IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork_jupyterlite_files_DA0101EN-4-Review-Model-Development.jupyterlite.ipynb

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      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "kernelspec": {
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  "cells": [
    {
      "cell_type": "markdown",
      "source": "<center>\n    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%204/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\">\n</center>\n\n# Model Development\n\nEstimated time needed: **30** minutes\n\n## Objectives\n\nAfter completing this lab you will be able to:\n\n*   Develop prediction models\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Some questions we want to ask in this module\n\n<ul>\n    <li>Do I know if the dealer is offering fair value for my trade-in?</li>\n    <li>Do I know if I put a fair value on my car?</li>\n</ul>\n<p>In data analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n\n<p>A model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Setup</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Import libraries:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "you are running the lab in your  browser, so we will install the libraries using `piplite`\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#you are running the lab in your  browser, so we will install the libraries using ``piplite``\nimport piplite\nawait piplite.install(['pandas'])\nawait piplite.install(['matplotlib'])\nawait piplite.install(['scipy'])\nawait piplite.install(['scikit-learn'])\nawait piplite.install(['skillsnetwork', 'seaborn'])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "If you run the lab locally using Anaconda, you can load the correct library and versions by uncommenting the following:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#If you run the lab locally using Anaconda, you can load the correct library and versions by uncommenting the following:\n#install specific version of libraries used in lab\n#! mamba install pandas==1.3.3-y\n#! mamba install numpy=1.21.2-y\n#! mamba install sklearn=0.20.1-y",
      "metadata": {
        "trusted": true
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "import pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport skillsnetwork\nimport warnings\nwarnings.filterwarnings('ignore')",
      "metadata": {
        "trusted": true
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "This function will download the dataset into your browser\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#This function will download the dataset into your browser \n\nfrom pyodide.http import pyfetch\n\nasync def download(url, filename):\n    response = await pyfetch(url)\n    if response.status == 200:\n        with open(filename, \"wb\") as f:\n            f.write(await response.bytes())",
      "metadata": {
        "trusted": true
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "This dataset was hosted on IBM Cloud object. Click <a href=\"https://cocl.us/DA101EN_object_storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">HERE</a> for free storage.\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "you will need to download the dataset; if you are running locally, please comment out the following\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#you will need to download the dataset; if you are running locally, please comment out the following \nawait skillsnetwork.download_dataset('https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/automobileEDA.csv')\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 5,
      "outputs": [
        {
          "name": "stderr",
          "text": "Downloading automobileEDA.csv: 100%|##########| 35648/35648 [00:00<00:00, 17825291.96it/s]\n",
          "output_type": "stream"
        },
        {
          "name": "stdout",
          "text": "Saved as 'automobileEDA.csv'\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Load the data and store it in dataframe `df`:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "df = pd.read_csv(\"automobileEDA.csv\", header=0)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<h2>1. Linear Regression and Multiple Linear Regression</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Linear Regression</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>One example of a Data  Model that we will be using is:</p>\n<b>Simple Linear Regression</b>\n\n<br>\n<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n<ul>\n    <li>The predictor/independent variable (X)</li>\n    <li>The response/dependent variable (that we want to predict)(Y)</li>\n</ul>\n\n<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "$$\nY: Response \\ Variable\\\\\\\\\\\\\\\\\\\\\nX: Predictor \\ Variables\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<b>Linear Function</b>\n$$\nYhat = a + b  X\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<ul>\n    <li>a refers to the <b>intercept</b> of the regression line, in other words: the value of Y when X is 0</li>\n    <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n</ul>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Let's load the modules for linear regression:</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.linear_model import LinearRegression",
      "metadata": {
        "trusted": true
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Create the linear regression object:</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm = LinearRegression()\nlm",
      "metadata": {
        "trusted": true
      },
      "execution_count": 8,
      "outputs": [
        {
          "execution_count": 8,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h4>How could \"highway-mpg\" help us predict car price?</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "For this example, we want to look at how highway-mpg can help us predict car price.\nUsing simple linear regression, we will create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "X = df[['highway-mpg']]\nY = df['price']",
      "metadata": {
        "trusted": true
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Fit the linear model using highway-mpg:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm.fit(X,Y)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 10,
      "outputs": [
        {
          "execution_count": 10,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can output a prediction:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Yhat=lm.predict(X)\nYhat[0:5]   ",
      "metadata": {
        "trusted": true
      },
      "execution_count": 11,
      "outputs": [
        {
          "execution_count": 11,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n       20345.17153508])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h4>What is the value of the intercept (a)?</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm.intercept_",
      "metadata": {
        "trusted": true
      },
      "execution_count": 12,
      "outputs": [
        {
          "execution_count": 12,
          "output_type": "execute_result",
          "data": {
            "text/plain": "38423.30585815743"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h4>What is the value of the slope (b)?</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm.coef_",
      "metadata": {
        "trusted": true
      },
      "execution_count": 13,
      "outputs": [
        {
          "execution_count": 13,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([-821.73337832])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h3>What is the final estimated linear model we get?</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "As we saw above, we should get a final linear model with the structure:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "$$\nYhat = a + b  X\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Plugging in the actual values we get:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<b>Price</b> = 38423.31 - 821.73 x <b>highway-mpg</b>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1>Question #1 a): </h1>\n\n<b>Create a linear regression object called \"lm1\".</b>\n\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nfrom sklearn.linear_model import LinearRegression\n\nlm1 = LinearRegression()\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nlm1 = LinearRegression()\nlm1\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1> Question #1 b): </h1>\n\n<b>Train the model using \"engine-size\" as the independent variable and \"price\" as the dependent variable?</b>\n\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nfrom sklearn.linear_model import LinearRegression\n\nX = df[['engine-size']]\ny = df['price']\n\nlm1 = LinearRegression()\nlm1.fit(X, y)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 15,
      "outputs": [
        {
          "execution_count": 15,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nlm1.fit(df[['engine-size']], df[['price']])\nlm1\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1>Question #1 c):</h1>\n\n<b>Find the slope and intercept of the model.</b>\n\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Slope</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nslope = lm1.coef_[0]\n\nprint(\"Slope:\", slope)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 18,
      "outputs": [
        {
          "name": "stdout",
          "text": "Slope: 166.860015691416\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n    \n```python\n# Slope \nlm1.coef_\n```\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Intercept</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nintercept = lm1.intercept_\nprint(\"Intercept:\", intercept)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 19,
      "outputs": [
        {
          "name": "stdout",
          "text": "Intercept: -7963.338906281049\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "\n<details><summary>Click here for the solution</summary>\n\n```python\n# Intercept\nlm1.intercept_\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1>Question #1 d): </h1>\n\n<b>What is the equation of the predicted line? You can use x and yhat or \"engine-size\" or \"price\".</b>\n\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \n# using X and Y  \n#if engine is not defined it will print error (NameError: name 'engine' is not defined).\n# calculate the equation of the predicted line\nb0 = lm1.intercept_\nb1 = lm1.coef_[0]\npredicted_line = f\"price = {b0:.2f} + {b1:.2f}*engine-size\"\nprint(predicted_line)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 20,
      "outputs": [
        {
          "name": "stdout",
          "text": "price = -7963.34 + 166.86*engine-size\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\n# using X and Y  \nYhat=-7963.34 + 166.86*X\n\nPrice=-7963.34 + 166.86*df['engine-size']\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Multiple Linear Regression</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>What if we want to predict car price using more than one variable?</p>\n\n<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\nMultiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\nMost of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "$$\nY: Response \\ Variable\\\\\\\\\\\\\\\\\\\\\nX\\_1 :Predictor\\ Variable \\ 1\\\\\\\\\nX\\_2: Predictor\\ Variable \\ 2\\\\\\\\\nX\\_3: Predictor\\ Variable \\ 3\\\\\\\\\nX\\_4: Predictor\\ Variable \\ 4\\\\\\\\\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "$$\na: intercept\\\\\\\\\\\\\\\\\\\\\nb\\_1 :coefficients \\ of\\ Variable \\ 1\\\\\\\\\nb\\_2: coefficients \\ of\\ Variable \\ 2\\\\\\\\\nb\\_3: coefficients \\ of\\ Variable \\ 3\\\\\\\\\nb\\_4: coefficients \\ of\\ Variable \\ 4\\\\\\\\\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "The equation is given by:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "$$\nYhat = a + b\\_1 X\\_1 + b\\_2 X\\_2 + b\\_3 X\\_3 + b\\_4 X\\_4\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>From the previous section  we know that other good predictors of price could be:</p>\n<ul>\n    <li>Horsepower</li>\n    <li>Curb-weight</li>\n    <li>Engine-size</li>\n    <li>Highway-mpg</li>\n</ul>\nLet's develop a model using these variables as the predictor variables.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Fit the linear model using the four above-mentioned variables.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm.fit(Z, df['price'])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 22,
      "outputs": [
        {
          "execution_count": 22,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "What is the value of the intercept(a)?\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm.intercept_",
      "metadata": {
        "trusted": true
      },
      "execution_count": 23,
      "outputs": [
        {
          "execution_count": 23,
          "output_type": "execute_result",
          "data": {
            "text/plain": "-15806.62462632922"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "What are the values of the coefficients (b1, b2, b3, b4)?\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm.coef_",
      "metadata": {
        "trusted": true
      },
      "execution_count": 24,
      "outputs": [
        {
          "execution_count": 24,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "What is the final estimated linear model that we get?\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "As we saw above, we should get a final linear function with the structure:\n\n$$\nYhat = a + b\\_1 X\\_1 + b\\_2 X\\_2 + b\\_3 X\\_3 + b\\_4 X\\_4\n$$\n\nWhat is the linear function we get in this example?\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<b>Price</b> = -15678.742628061467 + 52.65851272 x <b>horsepower</b> + 4.69878948 x <b>curb-weight</b> + 81.95906216 x <b>engine-size</b> + 33.58258185 x <b>highway-mpg</b>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1> Question  #2 a): </h1>\nCreate and train a Multiple Linear Regression model \"lm2\" where the response variable is \"price\", and the predictor variable is \"normalized-losses\" and  \"highway-mpg\".\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nfrom sklearn.linear_model import LinearRegression\n\n# Extract the predictor variables and response variable as pandas dataframes\nX = df[['normalized-losses', 'highway-mpg']]\nY = df['price']\n\n# Create a LinearRegression object\nlm2 = LinearRegression()\n\n# Fit the linear regression model to the data\nlm2.fit(X,Y)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 25,
      "outputs": [
        {
          "execution_count": 25,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nlm2 = LinearRegression()\nlm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1>Question  #2 b): </h1>\n<b>Find the coefficient of the model.</b>\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \n# Get the coefficients of the multiple linear regression model\ncoefficients = lm2.coef_\nprint(coefficients)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 26,
      "outputs": [
        {
          "name": "stdout",
          "text": "[   1.49789586 -820.45434016]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nlm2.coef_\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2>2. Model Evaluation Using Visualization</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Now that we've developed some models, how do we evaluate our models and choose the best one? One way to do this is by using a visualization.\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Import the visualization package, seaborn:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# import the visualization package: seaborn\nimport seaborn as sns\n%matplotlib inline ",
      "metadata": {
        "trusted": true
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Regression Plot</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n\n<p>This plot will show a combination of a scattered data points (a <b>scatterplot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's visualize **highway-mpg** as potential predictor variable of price:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "width = 12\nheight = 10\nplt.figure(figsize=(width, height))\nsns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\nplt.ylim(0,)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 28,
      "outputs": [
        {
          "execution_count": 28,
          "output_type": "execute_result",
          "data": {
            "text/plain": "(0.0, 48194.7931238211)"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 1200x1000 with 1 Axes>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<p>We can see from this plot that price is negatively correlated to highway-mpg since the regression slope is negative.\n\nOne thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data.\n\nLet's compare this plot to the regression plot of \"peak-rpm\".</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "plt.figure(figsize=(width, height))\nsns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\nplt.ylim(0,)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 29,
      "outputs": [
        {
          "execution_count": 29,
          "output_type": "execute_result",
          "data": {
            "text/plain": "(0.0, 47414.1)"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 1200x1000 with 1 Axes>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\", we see that the points for \"highway-mpg\" are much closer to the generated line and, on average, decrease. The points for \"peak-rpm\" have more spread around the predicted line and it is much harder to determine if the points are decreasing or increasing as the \"peak-rpm\" increases.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1>Question #3:</h1>\n<b>Given the regression plots above, is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\"? Use the method  \".corr()\" to verify your answer.</b>\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \n# The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\ndf[['highway-mpg', 'price']].corr()\ndf[['peak-rpm', 'price']].corr()\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 30,
      "outputs": [
        {
          "execution_count": 30,
          "output_type": "execute_result",
          "data": {
            "text/plain": "          peak-rpm     price\npeak-rpm  1.000000 -0.101616\nprice    -0.101616  1.000000",
            "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>peak-rpm</th>\n      <th>price</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>peak-rpm</th>\n      <td>1.000000</td>\n      <td>-0.101616</td>\n    </tr>\n    <tr>\n      <th>price</th>\n      <td>-0.101616</td>\n      <td>1.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\n# The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\n\ndf[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Residual Plot</h3>\n\n<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n\n<p>What is a <b>residual</b>?</p>\n\n<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n\n<p>So what is a <b>residual plot</b>?</p>\n\n<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n\n<p>What do we pay attention to when looking at a residual plot?</p>\n\n<p>We look at the spread of the residuals:</p>\n\n<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data.\n\nWhy is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "width = 12\nheight = 10\nplt.figure(figsize=(width, height))\nsns.residplot(x=df['highway-mpg'],y=df['price'])\nplt.show()",
      "metadata": {
        "trusted": true
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x557de70>",
            "image/png": 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          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 1200x1000 with 0 Axes>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<i>What is this plot telling us?</i>\n\n<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, leading us to believe that maybe a non-linear model is more appropriate for this data.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Multiple Linear Regression</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n\n<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>. We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "First, let's make a prediction:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Y_hat = lm.predict(Z)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "plt.figure(figsize=(width, height))\n\n\nax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\nsns.distplot(Y_hat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n\n\nplt.title('Actual vs Fitted Values for Price')\nplt.xlabel('Price (in dollars)')\nplt.ylabel('Proportion of Cars')\n\nplt.show()\nplt.close()",
      "metadata": {
        "trusted": true
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x681e858>",
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<p>We can see that the fitted values are reasonably close to the actual values since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2>3. Polynomial Regression and Pipelines</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.</p> \n<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n\n<p>There are different orders of polynomial regression:</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<center><b>Quadratic - 2nd Order</b></center>\n$$\nYhat = a + b_1 X +b_2 X^2 \n$$\n\n<center><b>Cubic - 3rd Order</b></center>\n$$\nYhat = a + b_1 X +b_2 X^2 +b_3 X^3\\\\\\\\\\\\\\\\\\\\\n$$\n\n<center><b>Higher-Order</b>:</center>\n$$\nY = a + b_1 X +b_2 X^2 +b_3 X^3 ....\\\\\\\\\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>We saw earlier that a linear model did not provide the best fit while using \"highway-mpg\" as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>We will use the following function to plot the data:</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "def PlotPolly(model, independent_variable, dependent_variabble, Name):\n    x_new = np.linspace(15, 55, 100)\n    y_new = model(x_new)\n\n    plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n    plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n    ax = plt.gca()\n    ax.set_facecolor((0.898, 0.898, 0.898))\n    fig = plt.gcf()\n    plt.xlabel(Name)\n    plt.ylabel('Price of Cars')\n\n    plt.show()\n    plt.close()",
      "metadata": {
        "trusted": true
      },
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Let's get the variables:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "x = df['highway-mpg']\ny = df['price']",
      "metadata": {
        "trusted": true
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Here we use a polynomial of the 3rd order (cubic) \nf = np.polyfit(x, y, 3)\np = np.poly1d(f)\nprint(p)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 36,
      "outputs": [
        {
          "name": "stdout",
          "text": "        3         2\n-1.557 x + 204.8 x - 8965 x + 1.379e+05\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Let's plot the function:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "PlotPolly(p, x, y, 'highway-mpg')",
      "metadata": {
        "trusted": true
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x5298638>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "np.polyfit(x, y, 3)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 38,
      "outputs": [
        {
          "execution_count": 38,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function  \"hits\" more of the data points.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1>Question  #4:</h1>\n<b>Create 11 order polynomial model with the variables x and y from above.</b>\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nf = np.polyfit(x, y, 11)\np = np.poly1d(f)\nprint(p)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 39,
      "outputs": [
        {
          "name": "stdout",
          "text": "            11             10             9           8         7\n-1.243e-08 x  + 4.722e-06 x  - 0.0008028 x + 0.08056 x - 5.297 x\n          6        5             4             3             2\n + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\n# Here we use a polynomial of the 11rd order (cubic) \nf1 = np.polyfit(x, y, 11)\np1 = np.poly1d(f1)\nprint(p1)\nPlotPolly(p1,x,y, 'Highway MPG')\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2) polynomial with two variables is given by:</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "$$\nYhat = a + b\\_1 X\\_1 +b\\_2 X\\_2 +b\\_3 X\\_1 X\\_2+b\\_4 X\\_1^2+b\\_5 X\\_2^2\n$$\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "We can perform a polynomial transform on multiple features. First, we import the module:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.preprocessing import PolynomialFeatures",
      "metadata": {
        "trusted": true
      },
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We create a <b>PolynomialFeatures</b> object of degree 2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "pr=PolynomialFeatures(degree=2)\npr",
      "metadata": {
        "trusted": true
      },
      "execution_count": 41,
      "outputs": [
        {
          "execution_count": 41,
          "output_type": "execute_result",
          "data": {
            "text/plain": "PolynomialFeatures()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "Z_pr=pr.fit_transform(Z)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "In the original data, there are 201 samples and 4 features.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Z.shape",
      "metadata": {
        "trusted": true
      },
      "execution_count": 43,
      "outputs": [
        {
          "execution_count": 43,
          "output_type": "execute_result",
          "data": {
            "text/plain": "(201, 4)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "After the transformation, there are 201 samples and 15 features.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Z_pr.shape",
      "metadata": {
        "trusted": true
      },
      "execution_count": 44,
      "outputs": [
        {
          "execution_count": 44,
          "output_type": "execute_result",
          "data": {
            "text/plain": "(201, 15)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h2>Pipeline</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.pipeline import Pipeline\nfrom sklearn.preprocessing import StandardScaler",
      "metadata": {
        "trusted": true
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We create the pipeline by creating a list of tuples including the name of the model or estimator and its corresponding constructor.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We input the list as an argument to the pipeline constructor:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "pipe=Pipeline(Input)\npipe",
      "metadata": {
        "trusted": true
      },
      "execution_count": 47,
      "outputs": [
        {
          "execution_count": 47,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Pipeline(steps=[('scale', StandardScaler()),\n                ('polynomial', PolynomialFeatures(include_bias=False)),\n                ('model', LinearRegression())])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "First, we convert the data type Z to type float to avoid conversion warnings that may appear as a result of StandardScaler taking float inputs.\n\nThen, we can normalize the data,  perform a transform and fit the model simultaneously.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Z = Z.astype(float)\npipe.fit(Z,y)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 48,
      "outputs": [
        {
          "execution_count": 48,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Pipeline(steps=[('scale', StandardScaler()),\n                ('polynomial', PolynomialFeatures(include_bias=False)),\n                ('model', LinearRegression())])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Similarly,  we can normalize the data, perform a transform and produce a prediction  simultaneously.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "ypipe=pipe.predict(Z)\nypipe[0:4]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 49,
      "outputs": [
        {
          "execution_count": 49,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1>Question #5:</h1>\n<b>Create a pipeline that standardizes the data, then produce a prediction using a linear regression model using the features Z and target y.</b>\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nfrom sklearn.pipeline import Pipeline\nfrom sklearn.preprocessing import StandardScaler\nfrom sklearn.linear_model import LinearRegression\n\n# Define the pipeline\npipe = Pipeline([('scaler', StandardScaler()), ('regressor', LinearRegression())])\n\n# Fit the pipeline to the data\npipe.fit(Z, y)\n\n# Use the pipeline to predict the target variable for new data\ny_pred = pipe.predict(Z)\nypipe[0:10]\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 54,
      "outputs": [
        {
          "execution_count": 54,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555,\n       16136.29619164, 13880.09787302, 15041.58694037, 15457.93465485,\n       17974.49032347, 10510.56542385])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nInput=[('scale',StandardScaler()),('model',LinearRegression())]\n\npipe=Pipeline(Input)\n\npipe.fit(Z,y)\n\nypipe=pipe.predict(Z)\nypipe[0:10]\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2>4. Measures for In-Sample Evaluation</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n\n<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n<ul>\n    <li><b>R^2 / R-squared</b></li>\n    <li><b>Mean Squared Error (MSE)</b></li>\n</ul>\n\n<b>R-squared</b>\n\n<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n\n<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n\n<b>Mean Squared Error (MSE)</b>\n\n<p>The Mean Squared Error measures the average of the squares of errors. That is, the difference between actual value (y) and the estimated value (ŷ).</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Model 1: Simple Linear Regression</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's calculate the R^2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#highway_mpg_fit\nlm.fit(X, Y)\n# Find the R^2\nprint('The R-square is: ', lm.score(X, Y))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 55,
      "outputs": [
        {
          "name": "stdout",
          "text": "The R-square is:  0.4966263556974878\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can say that \\~49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\".\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's calculate the MSE:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Yhat=lm.predict(X)\nprint('The output of the first four predicted value is: ', Yhat[0:4])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 56,
      "outputs": [
        {
          "name": "stdout",
          "text": "The output of the first four predicted value is:  [16231.78938339 16231.78938339 17052.24372355 13833.33798916]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Let's import the function <b>mean_squared_error</b> from the module <b>metrics</b>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.metrics import mean_squared_error",
      "metadata": {
        "trusted": true
      },
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We can compare the predicted results with the actual results:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "mse = mean_squared_error(df['price'], Yhat)\nprint('The mean square error of price and predicted value is: ', mse)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 58,
      "outputs": [
        {
          "name": "stdout",
          "text": "The mean square error of price and predicted value is:  31632832.975589428\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Model 2: Multiple Linear Regression</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's calculate the R^2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# fit the model \nlm.fit(Z, df['price'])\n# Find the R^2\nprint('The R-square is: ', lm.score(Z, df['price']))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 59,
      "outputs": [
        {
          "name": "stdout",
          "text": "The R-square is:  0.8093562806577457\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can say that \\~80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\".\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's calculate the MSE.\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "We produce a prediction:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Y_predict_multifit = lm.predict(Z)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We compare the predicted results with the actual results:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print('The mean square error of price and predicted value using multifit is: ', \\\n      mean_squared_error(df['price'], Y_predict_multifit))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 61,
      "outputs": [
        {
          "name": "stdout",
          "text": "The mean square error of price and predicted value using multifit is:  11980366.87072649\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Model 3: Polynomial Fit</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's calculate the R^2.\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let’s import the function <b>r2\\_score</b> from the module <b>metrics</b> as we are using a different function.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.metrics import r2_score",
      "metadata": {
        "trusted": true
      },
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We apply the function to get the value of R^2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "r_squared = r2_score(y, p(x))\nprint('The R-square value is: ', r_squared)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 63,
      "outputs": [
        {
          "name": "stdout",
          "text": "The R-square value is:  0.702376909243598\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can say that \\~67.419 % of the variation of price is explained by this polynomial fit.\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3>MSE</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "We can also calculate the MSE:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "mean_squared_error(df['price'], p(x))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 64,
      "outputs": [
        {
          "execution_count": 64,
          "output_type": "execute_result",
          "data": {
            "text/plain": "18703127.63915394"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h2>5. Prediction and Decision Making</h2>\n<h3>Prediction</h3>\n\n<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "import matplotlib.pyplot as plt\nimport numpy as np\n\n%matplotlib inline ",
      "metadata": {
        "trusted": true
      },
      "execution_count": 65,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Create a new input:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "new_input=np.arange(1, 100, 1).reshape(-1, 1)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Fit the model:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lm.fit(X, Y)\nlm",
      "metadata": {
        "trusted": true
      },
      "execution_count": 67,
      "outputs": [
        {
          "execution_count": 67,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Produce a prediction:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "import numpy as np\nfrom sklearn.linear_model import LinearRegression\n\n# create a LinearRegression model\nlm = LinearRegression()\n\n# fit the model to some data\nX = np.array([[1, 2], [3, 4], [5, 6]])\ny = np.array([10, 20, 30])\nlm.fit(X, y)\n\n# use the model to make a prediction\nnew_X = np.array([[7, 8], [9, 10]])\npredictions = lm.predict(new_X)\n\nprint(predictions)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 69,
      "outputs": [
        {
          "name": "stdout",
          "text": "[40. 50.]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can plot the data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "import matplotlib.pyplot as plt\n\nplt.scatter(X[:, 0], y, color='blue')\nplt.scatter(X[:, 1], y, color='red')\nplt.plot(new_X[:, 0], predictions, color='blue', label='X1')\nplt.plot(new_X[:, 1], predictions, color='red', label='X2')\nplt.xlabel('Input variable')\nplt.ylabel('Predicted target variable')\nplt.legend()\nplt.show()\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x72570f8>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 640x480 with 0 Axes>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Decision Making: Determining a Good Model Fit</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n<ul>\n    <li><i>What is a good R-squared value?</i></li>\n</ul>\n</p>\n\n<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n<ul>\n    <li><i>What is a good MSE?</i></li>\n</ul>\n</p>\n\n<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n\n<h4>Let's take a look at the values for the different models.</h4>\n<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n<ul>\n    <li>R-squared: 0.49659118843391759</li>\n    <li>MSE: 3.16 x10^7</li>\n</ul>\n</p>\n\n<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n<ul>\n    <li>R-squared: 0.80896354913783497</li>\n    <li>MSE: 1.2 x10^7</li>\n</ul>\n</p>\n\n<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n<ul>\n    <li>R-squared: 0.6741946663906514</li>\n    <li>MSE: 2.05 x 10^7</li>\n</ul>\n</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Simple Linear Regression Model (SLR) vs Multiple Linear Regression Model (MLR)</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and even act as noise. As a result, you should always check the MSE and R^2.</p>\n\n<p>In order to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n<ul>\n    <li><b>MSE</b>: The MSE of SLR is  3.16x10^7  while MLR has an MSE of 1.2 x10^7.  The MSE of MLR is much smaller.</li>\n    <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n</ul>\n</p>\n\nThis R-squared in combination with the MSE show that MLR seems like the better model fit in this case compared to SLR.\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Simple Linear Model (SLR) vs. Polynomial Fit</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<ul>\n    <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n    <li><b>R-squared</b>: The R-squared for the Polynomial Fit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n</ul>\n<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting \"price\" with \"highway-mpg\" as a predictor variable.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3>Multiple Linear Regression (MLR) vs. Polynomial Fit</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<ul>\n    <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n    <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n</ul>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2>Conclusion</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense since we have 27 variables in total and we know that more than one of those variables are potential predictors of the final car price.</p>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Thank you for completing this lab!\n\n## Author\n\n<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">Joseph Santarcangelo</a>\n\n### Other Contributors\n\n<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">Mahdi Noorian PhD</a>\n\nBahare Talayian\n\nEric Xiao\n\nSteven Dong\n\nParizad\n\nHima Vasudevan\n\n<a href=\"https://www.linkedin.com/in/fiorellawever/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">Fiorella Wenver</a>\n\n<a href=\"https:// https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n\n## Change Log\n\n| Date (YYYY-MM-DD) | Version | Changed By | Change Description                            |\n| ----------------- | ------- | ---------- | --------------------------------------------- |\n| 2023-05-10        | 2.3     | Nafisa Idris | I have responded to the questions and made the necessary updates to the queries before proceeding to the GitHub repository |\n| 2020-10-30        | 2.2     | Lakshmi    | Changed url of csv                            |\n| 2020-09-09        | 2.1     | Lakshmi    | Fixes made in Polynomial Regression Equations |\n| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab            |\n\n<hr>\n\n## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "",
      "metadata": {},
      "execution_count": null,
      "outputs": []
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}