AnaJaved-L06-AdRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lesson 6 Assignment - Advertising Sales Regression\n",
    "\n",
    "## Author - Ana Javed\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Instructions  \n",
    "Perform four different linear regressions on advertising sales data located in 'Advertising.csv'.  Your dependent feature is 'sales', a measure of sales of a product in a given market in thousands of dollars. \n",
    "\n",
    "The independent features for each of the first 3 separate regressions are:\n",
    "\n",
    " 1. 'TV': advertising dollars spent on TV ads for a single product in a given market\n",
    " 2. 'radio': advertising dollars spent on radio ads\n",
    " 3. 'newspaper': advertising dollars spent on newspaper ads\n",
    "\n",
    "For the first 3 linear regression performed:\n",
    "\n",
    "- Produce a labeled graph showing the best fit line with the data points.\n",
    "- Interpret both the slope and y-intercept.\n",
    " \n",
    "The final regression(#4) includes all 3 features: (a) TV, (b) radio, and (c) newspaper. \n",
    "- Interpret each partial slope and the intercept parameters.\n",
    "- Interpret the adjusted R-squared.\n",
    "- Find and report the mean-squared error.\n",
    "\n",
    "#### Please prepare this information for a client who may not understand what the parameters mean.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn import linear_model\n",
    "import statsmodels.formula.api as sm\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      TV  radio  newspaper  sales\n",
      "1  230.1   37.8       69.2   22.1\n",
      "2   44.5   39.3       45.1   10.4\n",
      "3   17.2   45.9       69.3    9.3\n",
      "4  151.5   41.3       58.5   18.5\n",
      "5  180.8   10.8       58.4   12.9\n",
      "(200, 4)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>147.042500</td>\n",
       "      <td>23.264000</td>\n",
       "      <td>30.554000</td>\n",
       "      <td>14.022500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>85.854236</td>\n",
       "      <td>14.846809</td>\n",
       "      <td>21.778621</td>\n",
       "      <td>5.217457</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>10.375000</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>12.900000</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>17.400000</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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TV       radio   newspaper       sales\n",
       "count  200.000000  200.000000  200.000000  200.000000\n",
       "mean   147.042500   23.264000   30.554000   14.022500\n",
       "std     85.854236   14.846809   21.778621    5.217457\n",
       "min      0.700000    0.000000    0.300000    1.600000\n",
       "25%     74.375000    9.975000   12.750000   10.375000\n",
       "50%    149.750000   22.900000   25.750000   12.900000\n",
       "75%    218.825000   36.525000   45.100000   17.400000\n",
       "max    296.400000   49.600000  114.000000   27.000000"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load data\n",
    "filename = 'https://library.startlearninglabs.uw.edu/DATASCI410/Datasets/Advertising.csv'\n",
    "ad_data = pd.read_csv(filename, index_col=0)\n",
    "print(ad_data.head())\n",
    "print(ad_data.shape)\n",
    "ad_data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 7.03259\n",
      "Slope : 0.04754\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## First Independent Feature: TV (Advertisting Dollars spent on TV ads) \n",
    "## Dependent Feature = Sales\n",
    "\n",
    "# First initialize the model.\n",
    "from sklearn import linear_model\n",
    "linear_model = linear_model.LinearRegression()\n",
    "\n",
    "\n",
    "# Fit the model to the data\n",
    "x_input = ad_data['TV'].values.reshape(len(ad_data['TV']), 1)\n",
    "y_output = ad_data['sales'].values.reshape(len(ad_data['sales']), 1)\n",
    "\n",
    "linear_model.fit(x_input, y_output)\n",
    "\n",
    "\n",
    "# Get predictions\n",
    "y_pred = linear_model.predict(x_input)\n",
    "\n",
    "# Plot output\n",
    "plt.scatter(x_input, y_output)\n",
    "plt.plot(x_input, y_pred, linewidth=2, color = 'black')\n",
    "plt.grid(True)\n",
    "plt.xlabel('TV')\n",
    "plt.ylabel('Sales')\n",
    "plt.title('TV vs Sales')\n",
    "\n",
    "# Print model parameters\n",
    "# Get slope (m) and y-intercept (b)\n",
    "print('Intercept: {0:.5f}'.format(linear_model.intercept_[0]))\n",
    "print('Slope : {0:.5f}'.format(linear_model.coef_[0][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 9.31164\n",
      "Slope : 0.20250\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Second Independent Feature: Radio  (Advertisting Dollars spent on Radio Ads)\n",
    "## Dependent Feature = Sales\n",
    "\n",
    "# First initialize the model.\n",
    "from sklearn import linear_model\n",
    "linear_model = linear_model.LinearRegression()\n",
    "\n",
    "\n",
    "# Fit the model to the data\n",
    "x_input = ad_data['radio'].values.reshape(len(ad_data['radio']), 1)\n",
    "y_output = ad_data['sales'].values.reshape(len(ad_data['sales']), 1)\n",
    "\n",
    "linear_model.fit(x_input, y_output)\n",
    "\n",
    "\n",
    "# Get predictions\n",
    "y_pred = linear_model.predict(x_input)\n",
    "\n",
    "# Plot output\n",
    "plt.scatter(x_input, y_output, color = 'red')\n",
    "plt.plot(x_input, y_pred, linewidth=2, color = 'black')\n",
    "plt.grid(True)\n",
    "plt.xlabel('Radio')\n",
    "plt.ylabel('Sales')\n",
    "plt.title('Radio vs Sales')\n",
    "\n",
    "# Print model parameters\n",
    "# Get slope (m) and y-intercept (b)\n",
    "print('Intercept: {0:.5f}'.format(linear_model.intercept_[0]))\n",
    "print('Slope : {0:.5f}'.format(linear_model.coef_[0][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 12.35141\n",
      "Slope : 0.05469\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Third Independent Feature: Newspaper (Advertisting Dollars spent on Newspaper Ads)\n",
    "## Dependent Feature = Sales\n",
    "\n",
    "# First initialize the model.\n",
    "from sklearn import linear_model\n",
    "linear_model = linear_model.LinearRegression()\n",
    "\n",
    "\n",
    "# Fit the model to the data\n",
    "x_input = ad_data['newspaper'].values.reshape(len(ad_data['newspaper']), 1)\n",
    "y_output = ad_data['sales'].values.reshape(len(ad_data['sales']), 1)\n",
    "\n",
    "linear_model.fit(x_input, y_output)\n",
    "\n",
    "\n",
    "# Get predictions\n",
    "y_pred = linear_model.predict(x_input)\n",
    "\n",
    "# Plot output\n",
    "plt.scatter(x_input, y_output, color = 'green')\n",
    "plt.plot(x_input, y_pred, linewidth=2, color='black')\n",
    "plt.grid(True)\n",
    "plt.xlabel('Newspaper')\n",
    "plt.ylabel('Sales')\n",
    "plt.title('Newspaper vs Sales')\n",
    "\n",
    "# Print model parameters\n",
    "# Get slope (m) and y-intercept (b)\n",
    "print('Intercept: {0:.5f}'.format(linear_model.intercept_[0]))\n",
    "print('Slope : {0:.5f}'.format(linear_model.coef_[0][0]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpretation of the Intercept & Slope for TV, Radio, and Newspaper Ads in relation to Sales \n",
    "\n",
    "For TV, the slope is small but positive, which means that as TV ad spending increased, the Sales increased at a rate of 0.047. The y-intercept is 7.03, which means that if TV ad spending was 0, then sales would be about 7.03. \n",
    "\n",
    "For Radio, the slope is slightly bigger than TV and positive. This means that as radio ad spending increased, sales increased at a rate of 0.20. The y-intercept is also higher than TV, and it is 9.31. This means that if Radio ad spending was 0, then sales would be at 9.311. \n",
    "\n",
    "For Newspaper, the slope is 0.055. This means that as newspaper ads spending increased, sales increased at this rate. The y-intercept is the highest out of all three, and sits at 12.35. This means that if newspaper spending was 0, then sales would be at 12.35. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Regression for All 3 Features: TV, Radio, and Newspaper\n",
    "\n",
    "## Separating the independent variables vs dependent variables \n",
    "x = ad_data[['TV','radio', 'newspaper']]\n",
    "y = ad_data['sales']\n",
    "\n",
    "# Scalining the data via sklearn \n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(x)\n",
    "x = scaler.transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 40.250563089633964\n",
      "SSR: 556.8252629021873\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.897\n",
      "Model:                            OLS   Adj. R-squared:                  0.896\n",
      "Method:                 Least Squares   F-statistic:                     570.3\n",
      "Date:                Mon, 18 Jan 2021   Prob (F-statistic):           1.58e-96\n",
      "Time:                        21:15:28   Log-Likelihood:                -386.18\n",
      "No. Observations:                 200   AIC:                             780.4\n",
      "Df Residuals:                     196   BIC:                             793.6\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         14.0225      0.119    117.655      0.000      13.787      14.258\n",
      "x1             3.9193      0.119     32.809      0.000       3.684       4.155\n",
      "x2             2.7921      0.128     21.893      0.000       2.541       3.044\n",
      "x3            -0.0225      0.128     -0.177      0.860      -0.274       0.229\n",
      "==============================================================================\n",
      "Omnibus:                       60.414   Durbin-Watson:                   2.084\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.241\n",
      "Skew:                          -1.327   Prob(JB):                     1.44e-33\n",
      "Kurtosis:                       6.332   Cond. No.                         1.46\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Conducting Multivariant Regression with statsmodels\n",
    "import statsmodels.api as sm \n",
    "X = sm.add_constant(x) # adding a constant variable \n",
    "\n",
    "# Fitting the model \n",
    "model = sm.OLS(y, X).fit()  \n",
    "print_model = model.summary()\n",
    "\n",
    "# Printing the Mean-Squared Error (RMSE)\n",
    "print('RMSE: {}'.format(np.sqrt(model.mse_model)))\n",
    "print('SSR: {}'.format(model.ssr))\n",
    "\n",
    "# Printing the model Summary \n",
    "print(print_model)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpretation of the Multivariant Linear Regression Model \n",
    "\n",
    "The partial slope for TV (or x1) is 3.92, which means if all other predictors are held constant, if the TV ads sales increased, average sales would increase by 3.92. The partial slope for radio (or x2) is 2.79, so if all predictors are held constant - if radio ads increased, average sales would increase by 2.79. This is smaller than TV. Finally, for newspaper (or x3) the partial slope is -0.022. This suggests that for each newspaper ad purchased, the sales would decrease by -0.022. The constant for the equation is 14.022. \n",
    "\n",
    "The adjusted r-squared is 0.896, which suggests the model can account for 89.6% of the variations seen in the sample data provided to the model. \n",
    "\n",
    "Lastly, the mean-squared error, or average measure of errors of the model, is 40.25. This is quite large and can suggest that our model has large errors.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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