Simple+Linear+Regression+in+Python.ipynb

{"cells":[{"cell_type":"markdown","metadata":{"id":"utNHyFt_1bRg"},"source":["# Simple Linear Regression\n","\n","In this notebook, we'll build a linear regression model to predict `Sales` using an appropriate predictor variable."]},{"cell_type":"markdown","metadata":{"id":"Bf1axP_01bRk"},"source":["## Step 1: Reading and Understanding the Data\n","\n","Let's start with the following steps:\n","\n","1. Importing data using the pandas library\n","2. Understanding the structure of the data"]},{"cell_type":"code","execution_count":2,"metadata":{"id":"UiyHc2mn1bRl","executionInfo":{"status":"ok","timestamp":1702828626892,"user_tz":-330,"elapsed":426,"user":{"displayName":"Vishal","userId":"12438504076986333142"}}},"outputs":[],"source":["# Supress Warnings\n","\n","import warnings\n","warnings.filterwarnings('ignore')"]},{"cell_type":"code","execution_count":3,"metadata":{"id":"B5DXvKD31bRm","executionInfo":{"status":"ok","timestamp":1702828629141,"user_tz":-330,"elapsed":607,"user":{"displayName":"Vishal","userId":"12438504076986333142"}}},"outputs":[],"source":["# Import the numpy and pandas package\n","\n","import numpy as np\n","import pandas as pd"]},{"cell_type":"code","source":["from google.colab import drive\n","drive.mount('/content/drive')"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"AyJvvdf-1hnt","executionInfo":{"status":"ok","timestamp":1702828657090,"user_tz":-330,"elapsed":27457,"user":{"displayName":"Vishal","userId":"12438504076986333142"}},"outputId":"b101ee38-eb10-41de-a257-a9a0a7b9ce5b"},"execution_count":4,"outputs":[{"output_type":"stream","name":"stdout","text":["Mounted at /content/drive\n"]}]},{"cell_type":"code","execution_count":5,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":206},"id":"s5q7BytD1bRn","executionInfo":{"status":"ok","timestamp":1702829026727,"user_tz":-330,"elapsed":762,"user":{"displayName":"Vishal","userId":"12438504076986333142"}},"outputId":"f74375c8-961e-4e90-b577-f992c8963e5b"},"outputs":[{"output_type":"execute_result","data":{"text/plain":["      TV  Radio  Newspaper  Sales\n","0  230.1   37.8       69.2   22.1\n","1   44.5   39.3       45.1   10.4\n","2   17.2   45.9       69.3   12.0\n","3  151.5   41.3       58.5   16.5\n","4  180.8   10.8       58.4   17.9"],"text/html":["\n","  <div id=\"df-c5211c52-25da-46d9-80f3-f744c8e0175e\" class=\"colab-df-container\">\n","    <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>TV</th>\n","      <th>Radio</th>\n","      <th>Newspaper</th>\n","      <th>Sales</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>230.1</td>\n","      <td>37.8</td>\n","      <td>69.2</td>\n","      <td>22.1</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>44.5</td>\n","      <td>39.3</td>\n","      <td>45.1</td>\n","      <td>10.4</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>17.2</td>\n","      <td>45.9</td>\n","      <td>69.3</td>\n","      <td>12.0</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>151.5</td>\n","      <td>41.3</td>\n","      <td>58.5</td>\n","      <td>16.5</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>180.8</td>\n","      <td>10.8</td>\n","      <td>58.4</td>\n","      <td>17.9</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>\n","    <div class=\"colab-df-buttons\">\n","\n","  <div class=\"colab-df-container\">\n","    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c5211c52-25da-46d9-80f3-f744c8e0175e')\"\n","            title=\"Convert this dataframe to an interactive table.\"\n","            style=\"display:none;\">\n","\n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n","    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 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4)"]},"metadata":{},"execution_count":6}],"source":["advertising.shape"]},{"cell_type":"code","execution_count":7,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"JQjdmTcQ1bRp","executionInfo":{"status":"ok","timestamp":1702829043111,"user_tz":-330,"elapsed":865,"user":{"displayName":"Vishal","userId":"12438504076986333142"}},"outputId":"e44d1326-790b-4cc4-d3a7-9044d43c7092"},"outputs":[{"output_type":"stream","name":"stdout","text":["<class 'pandas.core.frame.DataFrame'>\n","RangeIndex: 200 entries, 0 to 199\n","Data columns (total 4 columns):\n"," #   Column     Non-Null Count  Dtype  \n","---  ------     --------------  -----  \n"," 0   TV         200 non-null    float64\n"," 1   Radio      200 non-null    float64\n"," 2   Newspaper  200 non-null    float64\n"," 3   Sales      200 non-null    float64\n","dtypes: float64(4)\n","memory usage: 6.4 KB\n"]}],"source":["advertising.info()"]},{"cell_type":"code","execution_count":8,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":300},"id":"n0VLWReh1bRp","executionInfo":{"status":"ok","timestamp":1702829046593,"user_tz":-330,"elapsed":511,"user":{"displayName":"Vishal","userId":"12438504076986333142"}},"outputId":"ed964607-7131-49ce-a5e6-cfb86870fb46"},"outputs":[{"output_type":"execute_result","data":{"text/plain":["               TV       Radio   Newspaper       Sales\n","count  200.000000  200.000000  200.000000  200.000000\n","mean   147.042500   23.264000   30.554000   15.130500\n","std     85.854236   14.846809   21.778621    5.283892\n","min      0.700000    0.000000    0.300000    1.600000\n","25%     74.375000    9.975000   12.750000   11.000000\n","50%    149.750000   22.900000   25.750000   16.000000\n","75%    218.825000   36.525000   45.100000   19.050000\n","max    296.400000   49.600000  114.000000   27.000000"],"text/html":["\n","  <div 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<th>std</th>\n","      <td>85.854236</td>\n","      <td>14.846809</td>\n","      <td>21.778621</td>\n","      <td>5.283892</td>\n","    </tr>\n","    <tr>\n","      <th>min</th>\n","      <td>0.700000</td>\n","      <td>0.000000</td>\n","      <td>0.300000</td>\n","      <td>1.600000</td>\n","    </tr>\n","    <tr>\n","      <th>25%</th>\n","      <td>74.375000</td>\n","      <td>9.975000</td>\n","      <td>12.750000</td>\n","      <td>11.000000</td>\n","    </tr>\n","    <tr>\n","      <th>50%</th>\n","      <td>149.750000</td>\n","      <td>22.900000</td>\n","      <td>25.750000</td>\n","      <td>16.000000</td>\n","    </tr>\n","    <tr>\n","      <th>75%</th>\n","      <td>218.825000</td>\n","      <td>36.525000</td>\n","      <td>45.100000</td>\n","      <td>19.050000</td>\n","    </tr>\n","    <tr>\n","      <th>max</th>\n","      <td>296.400000</td>\n","      <td>49.600000</td>\n","      <td>114.000000</td>\n","      <td>27.000000</td>\n","    </tr>\n","  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We'll first make a pairplot of all the variables present to visualise which variables are most correlated to `Sales`."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"nqPE5OYA1bRq"},"outputs":[],"source":["import matplotlib.pyplot as plt\n","import seaborn as sns"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"8jg3r4F91bRq","outputId":"f4d38336-6de1-4582-a499-fa315fb81db1"},"outputs":[{"data":{"image/png":"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\n","text/plain":["<Figure size 864x288 with 3 Axes>"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["sns.pairplot(advertising, x_vars=['TV', 'Newspaper', 'Radio'], y_vars='Sales',size=4, aspect=1, kind='scatter')\n","plt.show()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"SoPqC_HN1bRq","outputId":"97bfdbde-4899-4100-b669-a32ba057155d"},"outputs":[{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 2 Axes>"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["sns.heatmap(advertising.corr(), cmap=\"YlGnBu\", annot = True)\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"T7KM2hjb1bRr"},"source":["As is visible from the pairplot and the heatmap, the variable `TV` seems to be most correlated with `Sales`. So let's go ahead and perform simple linear regression using `TV` as our feature variable."]},{"cell_type":"markdown","metadata":{"id":"lgs2Rdrs1bRr"},"source":["---\n","## Step 3: Performing Simple Linear Regression\n","\n","Equation of linear regression<br>\n","$y = c + m_1x_1 + m_2x_2 + ... + m_nx_n$\n","\n","-  $y$ is the response\n","-  $c$ is the intercept\n","-  $m_1$ is the coefficient for the first feature\n","-  $m_n$ is the coefficient for the nth feature<br>\n","\n","In our case:\n","\n","$y = c + m_1 \\times TV$\n","\n","The $m$ values are called the model **coefficients** or **model parameters**.\n","\n","---"]},{"cell_type":"markdown","metadata":{"id":"N3585bwX1bRr"},"source":["### Generic Steps in model building using `statsmodels`\n","\n","We first assign the feature variable, `TV`, in this case, to the variable `X` and the response variable, `Sales`, to the variable `y`."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"6-Y9AOwL1bRr"},"outputs":[],"source":["X = advertising['TV']\n","y = advertising['Sales']\n"]},{"cell_type":"markdown","metadata":{"id":"SD9hgj6c1bRr"},"source":["#### Train-Test Split\n","\n","You now need to split our variable into training and testing sets. You'll perform this by importing `train_test_split` from the `sklearn.model_selection` library. It is usually a good practice to keep 70% of the data in your train dataset and the rest 30% in your test dataset"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"7z6jkqb61bRr"},"outputs":[],"source":["from sklearn.model_selection import train_test_split\n","X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = 0.7, test_size = 0.3, random_state = 100)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"fVkzL56Y1bRr","outputId":"aa935e4b-31b9-4a6a-a95c-77f54788aa70"},"outputs":[{"data":{"text/plain":["74     213.4\n","3      151.5\n","185    205.0\n","26     142.9\n","90     134.3\n","Name: TV, dtype: float64"]},"execution_count":33,"metadata":{},"output_type":"execute_result"}],"source":["# Let's now take a look at the train dataset\n","\n","X_train.head()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"xkHqxvF61bRs","outputId":"6b6ecd97-8f70-4811-ada6-6dce3dd21c04"},"outputs":[{"data":{"text/plain":["74     17.0\n","3      16.5\n","185    22.6\n","26     15.0\n","90     14.0\n","Name: Sales, dtype: float64"]},"execution_count":25,"metadata":{},"output_type":"execute_result"}],"source":["y_train.head()"]},{"cell_type":"markdown","metadata":{"id":"Sc_aqlLs1bRs"},"source":["#### Building a Linear Model\n","\n","You first need to import the `statsmodel.api` library using which you'll perform the linear regression."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"CfSNu5Ep1bRs"},"outputs":[],"source":["import statsmodels.api as sm"]},{"cell_type":"markdown","metadata":{"id":"6o35yLl11bRs"},"source":["By default, the `statsmodels` library fits a line on the dataset which passes through the origin. But in order to have an intercept, you need to manually use the `add_constant` attribute of `statsmodels`. And once you've added the constant to your `X_train` dataset, you can go ahead and fit a regression line using the `OLS` (Ordinary Least Squares) attribute of `statsmodels` as shown below"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"kGTy1YFp1bRs"},"outputs":[],"source":["# Add a constant to get an intercept\n","X_train_sm = sm.add_constant(X_train)\n","\n","# Fit the resgression line using 'OLS'\n","lr = sm.OLS(y_train, X_train_sm).fit()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"iC8kkP_51bRs","outputId":"59a1e79b-c460-4b95-e7f4-71c60045604a"},"outputs":[{"data":{"text/plain":["const    6.948683\n","TV       0.054546\n","dtype: float64"]},"execution_count":38,"metadata":{},"output_type":"execute_result"}],"source":["# Print the parameters, i.e. the intercept and the slope of the regression line fitted\n","lr.params"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"iLSYd5851bRs","outputId":"d5d08585-ce10-431e-83cb-6480be7d16f3"},"outputs":[{"data":{"text/html":["<table class=\"simpletable\">\n","<caption>OLS Regression Results</caption>\n","<tr>\n","  <th>Dep. Variable:</th>          <td>Sales</td>      <th>  R-squared:         </th> <td>   0.816</td>\n","</tr>\n","<tr>\n","  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.814</td>\n","</tr>\n","<tr>\n","  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   611.2</td>\n","</tr>\n","<tr>\n","  <th>Date:</th>             <td>Wed, 27 Jul 2022</td> <th>  Prob (F-statistic):</th> <td>1.52e-52</td>\n","</tr>\n","<tr>\n","  <th>Time:</th>                 <td>00:34:40</td>     <th>  Log-Likelihood:    </th> <td> -321.12</td>\n","</tr>\n","<tr>\n","  <th>No. Observations:</th>      <td>   140</td>      <th>  AIC:               </th> <td>   646.2</td>\n","</tr>\n","<tr>\n","  <th>Df Residuals:</th>          <td>   138</td>      <th>  BIC:               </th> <td>   652.1</td>\n","</tr>\n","<tr>\n","  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n","</tr>\n","<tr>\n","  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n","</tr>\n","</table>\n","<table class=\"simpletable\">\n","<tr>\n","    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n","</tr>\n","<tr>\n","  <th>const</th> <td>    6.9487</td> <td>    0.385</td> <td>   18.068</td> <td> 0.000</td> <td>    6.188</td> <td>    7.709</td>\n","</tr>\n","<tr>\n","  <th>TV</th>    <td>    0.0545</td> <td>    0.002</td> <td>   24.722</td> <td> 0.000</td> <td>    0.050</td> <td>    0.059</td>\n","</tr>\n","</table>\n","<table class=\"simpletable\">\n","<tr>\n","  <th>Omnibus:</th>       <td> 0.027</td> <th>  Durbin-Watson:     </th> <td>   2.196</td>\n","</tr>\n","<tr>\n","  <th>Prob(Omnibus):</th> <td> 0.987</td> <th>  Jarque-Bera (JB):  </th> <td>   0.150</td>\n","</tr>\n","<tr>\n","  <th>Skew:</th>          <td>-0.006</td> <th>  Prob(JB):          </th> <td>   0.928</td>\n","</tr>\n","<tr>\n","  <th>Kurtosis:</th>      <td> 2.840</td> <th>  Cond. No.          </th> <td>    328.</td>\n","</tr>\n","</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."],"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  Sales   R-squared:                       0.816\n","Model:                            OLS   Adj. R-squared:                  0.814\n","Method:                 Least Squares   F-statistic:                     611.2\n","Date:                Wed, 27 Jul 2022   Prob (F-statistic):           1.52e-52\n","Time:                        00:34:40   Log-Likelihood:                -321.12\n","No. Observations:                 140   AIC:                             646.2\n","Df Residuals:                     138   BIC:                             652.1\n","Df Model:                           1                                         \n","Covariance Type:            nonrobust                                         \n","==============================================================================\n","                 coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------\n","const          6.9487      0.385     18.068      0.000       6.188       7.709\n","TV             0.0545      0.002     24.722      0.000       0.050       0.059\n","==============================================================================\n","Omnibus:                        0.027   Durbin-Watson:                   2.196\n","Prob(Omnibus):                  0.987   Jarque-Bera (JB):                0.150\n","Skew:                          -0.006   Prob(JB):                        0.928\n","Kurtosis:                       2.840   Cond. No.                         328.\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""]},"execution_count":41,"metadata":{},"output_type":"execute_result"}],"source":["# Performing a summary operation lists out all the different parameters of the regression line fitted\n","lr.summary()"]},{"cell_type":"markdown","metadata":{"id":"oKO-UFq31bRs"},"source":["####  Looking at some key statistics from the summary"]},{"cell_type":"markdown","metadata":{"id":"A4tTqNlI1bRt"},"source":["The values we are concerned with are -\n","1. The coefficients and significance (p-values)\n","2. R-squared\n","3. F statistic and its significance"]},{"cell_type":"markdown","metadata":{"id":"vEcf0ffR1bRt"},"source":["##### 1. The coefficient for TV is 0.054, with a very low p value\n","The coefficient is statistically significant. So the association is not purely by chance."]},{"cell_type":"markdown","metadata":{"id":"eGEB_7Db1bRt"},"source":["##### 2. R - squared is 0.816\n","Meaning that 81.6% of the variance in `Sales` is explained by `TV`\n","\n","This is a decent R-squared value."]},{"cell_type":"markdown","metadata":{"id":"pMbXRZhW1bRt"},"source":["###### 3. F statistic has a very low p value (practically low)\n","Meaning that the model fit is statistically significant, and the explained variance isn't purely by chance."]},{"cell_type":"markdown","metadata":{"id":"ZDknSG1m1bRt"},"source":["---\n","The fit is significant. Let's visualize how well the model fit the data.\n","\n","From the parameters that we get, our linear regression equation becomes:\n","\n","$ Sales = 6.948 + 0.054 \\times TV $"]},{"cell_type":"code","execution_count":null,"metadata":{"scrolled":true,"id":"EDstcBWr1bRt","outputId":"8a5fac6e-2f38-434e-d533-083b5b4c316b"},"outputs":[{"data":{"image/png":"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\n","text/plain":["<matplotlib.figure.Figure at 0x245694aedd8>"]},"metadata":{},"output_type":"display_data"}],"source":["plt.scatter(X_train, y_train)\n","plt.plot(X_train, 6.948 + 0.054*X_train, 'r')\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"ZBN-J3T-1bRt"},"source":["## Step 4: Residual analysis\n","To validate assumptions of the model, and hence the reliability for inference"]},{"cell_type":"markdown","metadata":{"id":"B5egbvcR1bRu"},"source":["#### Distribution of the error terms\n","We need to check if the error terms are also normally distributed (which is infact, one of the major assumptions of linear regression), let us plot the histogram of the error terms and see what it looks like."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"z8LKB32p1bRu"},"outputs":[],"source":["y_train_pred = lr.predict(X_train_sm)\n","res = (y_train - y_train_pred)"]},{"cell_type":"code","execution_count":null,"metadata":{"scrolled":true,"id":"ATvkOBGX1bRu","outputId":"a9c8489c-3607-4752-a351-333868099030"},"outputs":[{"data":{"image/png":"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\n","text/plain":["<matplotlib.figure.Figure at 0x245694ba7b8>"]},"metadata":{},"output_type":"display_data"}],"source":["fig = plt.figure()\n","sns.distplot(res, bins = 15)\n","fig.suptitle('Error Terms', fontsize = 15)                  # Plot heading\n","plt.xlabel('y_train - y_train_pred', fontsize = 15)         # X-label\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"egXKZJHP1bRu"},"source":["The residuals are following the normally distributed with a mean 0. All good!"]},{"cell_type":"markdown","metadata":{"id":"wTfPpbfG1bRy"},"source":["#### Looking for patterns in the residuals"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"BT3mRwnB1bRy","outputId":"2307345c-1f95-4db2-bb8e-d0e1b734aa95"},"outputs":[{"data":{"image/png":"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\n","text/plain":["<matplotlib.figure.Figure at 0x245698f7048>"]},"metadata":{},"output_type":"display_data"}],"source":["plt.scatter(X_train,res)\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"Zp1mILU51bRy"},"source":["We are confident that the model fit isn't by chance, and has decent predictive power. The normality of residual terms allows some inference on the coefficients.\n","\n","Although, the variance of residuals increasing with X indicates that there is significant variation that this model is unable to explain."]},{"cell_type":"markdown","metadata":{"id":"849nGN4a1bRy"},"source":["As you can see, the regression line is a pretty good fit to the data"]},{"cell_type":"markdown","metadata":{"id":"7Q0KHkzX1bRy"},"source":["## Step 5: Predictions on the Test Set\n","\n","Now that you have fitted a regression line on your train dataset, it's time to make some predictions on the test data. For this, you first need to add a constant to the `X_test` data like you did for `X_train` and then you can simply go on and predict the y values corresponding to `X_test` using the `predict` attribute of the fitted regression line."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"RGrn9Koy1bRy"},"outputs":[],"source":["# Add a constant to X_test\n","X_test_sm = sm.add_constant(X_test)\n","\n","# Predict the y values corresponding to X_test_sm\n","y_pred = lr.predict(X_test_sm)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"C6ElShQc1bRy","outputId":"70d2c5ca-e03a-4dd5-b289-99f8dc5ded19"},"outputs":[{"data":{"text/plain":["126     7.374140\n","104    19.941482\n","99     14.323269\n","92     18.823294\n","111    20.132392\n","dtype: float64"]},"execution_count":23,"metadata":{},"output_type":"execute_result"}],"source":["y_pred.head()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"sfWXpfQM1bRy"},"outputs":[],"source":["from sklearn.metrics import mean_squared_error\n","from sklearn.metrics import r2_score"]},{"cell_type":"markdown","metadata":{"id":"6wTEt4Ro1bRz"},"source":["##### Looking at the RMSE"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"m5cTGprQ1bRz","outputId":"1b0050da-63dd-4f1d-a7be-6152e0266e0d"},"outputs":[{"data":{"text/plain":["2.019296008966233"]},"execution_count":25,"metadata":{},"output_type":"execute_result"}],"source":["#Returns the mean squared error; we'll take a square root\n","np.sqrt(mean_squared_error(y_test, y_pred))"]},{"cell_type":"markdown","metadata":{"id":"CK7bTGSI1bRz"},"source":["###### Checking the R-squared on the test set"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"ujHnD1Lu1bRz","outputId":"ca180456-b8e2-4a19-b5a3-0b62fafd07f3"},"outputs":[{"data":{"text/plain":["0.7921031601245658"]},"execution_count":26,"metadata":{},"output_type":"execute_result"}],"source":["r_squared = r2_score(y_test, y_pred)\n","r_squared"]},{"cell_type":"markdown","metadata":{"id":"n7kxFr4C1bRz"},"source":["##### Visualizing the fit on the test set"]},{"cell_type":"code","execution_count":null,"metadata":{"scrolled":true,"id":"fD84LIXS1bRz","outputId":"773c458e-6b99-4c99-823b-8af7648d45aa"},"outputs":[{"data":{"image/png":"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\n","text/plain":["<matplotlib.figure.Figure at 0x245698f7e48>"]},"metadata":{},"output_type":"display_data"}],"source":["plt.scatter(X_test, y_test)\n","plt.plot(X_test, 6.948 + 0.054 * X_test, 'r')\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"U9iBOFM21bR0"},"source":[""]},{"cell_type":"markdown","metadata":{"id":"uqmRkNDS1bR0"},"source":[""]},{"cell_type":"markdown","metadata":{"id":"iLoaM8ZP1bR0"},"source":[""]},{"cell_type":"markdown","metadata":{"id":"EMlzU2Fz1bR0"},"source":[""]},{"cell_type":"markdown","metadata":{"id":"YHjEorAQ1bR0"},"source":["### Linear Regression using `linear_model` in `sklearn`\n","\n","Apart from `statsmodels`, there is another package namely `sklearn` that can be used to perform linear regression. We will use the `linear_model` library from `sklearn` to build the model. Since, we hae already performed a train-test split, we don't need to do it again.\n","\n","There's one small step that we need to add, though. When there's only a single feature, we need to add an additional column in order for the linear regression fit to be performed successfully."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"U6kxJ2ne1bR0"},"outputs":[],"source":["from sklearn.model_selection import train_test_split\n","X_train_lm, X_test_lm, y_train_lm, y_test_lm = train_test_split(X, y, train_size = 0.7, test_size = 0.3, random_state = 100)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"ZJ4K2_9C1bR0","outputId":"e804a5f4-9e96-425c-d0fa-3003a32e7d5d"},"outputs":[{"data":{"text/plain":["(140,)"]},"execution_count":29,"metadata":{},"output_type":"execute_result"}],"source":["X_train_lm.shape"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"WVatturI1bR0"},"outputs":[],"source":["X_train_lm = X_train_lm.reshape(-1,1)\n","X_test_lm = X_test_lm.reshape(-1,1)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Tr_IXCQ-1bR1","outputId":"271c2421-2275-44a6-8f38-21b3de7f6c10"},"outputs":[{"name":"stdout","output_type":"stream","text":["(140, 1)\n","(140,)\n","(60, 1)\n","(60,)\n"]}],"source":["print(X_train_lm.shape)\n","print(y_train_lm.shape)\n","print(X_test_lm.shape)\n","print(y_test_lm.shape)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Qrck7nmC1bR1","outputId":"ae6810aa-0851-4e33-bc87-505a67c30b0e"},"outputs":[{"data":{"text/plain":["LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"]},"execution_count":32,"metadata":{},"output_type":"execute_result"}],"source":["from sklearn.linear_model import LinearRegression\n","\n","# Representing LinearRegression as lr(Creating LinearRegression Object)\n","lm = LinearRegression()\n","\n","# Fit the model using lr.fit()\n","lm.fit(X_train_lm, y_train_lm)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Z3TPhUD31bR1","outputId":"074a8ea0-904a-4b1e-c06f-d97e1c45c3e8"},"outputs":[{"name":"stdout","output_type":"stream","text":["6.948683200001357\n","[0.05454575]\n"]}],"source":["print(lm.intercept_)\n","print(lm.coef_)"]},{"cell_type":"markdown","metadata":{"id":"koElqrbM1bR1"},"source":["The equationwe get is the same as what we got before!\n","\n","$ Sales = 6.948 + 0.054* TV $"]},{"cell_type":"markdown","metadata":{"id":"wiEvKbT31bR1"},"source":["Sklearn linear model is useful as it is compatible with a lot of sklearn utilites (cross validation, grid search etc.)"]},{"cell_type":"markdown","metadata":{"id":"mUb5YyvZ1bR2"},"source":[""]},{"cell_type":"markdown","metadata":{"id":"MGulFAr_1bR2"},"source":[""]},{"cell_type":"code","execution_count":null,"metadata":{"scrolled":true,"id":"XDV1yULi1bR3","outputId":"5d345b2c-f3a6-4c16-c386-ad47ec027365"},"outputs":[{"name":"stdout","output_type":"stream","text":["[[1.         0.90321277]\n"," [0.90321277 1.        ]]\n"]}],"source":["corrs = np.corrcoef(X_train, y_train)\n","print(corrs)  #R"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"CuazzAFM1bR3","outputId":"250975c7-d249-4aed-d2c0-e42db144990c"},"outputs":[{"data":{"text/plain":["0.8157933136480384"]},"execution_count":35,"metadata":{},"output_type":"execute_result"}],"source":["corrs[0,1] ** 2  #R2"]},{"cell_type":"markdown","metadata":{"id":"Gg5J9gjH1bR3"},"source":["Correlation (Pearson) is also called **\"r\"** or **\"Pearson's R\"**"]},{"cell_type":"markdown","metadata":{"id":"GG4PSJJE1bR4"},"source":["\n","\n","\n","\n","\n","\n",""]},{"cell_type":"markdown","metadata":{"id":"eL1xcedZ1bR4"},"source":[""]},{"cell_type":"markdown","metadata":{"id":"xKPUvp7d1bR4"},"source":["### Q: What is a good RMSE? Is there some RMSE that I should aim for?"]},{"cell_type":"markdown","metadata":{"id":"yyp6SLOI1bR4"},"source":[".\n","\n",".\n","\n",".\n","\n",".\n","\n","  #### Drumroll...\n","  \n",".\n","\n",".\n","\n",".\n","\n","."]},{"cell_type":"markdown","metadata":{"id":"EZxhdNHq1bR4"},"source":["\n","\n","\n","\n","\n","\n",""]},{"cell_type":"markdown","metadata":{"id":"mCpaA7Q21bR4"},"source":["The RMSE:\n"," - depends on the units of the Y variables\n"," - is NOT a normalized measure\n","\n","While it can't really tell you of the gooodness of the particular model, it can help you compare models.\n","\n","A better measure is R squared, which is normalized."]},{"cell_type":"markdown","metadata":{"id":"mhzSQxsp1bR5"},"source":["<br>\n","<br>\n","<br>\n","<br>\n","<br>\n","<br>\n","<br>\n","<br>\n","<br>\n","<br>\n","<br>"]},{"cell_type":"markdown","metadata":{"id":"hcDNZtK31bR5"},"source":["### Q: Does scaling have an impact on the model? When should I scale?"]},{"cell_type":"markdown","metadata":{"id":"5xQCe_QO1bR5"},"source":["<br>\n","<br>\n","<br>\n","<br>\n","<br>\n","<br>"]},{"cell_type":"markdown","metadata":{"id":"kmn5QxSy1bR5"},"source":["While the true benefits of scaling will be apparent during future modules, at this juncture we can discuss if it has an impact on the model.\n","\n","We'll rebuild the model after scaling the predictor and see what changes.\n","\n","The most popular methods for scaling:\n","1. Min-Max Scaling\n","2. Standard Scaling"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"JEfaKz3S1bR5"},"outputs":[],"source":["from sklearn.model_selection import train_test_split\n","X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = 0.7, test_size = 0.3, random_state = 100)"]},{"cell_type":"markdown","metadata":{"id":"wl1f1B1f1bR5"},"source":["#### SciKit Learn has these scaling utilities handy"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"f5s1TkUT1bR5"},"outputs":[],"source":["from sklearn.preprocessing import StandardScaler, MinMaxScaler"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"DscRAFq31bR5"},"outputs":[],"source":["# One aspect that you need to take care of is that the 'fit_transform' can be performed on 2D arrays only. So you need to\n","# reshape your 'X_train_scaled' and 'y_trained_scaled' data in order to perform the standardisation.\n","X_train_scaled = X_train.reshape(-1,1)\n","y_train_scaled = y_train.reshape(-1,1)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"ChF2e36_1bR5","outputId":"230d9c3a-1585-4f18-9574-bd268592cb01"},"outputs":[{"data":{"text/plain":["(140, 1)"]},"execution_count":39,"metadata":{},"output_type":"execute_result"}],"source":["X_train_scaled.shape"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"2oI90Csv1bR5"},"outputs":[],"source":["# Create a scaler object using StandardScaler()\n","scaler = StandardScaler()\n","#'Fit' and transform the train set; and transform using the fit on the test set later\n","X_train_scaled = scaler.fit_transform(X_train_scaled)\n","y_train_scaled = scaler.fit_transform(y_train_scaled)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"YwS1EU0c1bR6","outputId":"6c968f96-7589-43e5-994e-9ddcd13db10b"},"outputs":[{"name":"stdout","output_type":"stream","text":["mean and sd for X_train_scaled: 2.5376526277146434e-17 0.9999999999999999\n","mean and sd for y_train_scaled: -2.5376526277146434e-16 1.0\n"]}],"source":["print(\"mean and sd for X_train_scaled:\", np.mean(X_train_scaled), np.std(X_train_scaled))\n","print(\"mean and sd for y_train_scaled:\", np.mean(y_train_scaled), np.std(y_train_scaled))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"betCCWKt1bR6"},"outputs":[],"source":["# Let's fit the regression line following exactly the same steps as done before\n","X_train_scaled = sm.add_constant(X_train_scaled)\n","\n","lr_scaled = sm.OLS(y_train_scaled, X_train_scaled).fit()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"YHaJmbT01bR6","outputId":"452cba35-f5b5-4c08-fb46-1425baf95637"},"outputs":[{"data":{"text/plain":["array([-2.91433544e-16,  9.03212773e-01])"]},"execution_count":43,"metadata":{},"output_type":"execute_result"}],"source":["# Check the parameters\n","lr_scaled.params"]},{"cell_type":"markdown","metadata":{"id":"HoP0K35k1bR6"},"source":["As you might notice, the value of the parameters have changed since we have changed the scale."]},{"cell_type":"markdown","metadata":{"id":"p4PSPhsW1bR6"},"source":["Let's look at the statistics of the model, to see if any other aspect of the model has changed."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"f7J1uIjM1bR6","outputId":"0a6b8588-394a-445b-9c3e-d2f7cf7ca93c"},"outputs":[{"name":"stdout","output_type":"stream","text":["                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                      y   R-squared:                       0.816\n","Model:                            OLS   Adj. R-squared:                  0.814\n","Method:                 Least Squares   F-statistic:                     611.2\n","Date:                Thu, 13 Sep 2018   Prob (F-statistic):           1.52e-52\n","Time:                        22:39:46   Log-Likelihood:                -80.233\n","No. Observations:                 140   AIC:                             164.5\n","Df Residuals:                     138   BIC:                             170.3\n","Df Model:                           1                                         \n","Covariance Type:            nonrobust                                         \n","==============================================================================\n","                 coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------\n","const      -2.914e-16      0.037  -7.98e-15      1.000      -0.072       0.072\n","x1             0.9032      0.037     24.722      0.000       0.831       0.975\n","==============================================================================\n","Omnibus:                        0.027   Durbin-Watson:                   2.196\n","Prob(Omnibus):                  0.987   Jarque-Bera (JB):                0.150\n","Skew:                          -0.006   Prob(JB):                        0.928\n","Kurtosis:                       2.840   Cond. No.                         1.00\n","==============================================================================\n","\n","Warnings:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"]}],"source":["print(lr_scaled.summary())"]},{"cell_type":"markdown","metadata":{"id":"4WpVPTyR1bR6"},"source":["#### Model statistics and goodness of fit remain unchanged.\n","\n","##### So why scale at all?\n","- Helps with interpretation (we'll be able to appreciate this better in later modules)\n","- Faster convergence of gradient descent"]}],"metadata":{"kernelspec":{"display_name":"Python 3 (ipykernel)","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.9.7"},"colab":{"provenance":[]}},"nbformat":4,"nbformat_minor":0}