Salinee_Kingbaisomboon-L06-AdRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lesson 6 Assignment - Advertising Sales Regression\n",
    "## Author - Salinee Kingbaisomboon\n",
    "### UW NetID: 1950831"
   ]
  },
  {
   "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": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from IPython.display import display\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "import statsmodels.formula.api as sm\n",
    "import seaborn as sns\n",
    "\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\") # To suppress warning\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Declare Functions used in this assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a scale function for a column in a pandas df\n",
    "def scale(col):\n",
    "    mean_col = np.mean(col)\n",
    "    sd_col = np.std(col)\n",
    "    std = (col - mean_col) / sd_col\n",
    "    return std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to plot the Linear Regression Model's graph\n",
    "def plot_linear_regression_model(data, x_column, y_column):\n",
    "    # First initialize the model.\n",
    "    model = linear_model.LinearRegression()\n",
    "    \n",
    "    # Fit the model to the data\n",
    "    n_points = len(data)\n",
    "    x_input = data[x_column].values.reshape(n_points, 1)\n",
    "    y_output = data[y_column].values.reshape(n_points, 1)\n",
    "    \n",
    "    model.fit(x_input, y_output)\n",
    "    \n",
    "    # Get predictions\n",
    "    y_pred = model.predict(x_input)\n",
    "\n",
    "    # Plot output\n",
    "    plt.scatter(x_input, y_output)\n",
    "    plt.plot(x_input, y_pred, linewidth=2)\n",
    "    plt.grid(True)\n",
    "    plt.xlabel(x_column)\n",
    "    plt.ylabel(y_column)\n",
    "    plt.title(x_column + ' vs' + y_column)\n",
    "    \n",
    "    # Print model parameters\n",
    "    # Get slope (m) and y-intercept (b)\n",
    "    print('Intercept: {0:.5f}'.format(model.intercept_[0]))\n",
    "    print('Slope : {0:.5f}'.format(model.coef_[0][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to compute the Linear Regression Statistic\n",
    "def compute_linear_regression_statistic(data, formula, y_column):\n",
    "    # Fit the model to the data\n",
    "    n_points = len(data)\n",
    "    y_output = data[y_column].values.reshape(n_points, 1)\n",
    "    \n",
    "    ols_model = sm.ols(formula = formula, data=data)\n",
    "    \n",
    "    results = ols_model.fit()\n",
    "    y_pred = results.predict()\n",
    "    \n",
    "    data['predicted'] = y_pred\n",
    "    \n",
    "    string = '               View Y predict based on all input features:'\n",
    "    print(f'\\033[92m\\033[1m{string}\\033[0m')\n",
    "    display(data)\n",
    "    \n",
    "    print('\\nSSE, SST, SSR, and RMSE:')\n",
    "    mean_y = np.mean(y_output)\n",
    "    sst = np.sum((y_output - mean_y)**2)\n",
    "    sse = sst - results.ssr\n",
    "    print('SSE: {}'.format(sse))\n",
    "    print('SST: {}'.format(sst))\n",
    "    print('SSR: {}'.format(results.ssr))\n",
    "    print('RMSE: {}'.format(np.sqrt(results.mse_model)))\n",
    "    \n",
    "    # Get most of the linear regression statistics we are interested in:\n",
    "    print(results.summary())\n",
    "    \n",
    "    # Plot a histogram of the residuals\n",
    "    sns.distplot(results.resid, hist=True)\n",
    "    plt.xlabel('Residual')\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.title('Residual Histogram')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      TV  radio  newspaper  sales  TV_scale  radio_scale  newspaper_scale\n",
      "1  230.1   37.8       69.2   22.1  0.969852     0.981522         1.778945\n",
      "2   44.5   39.3       45.1   10.4 -1.197376     1.082808         0.669579\n",
      "3   17.2   45.9       69.3    9.3 -1.516155     1.528463         1.783549\n",
      "4  151.5   41.3       58.5   18.5  0.052050     1.217855         1.286405\n",
      "5  180.8   10.8       58.4   12.9  0.394182    -0.841614         1.281802\n",
      "(200, 7)\n"
     ]
    },
    {
     "data": {
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       "</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",
       "      <th>TV_scale</th>\n",
       "      <th>radio_scale</th>\n",
       "      <th>newspaper_scale</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",
       "      <td>2.000000e+02</td>\n",
       "      <td>2.000000e+02</td>\n",
       "      <td>2.000000e+02</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",
       "      <td>1.121325e-16</td>\n",
       "      <td>-1.638689e-15</td>\n",
       "      <td>2.031708e-16</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",
       "      <td>1.002509e+00</td>\n",
       "      <td>1.002509e+00</td>\n",
       "      <td>1.002509e+00</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",
       "      <td>-1.708823e+00</td>\n",
       "      <td>-1.570868e+00</td>\n",
       "      <td>-1.392646e+00</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",
       "      <td>-8.485295e-01</td>\n",
       "      <td>-8.973206e-01</td>\n",
       "      <td>-8.195504e-01</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",
       "      <td>3.161515e-02</td>\n",
       "      <td>-2.457858e-02</td>\n",
       "      <td>-2.211368e-01</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",
       "      <td>8.381955e-01</td>\n",
       "      <td>8.954299e-01</td>\n",
       "      <td>6.695788e-01</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",
       "      <td>1.744029e+00</td>\n",
       "      <td>1.778300e+00</td>\n",
       "      <td>3.841171e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TV       radio   newspaper       sales      TV_scale  \\\n",
       "count  200.000000  200.000000  200.000000  200.000000  2.000000e+02   \n",
       "mean   147.042500   23.264000   30.554000   14.022500  1.121325e-16   \n",
       "std     85.854236   14.846809   21.778621    5.217457  1.002509e+00   \n",
       "min      0.700000    0.000000    0.300000    1.600000 -1.708823e+00   \n",
       "25%     74.375000    9.975000   12.750000   10.375000 -8.485295e-01   \n",
       "50%    149.750000   22.900000   25.750000   12.900000  3.161515e-02   \n",
       "75%    218.825000   36.525000   45.100000   17.400000  8.381955e-01   \n",
       "max    296.400000   49.600000  114.000000   27.000000  1.744029e+00   \n",
       "\n",
       "        radio_scale  newspaper_scale  \n",
       "count  2.000000e+02     2.000000e+02  \n",
       "mean  -1.638689e-15     2.031708e-16  \n",
       "std    1.002509e+00     1.002509e+00  \n",
       "min   -1.570868e+00    -1.392646e+00  \n",
       "25%   -8.973206e-01    -8.195504e-01  \n",
       "50%   -2.457858e-02    -2.211368e-01  \n",
       "75%    8.954299e-01     6.695788e-01  \n",
       "max    1.778300e+00     3.841171e+00  "
      ]
     },
     "execution_count": 11,
     "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",
    "\n",
    "# Scale the features or independent variables (the most common practice)\n",
    "ad_data['TV_scale'] = scale(ad_data['TV'])\n",
    "ad_data['radio_scale'] = scale(ad_data['radio'])\n",
    "ad_data['newspaper_scale'] = scale(ad_data['newspaper'])\n",
    "\n",
    "print(ad_data.head())\n",
    "print(ad_data.shape)\n",
    "ad_data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Linear Regression between Sales (dependent) and TV (independent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 14.02250\n",
      "Slope : 4.07101\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": [
    "plot_linear_regression_model(ad_data, 'TV_scale', 'sales')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "### Examine result:\n",
    "**Y Intercept = 14.02250**:  When spends no money on TV ads  (zero), sales will be 14,022.50 dollars.\n",
    "    \n",
    "**Slope = 4.07101**:  When we spends money on TV ads by 1 dollar, then we expect that sales will go up by 4,071.01 dollars.\n",
    "\n",
    "**Based on the plot:** We found that the TV advertising has a strong positive effects on Sales. \n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Linear Regression between Sales (dependent) and Radio (independent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 14.02250\n",
      "Slope : 2.99889\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": [
    "plot_linear_regression_model(ad_data, 'radio_scale', 'sales')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "### Examine result:\n",
    "**Y Intercept = 14.02250**:  When spends no money on radio advertising (zero), sales will be 14,022.50 dollars.\n",
    "    \n",
    "**Slope = 2.99889**:  When we spends money on radio advertising by 1 dollar, then we expect that sales will go up by 2,998.89 dollars.\n",
    "\n",
    "**Based on the plot:** We found that the radio advertising has medium positive effects on Sales (compared with TV ads since the slope of TV ads is greater). \n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Linear Regression between Sales (dependent) and Newspaper (independent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 14.02250\n",
      "Slope : 1.18816\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": [
    "plot_linear_regression_model(ad_data, 'newspaper_scale', 'sales')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "### Examine result:\n",
    "**Y Intercept = 14.02250**:  When spends no money on newspaper advertising (zero), sales will be 14,022.50 dollars.\n",
    "    \n",
    "**Slope = 1.18816**:  When we spends money on radio advertising by 1 dollar, then we expect that sales will go up by 1,188.16 dollars.\n",
    "\n",
    "**Based on the plot:** We found that the radio advertising has less positive effects on Sales (compared with TV and radio advertising since the slope is lesser). \n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Linear Regression between Sales (dependent) and All Three Features - TV, Radio, Newspaper (independent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[92m\u001b[1m               View Y predict based on all input features:\u001b[0m\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",
       "      <th>TV_scale</th>\n",
       "      <th>radio_scale</th>\n",
       "      <th>newspaper_scale</th>\n",
       "      <th>predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "      <td>0.969852</td>\n",
       "      <td>0.981522</td>\n",
       "      <td>1.778945</td>\n",
       "      <td>20.523974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "      <td>-1.197376</td>\n",
       "      <td>1.082808</td>\n",
       "      <td>0.669579</td>\n",
       "      <td>12.337855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "      <td>-1.516155</td>\n",
       "      <td>1.528463</td>\n",
       "      <td>1.783549</td>\n",
       "      <td>12.307671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "      <td>0.052050</td>\n",
       "      <td>1.217855</td>\n",
       "      <td>1.286405</td>\n",
       "      <td>17.597830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "      <td>0.394182</td>\n",
       "      <td>-0.841614</td>\n",
       "      <td>1.281802</td>\n",
       "      <td>13.188672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>38.2</td>\n",
       "      <td>3.7</td>\n",
       "      <td>13.8</td>\n",
       "      <td>7.6</td>\n",
       "      <td>-1.270941</td>\n",
       "      <td>-1.321031</td>\n",
       "      <td>-0.771217</td>\n",
       "      <td>5.370342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>94.2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>8.1</td>\n",
       "      <td>9.7</td>\n",
       "      <td>-0.617035</td>\n",
       "      <td>-1.240003</td>\n",
       "      <td>-1.033598</td>\n",
       "      <td>8.165312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>177.0</td>\n",
       "      <td>9.3</td>\n",
       "      <td>6.4</td>\n",
       "      <td>12.8</td>\n",
       "      <td>0.349810</td>\n",
       "      <td>-0.942899</td>\n",
       "      <td>-1.111852</td>\n",
       "      <td>12.785921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>283.6</td>\n",
       "      <td>42.0</td>\n",
       "      <td>66.2</td>\n",
       "      <td>25.5</td>\n",
       "      <td>1.594565</td>\n",
       "      <td>1.265121</td>\n",
       "      <td>1.640850</td>\n",
       "      <td>23.767321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>232.1</td>\n",
       "      <td>8.6</td>\n",
       "      <td>8.7</td>\n",
       "      <td>13.4</td>\n",
       "      <td>0.993206</td>\n",
       "      <td>-0.990165</td>\n",
       "      <td>-1.005979</td>\n",
       "      <td>15.173196</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        TV  radio  newspaper  sales  TV_scale  radio_scale  newspaper_scale  \\\n",
       "1    230.1   37.8       69.2   22.1  0.969852     0.981522         1.778945   \n",
       "2     44.5   39.3       45.1   10.4 -1.197376     1.082808         0.669579   \n",
       "3     17.2   45.9       69.3    9.3 -1.516155     1.528463         1.783549   \n",
       "4    151.5   41.3       58.5   18.5  0.052050     1.217855         1.286405   \n",
       "5    180.8   10.8       58.4   12.9  0.394182    -0.841614         1.281802   \n",
       "..     ...    ...        ...    ...       ...          ...              ...   \n",
       "196   38.2    3.7       13.8    7.6 -1.270941    -1.321031        -0.771217   \n",
       "197   94.2    4.9        8.1    9.7 -0.617035    -1.240003        -1.033598   \n",
       "198  177.0    9.3        6.4   12.8  0.349810    -0.942899        -1.111852   \n",
       "199  283.6   42.0       66.2   25.5  1.594565     1.265121         1.640850   \n",
       "200  232.1    8.6        8.7   13.4  0.993206    -0.990165        -1.005979   \n",
       "\n",
       "     predicted  \n",
       "1    20.523974  \n",
       "2    12.337855  \n",
       "3    12.307671  \n",
       "4    17.597830  \n",
       "5    13.188672  \n",
       "..         ...  \n",
       "196   5.370342  \n",
       "197   8.165312  \n",
       "198  12.785921  \n",
       "199  23.767321  \n",
       "200  15.173196  \n",
       "\n",
       "[200 rows x 8 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "SSE, SST, SSR, and RMSE:\n",
      "SSE: 4860.323487097813\n",
      "SST: 5417.14875\n",
      "SSR: 556.8252629021872\n",
      "RMSE: 40.250563089633964\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, 06 Jan 2020   Prob (F-statistic):           1.58e-96\n",
      "Time:                        14:11:15   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",
      "Intercept          14.0225      0.119    117.655      0.000      13.787      14.258\n",
      "TV_scale            3.9193      0.119     32.809      0.000       3.684       4.155\n",
      "radio_scale         2.7921      0.128     21.893      0.000       2.541       3.044\n",
      "newspaper_scale    -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",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "compute_linear_regression_statistic(ad_data, 'sales ~ TV_scale + radio_scale + newspaper_scale', 'sales')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we put all three features (TV, Radio and Newspaper) together in a model, we found a slighly different statistics as following:\n",
    "\n",
    "***\n",
    "### Summary for TV:\n",
    "**Y Intercept = 14.02250**:  When spends no money on TV ads  (zero), sales will be 14,022.50 dollars.\n",
    "    \n",
    "**Slope = 3.9193**:  When we spends money on TV ads by 1 dollar, then we expect that sales will go up by 3,919.3 dollars.\n",
    "\n",
    "**Based on the plot:** We found that the TV advertising still has a strongest positive effects on Sales but in a lesser degree since the slope is decrease when the model has only TV as an only one feature. (From 4,071.01 to 3,919.3 dollars)\n",
    "### Summary for Radio:\n",
    "**Y Intercept = 14.02250**:  When spends no money on radio advertising (zero), sales will be 14,022.50 dollars.\n",
    "    \n",
    "**Slope = 2.7921**:  When we spends money on radio advertising by 1 dollar, then we expect that sales will go up by 2,792.1 dollars.\n",
    "\n",
    "**Based on the plot:** We found that the radio advertising has medium positive effects on Sales but in a lesser degree since the slope is decrease when the model has only radio as an only one feature. (From 2,998.89 to 2,792.1 dollars) \n",
    "\n",
    "### Summary for Newspaper:\n",
    "**Y Intercept = 14.02250**:  When spends no money on newspaper advertising (zero), sales will be 14,022.50 dollars.\n",
    "    \n",
    "**Slope = -0.0225**:  When we spends money on radio advertising by 1 dollar, then we expect that sales will decreate by 225 dollars.\n",
    "\n",
    "**Based on the plot:** We found that the radio advertising has negative effects on Sales (compared when the model has only newspaper as an only one feature). This may due to the fact that people this day consume less from newspapers (compared with TV and radio altogether). So, it's better for the client not to spend money on the newspaper advertising any more. \n",
    "***\n",
    "\n",
    "- **Adjusted R-suqared = 0.896**: 89.6% of the variation in the output variable is explained by the input variables. This tells us that by adding variables will improve our existing model.\n",
    "- **Mean-Qquared Error (RMSE) = 40.250563089633964**: 40.250563089633964x1,000 = 40,250.56 dollars is the square root of the average of squared differences between the prediction of sales and your actual observation. In terms of thousand dollars in sales, this error is quite significant. Therefore, this model didn't represent the data very well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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