK1H8/8/HxERERAJpNhz549OHjwIIqLizF06FBotVr9c9nCeO7btw+vvPIKjhw5gt27d6O0tBQRERHlvvc++eQTfPbZZ1i8eDGOHz8OX19fDBo0SH+tMACYPXs2tm3bhk2bNuHAgQPIy8vDk08+CY1Go+9j7eNpqrEsKCjA4MGD8c4771T5WlY9lsKKABDbtm3Tf33x4kUBQJw5c0bfVlpaKtzd3cWqVav0bT179hTvvfdelc977tw5AUAcOXJE33b48GEBQFy4cMG0b8KM1HQ879e5c2cxadIk/de2OJ41HUsXFxexfv36cs/l7u4uvvrqKyGEbY6lEDUbz19//VXY2dkJtVqt75OdnS0AiN27dwshbHc8MzIyBACxb98+IYQQWq1W+Pr6io8//ljfp7CwUCiVSrF8+XIhhBB37twRDg4OYtOmTfo+aWlpws7OTuzatUsIYZvjWZOxvNeff/4pAIjbt2+Xa7f2sbT4mZHqFBUVAQCcnJz0bXK5HI6Ojjhw4AAAICMjA0ePHoW3tzf69OkDHx8f9OvXT38/oJs5USqV6Nmzp76tV69eUCqVOHToUD29G+kZMp73i4uLQ0JCAiZPnqxv43gaPpZ9+/bF5s2bkZ2dDa1Wi02bNqGoqAj9+/cHwLEsY8h4FhUVQSaTldtcysnJCXZ2dvo+tjqearUaAODu7g4ASEpKQnp6OiIiIvR9FAoF+vXrpx+HuLg4lJSUlOvj7++PkJAQfR9bHM+ajKUhrH0srTqMtG3bFkFBQZg7dy5u376N4uJifPzxx0hPT4dKpQIAJCYmAgDmz5+PqVOnYteuXejatSseeeQR/fHm9PR0eHt7V3h+b29vpKen198bkpgh43m/1atXo127dujTp4++jeNp+Fhu3rwZpaWl8PDwgEKhwLRp07Bt2za0aNECAMeyjCHj2atXL7i4uOCtt95CQUEB8vPz8eabb0Kr1er72OJ4CiEwZ84c9O3bFyEhIQCgf68+Pj7l+vr4+OjvS09Ph6OjIxo3blxtH1saz5qOpSGsfSytOow4ODjghx9+wKVLl+Du7o4GDRpg7969GDJkCORyOQDojxVPmzYNEydORJcuXfD555+jTZs2WLNmjf65ZDJZhecXQlTabq0MGc973b17F9999125WZEytj6eho7le++9h9u3b+P3339HbGws5syZg2effRanT5/W97H1sQQMG08vLy9s2bIFP/30Exo2bAilUgm1Wo2uXbuWG3NbG88ZM2bg1KlT2LhxY4X77n/PhozD/X1saTxNPZYPeo6aPo85spe6gLoWFhaGhIQEqNVqFBcXw8vLCz179kS3bt0AAH5+fgCA9u3bl3tcu3btkJycDADw9fWtcMY9ANy6datC2rV2DxrPe23duhUFBQUYN25cuXaOp86DxvLq1atYvHgxzpw5gw4dOgAAQkNDERMTgyVLlmD58uUcy3sY8r0ZERGBq1evIjMzE/b29mjUqBF8fX0RHBwMwPa+N1999VXs2LED+/fvR0BAgL7d19cXgO6v8bLfkYDusHbZOPj6+qK4uBi3b98uNzuSkZGhnwm1pfGszVgawtrH0qpnRu6lVCrh5eWFy5cvIzY2FsOGDQMANGvWDP7+/hWWYl26dAlBQUEAgN69e0OtVuPYsWP6+48ePQq1Wl3u8IMtqWo877V69Wo89dRT8PLyKtfO8SyvqrEsKCgAgHKrugDduRBlM3ocy4oM+d709PREo0aNsGfPHmRkZOCpp54CYDvjKYTAjBkzEB0djT179ujDWJng4GD4+vpi9+7d+rbi4mLs27dPPw5hYWFwcHAo10elUuHMmTP6PrYwnqYYS0NY/VhKctqsCeXm5or4+HgRHx8vAIjPPvtMxMfHi+vXrwshhPj+++/Fn3/+Ka5evSq2b98ugoKCRGRkZLnn+Pzzz4Wbm5vYsmWLuHz5snjvvfeEk5OTuHLlir7P4MGDRadOncThw4fF4cOHRceOHcWTTz5Zr++1PphiPIUQ4vLly0Imk4lffvml0texhfGs7VgWFxeLli1bivDwcHH06FFx5coV8d///lfIZDLx888/6/vZwlgKYZrvzTVr1ojDhw+LK1euiG+++Ua4u7uLOXPmlOtjC+P50ksvCaVSKfbu3StUKpX+VlBQoO/z8ccfC6VSKaKjo8Xp06fF888/L/z8/EROTo6+z/Tp00VAQID4/fffxYkTJ8TAgQNFaGioKC0t1fex9vE01ViqVCoRHx8vVq1aJQCI/fv3i/j4eJGVlaXvY81jafFhpGwZ1P238ePHCyGEWLRokQgICBAODg6iadOm4r333hNFRUUVnicqKkoEBASIBg0aiN69e4uYmJhy92dlZYkxY8YIV1dX4erqKsaMGVNh6ZU1MNV4zp07VwQEBAiNRlPp69jCeJpiLC9duiQiIyOFt7e3aNCggejUqVOFpb62MJZCmGY833rrLeHj4yMcHBxEq1atxKeffiq0Wm25PrYwnpWNIwCxdu1afR+tVivmzZsnfH19hUKhEA8//LA4ffp0uee5e/eumDFjhnB3dxfOzs7iySefFMnJyeX6WPt4mmos582b98DnseaxlAkhRF3NuhARERE9iM2cM0JERETmiWGEiIiIJMUwQkRERJJiGCEiIiJJMYwQERGRpBhGiIiISFIMI0RERCQphhEiIiKSFMMIERERSYphhIiIiCTFMEJERESSYhghIiIiSf0/pg+c+exO4f8AAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "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": 29,
+   "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": 30,
+   "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": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 800x500 with 1 Axes>"
+      ]
+     },
+     "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": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Mean absolute error: 0.03\n",
+      "Residual sum of squares (MSE): 0.00\n",
+      "R2-score: 0.97\n"
+     ]
+    }
+   ],
+   "source": [
+    "# 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"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<details><summary>Click here for the solution</summary>\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",
+    "</details>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h2>Want to learn more?</h2>\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: <a href=\"https://www.ibm.com/analytics/spss-statistics-software?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">SPSS Modeler</a>\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 <a href=\"https://www.ibm.com/cloud/watson-studio?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">Watson Studio</a>\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",
+    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
+    "\n",
+    "\n",
+    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
+    "\n",
+    "<!--## Change Log\n",
+    "\n",
+    "\n",
+    "|  Date (YYYY-MM-DD) |  Version | Changed By  |  Change Description |\n",
+    "|---|---|---|---|\n",
+    "| 2020-11-03  | 2.1 | Lakshmi |  Made changes in URL |\n",
+    "| 2020-08-27  | 2.0  | Lavanya  |  Moved lab to course repo in GitLab |\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/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-Polynomial-Regression-Co2.ipynb b/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-Polynomial-Regression-Co2.ipynb
new file mode 100644
index 0000000..143240f
--- /dev/null
+++ b/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Reg-Polynomial-Regression-Co2.ipynb	
@@ -0,0 +1 @@
+{"cells":[{"cell_type":"markdown","id":"2e6762b5-6b8c-4ce9-ad41-92e4bcb6d8df","metadata":{},"outputs":[],"source":["<p style=\"text-align:center\">\n","    <a href=\"https://skills.network\" target=\"_blank\">\n","    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n","    </a>\n","</p>\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","id":"e618a869-5310-4ba0-b490-c8e579f93c1c","metadata":{},"outputs":[],"source":["<h1>Table of contents</h1>\n","\n","<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n","    <ol>\n","        <li><a href=\"#download_data\">Downloading Data</a></li>\n","        <li><a href=\"#polynomial_regression\">Polynomial regression</a></li>\n","        <li><a href=\"#evaluation\">Evaluation</a></li>\n","        <li><a href=\"#practice\">Practice</a></li>\n","    </ol>\n","</div>\n","<br>\n","<hr>\n"]},{"cell_type":"markdown","id":"392f7014-a344-431e-9b8d-64cc6f1b0ade","metadata":{},"outputs":[],"source":["### Importing Needed packages\n"]},{"cell_type":"code","id":"bf6caec0-6da0-4325-b416-fe9c29afd1cb","metadata":{},"outputs":[],"source":["import matplotlib.pyplot as plt\nimport pandas as pd\nimport pylab as pl\nimport numpy as np\n%matplotlib inline\n"]},{"cell_type":"markdown","id":"f6af5655-0d6a-408f-8120-6b173d4e9bc1","metadata":{},"outputs":[],"source":["<h2 id=\"download_data\">Downloading Data</h2>\n","To download the data, we will use !wget to download it from IBM Object Storage.\n"]},{"cell_type":"code","id":"e1931ff3-e73f-4816-8dfb-e8ac5aac8c34","metadata":{},"outputs":[],"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","id":"f748b822-0e87-485b-91bc-bf4eaebe65da","metadata":{},"outputs":[],"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","id":"8e80841b-77f9-4bb2-b8b1-3497973e5e13","metadata":{},"outputs":[],"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","id":"01d4769f-560a-4fa4-98ed-1d3745686717","metadata":{},"outputs":[],"source":["## Reading the data in\n"]},{"cell_type":"code","id":"3f105bf0-8870-4df8-9cc7-a6e33c0d5383","metadata":{},"outputs":[],"source":["df = pd.read_csv(\"FuelConsumption.csv\")\n\n# take a look at the dataset\ndf.head()"]},{"cell_type":"markdown","id":"93280331-49b0-42a2-b311-6b249758130b","metadata":{},"outputs":[],"source":["Let's select some features that we want to use for regression.\n"]},{"cell_type":"code","id":"2c5f0bc6-c86f-4009-bf7b-bf2f20873e6a","metadata":{},"outputs":[],"source":["cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\ncdf.head(9)"]},{"cell_type":"markdown","id":"55ec7be8-812d-42d7-8dd7-c59aa947ac67","metadata":{},"outputs":[],"source":["Let's plot Emission values with respect to Engine size:\n"]},{"cell_type":"code","id":"d1f7a5f2-859c-4d08-b9ec-139174e33618","metadata":{},"outputs":[],"source":["plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS,  color='blue')\nplt.xlabel(\"Engine size\")\nplt.ylabel(\"Emission\")\nplt.show()"]},{"cell_type":"markdown","id":"aa3dbb2a-b254-495a-9c32-c25318dbf259","metadata":{},"outputs":[],"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","id":"041baf27-177d-43ac-86e8-aa8da671de60","metadata":{},"outputs":[],"source":["msk = np.random.rand(len(df)) < 0.8\ntrain = cdf[msk]\ntest = cdf[~msk]"]},{"cell_type":"markdown","id":"4aba329a-721c-4191-b33d-d23f7c35e096","metadata":{},"outputs":[],"source":["<h2 id=\"polynomial_regression\">Polynomial regression</h2>\n"]},{"cell_type":"markdown","id":"650dc952-826f-4585-961d-c3ecf3fc0973","metadata":{},"outputs":[],"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","id":"be8fb5a0-3b0b-4dd2-b38d-215c43d1da8b","metadata":{},"outputs":[],"source":["from sklearn.preprocessing import PolynomialFeatures\nfrom sklearn import linear_model\ntrain_x = np.asanyarray(train[['ENGINESIZE']])\ntrain_y = np.asanyarray(train[['CO2EMISSIONS']])\n\ntest_x = np.asanyarray(test[['ENGINESIZE']])\ntest_y = np.asanyarray(test[['CO2EMISSIONS']])\n\n\npoly = PolynomialFeatures(degree=2)\ntrain_x_poly = poly.fit_transform(train_x)\ntrain_x_poly"]},{"cell_type":"markdown","id":"3487a10a-f2d0-4a17-93da-5b8397b03af9","metadata":{},"outputs":[],"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","id":"7e8aea33-3093-43ec-b672-d87876c1934d","metadata":{},"outputs":[],"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","id":"c791a9c5-c04d-42c6-a969-2733b7e7efb5","metadata":{},"outputs":[],"source":["clf = linear_model.LinearRegression()\ntrain_y_ = clf.fit(train_x_poly, train_y)\n# The coefficients\nprint ('Coefficients: ', clf.coef_)\nprint ('Intercept: ',clf.intercept_)"]},{"cell_type":"markdown","id":"2fc70f08-4833-4909-b248-1bca75dd98aa","metadata":{},"outputs":[],"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","id":"024baf01-2cc6-4c84-aea6-eac7878503ee","metadata":{},"outputs":[],"source":["plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\nXX = np.arange(0.0, 10.0, 0.1)\nyy = clf.intercept_[0]+ clf.coef_[0][1]*XX+ clf.coef_[0][2]*np.power(XX, 2)\nplt.plot(XX, yy, '-r' )\nplt.xlabel(\"Engine size\")\nplt.ylabel(\"Emission\")"]},{"cell_type":"markdown","id":"a34efe55-de31-4429-8a29-22ea5e53dfc7","metadata":{},"outputs":[],"source":["<h2 id=\"evaluation\">Evaluation</h2>\n"]},{"cell_type":"code","id":"147f62a3-ef21-4232-bcf3-06895af65885","metadata":{},"outputs":[],"source":["from sklearn.metrics import r2_score\n\ntest_x_poly = poly.transform(test_x)\ntest_y_ = clf.predict(test_x_poly)\n\nprint(\"Mean absolute error: %.2f\" % np.mean(np.absolute(test_y_ - test_y)))\nprint(\"Residual sum of squares (MSE): %.2f\" % np.mean((test_y_ - test_y) ** 2))\nprint(\"R2-score: %.2f\" % r2_score(test_y,test_y_ ) )"]},{"cell_type":"markdown","id":"ed1a2376-423d-4865-a162-adfa3aa6c300","metadata":{},"outputs":[],"source":["<h2 id=\"practice\">Practice</h2>\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","id":"44e40472-db2b-40b8-9154-9ca9c86665f6","metadata":{},"outputs":[],"source":["# write your code here\n"]},{"cell_type":"markdown","id":"52a5872c-4f67-4520-83d2-69dcace137c8","metadata":{},"outputs":[],"source":["<details><summary>Click here for the solution</summary>\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","</details>\n"]},{"cell_type":"code","id":"587e67ef-13d6-4074-b453-a9cec18a1c7a","metadata":{},"outputs":[],"source":[""]},{"cell_type":"markdown","id":"8c8879bf-1012-49a8-89b3-7f26e6eaa711","metadata":{},"outputs":[],"source":["<h2>Want to learn more?</h2>\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: <a href=\"https://www.ibm.com/analytics/spss-statistics-software?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">SPSS Modeler</a>\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 <a href=\"https://www.ibm.com/cloud/watson-studio?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">Watson Studio</a>\n","\n"]},{"cell_type":"markdown","id":"a944585d-72ba-4f20-a2d9-d0b1cbdc1970","metadata":{},"outputs":[],"source":["### Thank you for completing this lab!\n","\n","\n","## Author\n","\n","Saeed Aghabozorgi\n","\n","\n","### Other Contributors\n","\n","<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n","\n","\n","## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n","\n","\n","<!--## Change Log\n","\n","\n","|  Date (YYYY-MM-DD) |  Version | Changed By  |  Change Description |\n","|---|---|---|---|\n","| 2021-01-11  | 2.3  | Lakshmi  |  Changed R2-score calculation in polynomial regression |\n","| 2020-11-04  | 2.2  | Lakshmi  |  Made changes in markdown of equations |\n","| 2020-11-03  | 2.1  | Lakshmi  |  Made changes in URL |\n","| 2020-08-27  | 2.0  | Lavanya  |  Moved lab to course repo in GitLab |\n","|   |   |   |   |\n","|   |   |   |   | --!>\n","\n","\n"]},{"cell_type":"code","id":"6720e322-2f87-4db4-a31c-380f8048b35d","metadata":{},"outputs":[],"source":[""]}],"metadata":{"kernelspec":{"display_name":"Python","language":"python","name":"conda-env-python-py"},"language_info":{"name":"python","version":"3.7.12","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"prev_pub_hash":"4dc110debac287dfd374a575573c16e62a80a935b3bbe2b2f6d5a0598e6e33f6"},"nbformat":4,"nbformat_minor":4}
\ No newline at end of file
diff --git a/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Simple Linear Regression.ipynb b/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Simple Linear Regression.ipynb
new file mode 100644
index 0000000..5532e7a
--- /dev/null
+++ b/Tugas.Regression/Muhammad Shaddam Maghany Suryasaputra (202310715093)-Simple Linear Regression.ipynb	
@@ -0,0 +1,1152 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<p style=\"text-align:center\">\n",
+    "    <a href=\"https://skills.network\" target=\"_blank\">\n",
+    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
+    "    </a>\n",
+    "</p>\n",
+    "\n",
+    "\n",
+    "# Simple Linear Regression\n",
+    "\n",
+    "\n",
+    "Estimated time needed: **15** minutes\n",
+    "    \n",
+    "\n",
+    "## Objectives\n",
+    "\n",
+    "After completing this lab you will be able to:\n",
+    "\n",
+    "* Use scikit-learn to implement simple Linear Regression\n",
+    "* Create a model, train it, test it and use the model\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Importing Needed packages\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import pandas as pd\n",
+    "import pylab as pl\n",
+    "import numpy as np\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Downloading Data\n",
+    "To download the data, we will use !wget to download it from IBM Object Storage.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "--2025-10-20 16:09:33--  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 16:09:33 (37.3 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": [
+    "In case you're working **locally** uncomment the below line. \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#!curl https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/FuelConsumptionCo2.csv -o FuelConsumptionCo2.csv"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "## Understanding the Data\n",
+    "\n",
+    "### `FuelConsumption.csv`:\n",
+    "We have downloaded a fuel consumption dataset, **`FuelConsumption.csv`**, which contains model-specific fuel consumption ratings and estimated carbon dioxide emissions for new light-duty vehicles for retail sale in Canada. [Dataset source](http://open.canada.ca/data/en/dataset/98f1a129-f628-4ce4-b24d-6f16bf24dd64)\n",
+    "\n",
+    "- **MODELYEAR** e.g. 2014\n",
+    "- **MAKE** e.g. Acura\n",
+    "- **MODEL** e.g. ILX\n",
+    "- **VEHICLE CLASS** e.g. SUV\n",
+    "- **ENGINE SIZE** e.g. 4.7\n",
+    "- **CYLINDERS** e.g 6\n",
+    "- **TRANSMISSION** e.g. A6\n",
+    "- **FUEL CONSUMPTION in CITY(L/100 km)** e.g. 9.9\n",
+    "- **FUEL CONSUMPTION in HWY (L/100 km)** e.g. 8.9\n",
+    "- **FUEL CONSUMPTION COMB (L/100 km)** e.g. 9.2\n",
+    "- **CO2 EMISSIONS (g/km)** e.g. 182   --> low --> 0\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Reading the data in\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>MODELYEAR</th>\n",
+       "      <th>MAKE</th>\n",
+       "      <th>MODEL</th>\n",
+       "      <th>VEHICLECLASS</th>\n",
+       "      <th>ENGINESIZE</th>\n",
+       "      <th>CYLINDERS</th>\n",
+       "      <th>TRANSMISSION</th>\n",
+       "      <th>FUELTYPE</th>\n",
+       "      <th>FUELCONSUMPTION_CITY</th>\n",
+       "      <th>FUELCONSUMPTION_HWY</th>\n",
+       "      <th>FUELCONSUMPTION_COMB</th>\n",
+       "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
+       "      <th>CO2EMISSIONS</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>2014</td>\n",
+       "      <td>ACURA</td>\n",
+       "      <td>ILX</td>\n",
+       "      <td>COMPACT</td>\n",
+       "      <td>2.0</td>\n",
+       "      <td>4</td>\n",
+       "      <td>AS5</td>\n",
+       "      <td>Z</td>\n",
+       "      <td>9.9</td>\n",
+       "      <td>6.7</td>\n",
+       "      <td>8.5</td>\n",
+       "      <td>33</td>\n",
+       "      <td>196</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2014</td>\n",
+       "      <td>ACURA</td>\n",
+       "      <td>ILX</td>\n",
+       "      <td>COMPACT</td>\n",
+       "      <td>2.4</td>\n",
+       "      <td>4</td>\n",
+       "      <td>M6</td>\n",
+       "      <td>Z</td>\n",
+       "      <td>11.2</td>\n",
+       "      <td>7.7</td>\n",
+       "      <td>9.6</td>\n",
+       "      <td>29</td>\n",
+       "      <td>221</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>2014</td>\n",
+       "      <td>ACURA</td>\n",
+       "      <td>ILX HYBRID</td>\n",
+       "      <td>COMPACT</td>\n",
+       "      <td>1.5</td>\n",
+       "      <td>4</td>\n",
+       "      <td>AV7</td>\n",
+       "      <td>Z</td>\n",
+       "      <td>6.0</td>\n",
+       "      <td>5.8</td>\n",
+       "      <td>5.9</td>\n",
+       "      <td>48</td>\n",
+       "      <td>136</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>2014</td>\n",
+       "      <td>ACURA</td>\n",
+       "      <td>MDX 4WD</td>\n",
+       "      <td>SUV - SMALL</td>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>AS6</td>\n",
+       "      <td>Z</td>\n",
+       "      <td>12.7</td>\n",
+       "      <td>9.1</td>\n",
+       "      <td>11.1</td>\n",
+       "      <td>25</td>\n",
+       "      <td>255</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>2014</td>\n",
+       "      <td>ACURA</td>\n",
+       "      <td>RDX AWD</td>\n",
+       "      <td>SUV - SMALL</td>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>AS6</td>\n",
+       "      <td>Z</td>\n",
+       "      <td>12.1</td>\n",
+       "      <td>8.7</td>\n",
+       "      <td>10.6</td>\n",
+       "      <td>27</td>\n",
+       "      <td>244</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   MODELYEAR   MAKE       MODEL VEHICLECLASS  ENGINESIZE  CYLINDERS  \\\n",
+       "0       2014  ACURA         ILX      COMPACT         2.0          4   \n",
+       "1       2014  ACURA         ILX      COMPACT         2.4          4   \n",
+       "2       2014  ACURA  ILX HYBRID      COMPACT         1.5          4   \n",
+       "3       2014  ACURA     MDX 4WD  SUV - SMALL         3.5          6   \n",
+       "4       2014  ACURA     RDX AWD  SUV - SMALL         3.5          6   \n",
+       "\n",
+       "  TRANSMISSION FUELTYPE  FUELCONSUMPTION_CITY  FUELCONSUMPTION_HWY  \\\n",
+       "0          AS5        Z                   9.9                  6.7   \n",
+       "1           M6        Z                  11.2                  7.7   \n",
+       "2          AV7        Z                   6.0                  5.8   \n",
+       "3          AS6        Z                  12.7                  9.1   \n",
+       "4          AS6        Z                  12.1                  8.7   \n",
+       "\n",
+       "   FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  CO2EMISSIONS  \n",
+       "0                   8.5                        33           196  \n",
+       "1                   9.6                        29           221  \n",
+       "2                   5.9                        48           136  \n",
+       "3                  11.1                        25           255  \n",
+       "4                  10.6                        27           244  "
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_csv(\"FuelConsumption.csv\")\n",
+    "\n",
+    "# take a look at the dataset\n",
+    "df.head()\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Data Exploration\n",
+    "Let's first have a descriptive exploration on our data.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>MODELYEAR</th>\n",
+       "      <th>ENGINESIZE</th>\n",
+       "      <th>CYLINDERS</th>\n",
+       "      <th>FUELCONSUMPTION_CITY</th>\n",
+       "      <th>FUELCONSUMPTION_HWY</th>\n",
+       "      <th>FUELCONSUMPTION_COMB</th>\n",
+       "      <th>FUELCONSUMPTION_COMB_MPG</th>\n",
+       "      <th>CO2EMISSIONS</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>count</th>\n",
+       "      <td>1067.0</td>\n",
+       "      <td>1067.000000</td>\n",
+       "      <td>1067.000000</td>\n",
+       "      <td>1067.000000</td>\n",
+       "      <td>1067.000000</td>\n",
+       "      <td>1067.000000</td>\n",
+       "      <td>1067.000000</td>\n",
+       "      <td>1067.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>mean</th>\n",
+       "      <td>2014.0</td>\n",
+       "      <td>3.346298</td>\n",
+       "      <td>5.794752</td>\n",
+       "      <td>13.296532</td>\n",
+       "      <td>9.474602</td>\n",
+       "      <td>11.580881</td>\n",
+       "      <td>26.441425</td>\n",
+       "      <td>256.228679</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>std</th>\n",
+       "      <td>0.0</td>\n",
+       "      <td>1.415895</td>\n",
+       "      <td>1.797447</td>\n",
+       "      <td>4.101253</td>\n",
+       "      <td>2.794510</td>\n",
+       "      <td>3.485595</td>\n",
+       "      <td>7.468702</td>\n",
+       "      <td>63.372304</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>min</th>\n",
+       "      <td>2014.0</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>3.000000</td>\n",
+       "      <td>4.600000</td>\n",
+       "      <td>4.900000</td>\n",
+       "      <td>4.700000</td>\n",
+       "      <td>11.000000</td>\n",
+       "      <td>108.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>25%</th>\n",
+       "      <td>2014.0</td>\n",
+       "      <td>2.000000</td>\n",
+       "      <td>4.000000</td>\n",
+       "      <td>10.250000</td>\n",
+       "      <td>7.500000</td>\n",
+       "      <td>9.000000</td>\n",
+       "      <td>21.000000</td>\n",
+       "      <td>207.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>50%</th>\n",
+       "      <td>2014.0</td>\n",
+       "      <td>3.400000</td>\n",
+       "      <td>6.000000</td>\n",
+       "      <td>12.600000</td>\n",
+       "      <td>8.800000</td>\n",
+       "      <td>10.900000</td>\n",
+       "      <td>26.000000</td>\n",
+       "      <td>251.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>75%</th>\n",
+       "      <td>2014.0</td>\n",
+       "      <td>4.300000</td>\n",
+       "      <td>8.000000</td>\n",
+       "      <td>15.550000</td>\n",
+       "      <td>10.850000</td>\n",
+       "      <td>13.350000</td>\n",
+       "      <td>31.000000</td>\n",
+       "      <td>294.000000</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>max</th>\n",
+       "      <td>2014.0</td>\n",
+       "      <td>8.400000</td>\n",
+       "      <td>12.000000</td>\n",
+       "      <td>30.200000</td>\n",
+       "      <td>20.500000</td>\n",
+       "      <td>25.800000</td>\n",
+       "      <td>60.000000</td>\n",
+       "      <td>488.000000</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "       MODELYEAR   ENGINESIZE    CYLINDERS  FUELCONSUMPTION_CITY  \\\n",
+       "count     1067.0  1067.000000  1067.000000           1067.000000   \n",
+       "mean      2014.0     3.346298     5.794752             13.296532   \n",
+       "std          0.0     1.415895     1.797447              4.101253   \n",
+       "min       2014.0     1.000000     3.000000              4.600000   \n",
+       "25%       2014.0     2.000000     4.000000             10.250000   \n",
+       "50%       2014.0     3.400000     6.000000             12.600000   \n",
+       "75%       2014.0     4.300000     8.000000             15.550000   \n",
+       "max       2014.0     8.400000    12.000000             30.200000   \n",
+       "\n",
+       "       FUELCONSUMPTION_HWY  FUELCONSUMPTION_COMB  FUELCONSUMPTION_COMB_MPG  \\\n",
+       "count          1067.000000           1067.000000               1067.000000   \n",
+       "mean              9.474602             11.580881                 26.441425   \n",
+       "std               2.794510              3.485595                  7.468702   \n",
+       "min               4.900000              4.700000                 11.000000   \n",
+       "25%               7.500000              9.000000                 21.000000   \n",
+       "50%               8.800000             10.900000                 26.000000   \n",
+       "75%              10.850000             13.350000                 31.000000   \n",
+       "max              20.500000             25.800000                 60.000000   \n",
+       "\n",
+       "       CO2EMISSIONS  \n",
+       "count   1067.000000  \n",
+       "mean     256.228679  \n",
+       "std       63.372304  \n",
+       "min      108.000000  \n",
+       "25%      207.000000  \n",
+       "50%      251.000000  \n",
+       "75%      294.000000  \n",
+       "max      488.000000  "
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# summarize the data\n",
+    "df.describe()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's select some features to explore more.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>ENGINESIZE</th>\n",
+       "      <th>CYLINDERS</th>\n",
+       "      <th>FUELCONSUMPTION_COMB</th>\n",
+       "      <th>CO2EMISSIONS</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>2.0</td>\n",
+       "      <td>4</td>\n",
+       "      <td>8.5</td>\n",
+       "      <td>196</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2.4</td>\n",
+       "      <td>4</td>\n",
+       "      <td>9.6</td>\n",
+       "      <td>221</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>1.5</td>\n",
+       "      <td>4</td>\n",
+       "      <td>5.9</td>\n",
+       "      <td>136</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>11.1</td>\n",
+       "      <td>255</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>10.6</td>\n",
+       "      <td>244</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>10.0</td>\n",
+       "      <td>230</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>3.5</td>\n",
+       "      <td>6</td>\n",
+       "      <td>10.1</td>\n",
+       "      <td>232</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>3.7</td>\n",
+       "      <td>6</td>\n",
+       "      <td>11.1</td>\n",
+       "      <td>255</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>8</th>\n",
+       "      <td>3.7</td>\n",
+       "      <td>6</td>\n",
+       "      <td>11.6</td>\n",
+       "      <td>267</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   ENGINESIZE  CYLINDERS  FUELCONSUMPTION_COMB  CO2EMISSIONS\n",
+       "0         2.0          4                   8.5           196\n",
+       "1         2.4          4                   9.6           221\n",
+       "2         1.5          4                   5.9           136\n",
+       "3         3.5          6                  11.1           255\n",
+       "4         3.5          6                  10.6           244\n",
+       "5         3.5          6                  10.0           230\n",
+       "6         3.5          6                  10.1           232\n",
+       "7         3.7          6                  11.1           255\n",
+       "8         3.7          6                  11.6           267"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cdf = df[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB','CO2EMISSIONS']]\n",
+    "cdf.head(9)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can plot each of these features:\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 4 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "viz = cdf[['CYLINDERS','ENGINESIZE','CO2EMISSIONS','FUELCONSUMPTION_COMB']]\n",
+    "viz.hist()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now, let's plot each of these features against the Emission, to see how linear their relationship is:\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(cdf.FUELCONSUMPTION_COMB, cdf.CO2EMISSIONS,  color='blue')\n",
+    "plt.xlabel(\"FUELCONSUMPTION_COMB\")\n",
+    "plt.ylabel(\"Emission\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS,  color='blue')\n",
+    "plt.xlabel(\"Engine size\")\n",
+    "plt.ylabel(\"Emission\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Practice\n",
+    "Plot __CYLINDER__ vs the Emission, to see how linear is their relationship is:\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(cdf.CYLINDERS, cdf.CO2EMISSIONS, color='blue')\n",
+    "plt.xlabel(\"Cylinders\")\n",
+    "plt.ylabel(\"Emission\")\n",
+    "plt.show()\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<details><summary>Click here for the solution</summary>\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",
+    "</details>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Creating train and test dataset\n",
+    "Train/Test Split involves splitting the dataset into training and testing sets that are mutually exclusive. After which, you train with the training set and test with the testing set. \n",
+    "This will provide a more accurate evaluation on out-of-sample accuracy because the testing dataset is not part of the dataset that have been used to train the model. Therefore, it gives us a better understanding of how well our model generalizes on new data.\n",
+    "\n",
+    "This means that we know the outcome of each data point in the testing dataset, making it great to test with! Since this data has not been used to train the model, the model has no knowledge of the outcome of these data points. So, in essence, it is truly an out-of-sample testing.\n",
+    "\n",
+    "Let's split our dataset into train and test sets. 80% of the entire dataset will be used for training and 20% for testing. We create a mask to select random rows using __np.random.rand()__ function: \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "msk = np.random.rand(len(df)) < 0.8\n",
+    "train = cdf[msk]\n",
+    "test = cdf[~msk]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Simple Regression Model\n",
+    "Linear Regression fits a linear model with coefficients B = (B1, ..., Bn) to minimize the 'residual sum of squares' between the actual value y in the dataset, and the predicted value yhat using linear approximation. \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Train data distribution\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
+    "plt.xlabel(\"Engine size\")\n",
+    "plt.ylabel(\"Emission\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Modeling\n",
+    "Using sklearn package to model data.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Coefficients:  [[38.59777163]]\n",
+      "Intercept:  [127.29727605]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sklearn import linear_model\n",
+    "regr = linear_model.LinearRegression()\n",
+    "train_x = np.asanyarray(train[['ENGINESIZE']])\n",
+    "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+    "regr.fit(train_x, train_y)\n",
+    "# The coefficients\n",
+    "print ('Coefficients: ', regr.coef_)\n",
+    "print ('Intercept: ',regr.intercept_)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As mentioned before, __Coefficient__ and __Intercept__ in the simple linear regression, are the parameters of the fit line. \n",
+    "Given that it is a simple linear regression, with only 2 parameters, and knowing that the parameters are the intercept and slope of the line, sklearn can estimate them directly from our data. \n",
+    "Notice that all of the data must be available to traverse and calculate the parameters.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Plot outputs\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can plot the fit line over the data:\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0, 0.5, 'Emission')"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')\n",
+    "plt.plot(train_x, regr.coef_[0][0]*train_x + regr.intercept_[0], '-r')\n",
+    "plt.xlabel(\"Engine size\")\n",
+    "plt.ylabel(\"Emission\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Evaluation\n",
+    "We compare the actual values and predicted values to calculate the accuracy of a regression model. Evaluation metrics provide a key role in the development of a model, as it provides insight to areas that require improvement.\n",
+    "\n",
+    "There are different model evaluation metrics, lets use MSE here to calculate the accuracy of our model based on the test set: \n",
+    "* Mean Absolute Error: It is the mean of the absolute value of the errors. This is the easiest of the metrics to understand since it’s just average error.\n",
+    "\n",
+    "* Mean Squared Error (MSE): Mean Squared Error (MSE) is the mean of the squared error. It’s more popular than Mean Absolute Error because the focus is geared more towards large errors. This is due to the squared term exponentially increasing larger errors in comparison to smaller ones.\n",
+    "\n",
+    "* Root Mean Squared Error (RMSE). \n",
+    "\n",
+    "* R-squared is not an error, but rather a popular metric to measure the performance of your regression model. It represents how close the data points are to the fitted regression line. The higher the R-squared value, the better the model fits your data. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse).\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Mean absolute error: 22.59\n",
+      "Residual sum of squares (MSE): 897.10\n",
+      "R2-score: 0.78\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": 36,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "train_x = train[[\"FUELCONSUMPTION_COMB\"]]\n",
+    "\n",
+    "test_x = test[[\"FUELCONSUMPTION_COMB\"]]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<details><summary>Click here for the solution</summary>\n",
+    "\n",
+    "```python    \n",
+    "train_x = train[[\"FUELCONSUMPTION_COMB\"]]\n",
+    "\n",
+    "test_x = test[[\"FUELCONSUMPTION_COMB\"]]\n",
+    "\n",
+    "```\n",
+    "\n",
+    "</details>\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": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
+       "         normalize=False)"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "regr = linear_model.LinearRegression()\n",
+    "\n",
+    "regr.fit(train_x, train_y)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<details><summary>Click here for the solution</summary>\n",
+    "\n",
+    "```python    \n",
+    "regr = linear_model.LinearRegression()\n",
+    "\n",
+    "regr.fit(train_x, train_y)\n",
+    "\n",
+    "```\n",
+    "\n",
+    "</details>\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": 38,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "predictions = regr.predict(test_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<details><summary>Click here for the solution</summary>\n",
+    "\n",
+    "```python    \n",
+    "predictions = regr.predict(test_x)\n",
+    "\n",
+    "```\n",
+    "\n",
+    "</details>\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": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Mean Absolute Error: 20.61\n"
+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "print(\"Mean Absolute Error: %.2f\" % np.mean(np.absolute(predictions - test_y)))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<details><summary>Click here for the solution</summary>\n",
+    "\n",
+    "```python    \n",
+    "print(\"Mean Absolute Error: %.2f\" % np.mean(np.absolute(predictions - test_y)))\n",
+    "\n",
+    "```\n",
+    "\n",
+    "</details>\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",
+    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
+    "\n",
+    "Azim Hirjani\n",
+    "\n",
+    "## <h3 align=\"center\"> © IBM Corporation. All rights reserved. <h3/>\n",
+    "\n",
+    "<!--\n",
+    "## Change Log\n",
+    "\n",
+    "\n",
+    "|  Date (YYYY-MM-DD) |  Version | Changed By  |  Change Description |\n",
+    "|---|---|---|---|\n",
+    "| 2020-11-03 | 2.1  | Lakshmi Holla  |  Changed URL of the csv |\n",
+    "| 2020-08-27  | 2.0  | Lavanya  |  Moved lab to course repo in GitLab |\n",
+    "|   |   |   |   |\n",
+    "|   |   |   |   |\n",
+    "\n",
+    "--!>\n",
+    "\n",
+    "\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python",
+   "language": "python",
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+  },
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+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
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+   "mimetype": "text/x-python",
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+   "version": "3.7.12"
+  },
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