Discount Analysis with Elasticity Modelling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Price elasticity and discounts\n",
    "> - Discounts have been trending higher QoQ for the past 3 years.  Marketing has been offering aggressive pricing to certain customers.  From the data, we want to see if we can detect any anomalies: e.g. we give high discounts to Customer X.  Ultimately, we're indentifying where we can lower discounts.\n",
    "- How sensitive is change in orders to a change in discount?  Start by computing the price elasticity for each customer based off changes in purchases and changes in price over time.  Measure total revenue.\n",
    "- grigsby ch 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elasticity:\n",
    "- measures how sensitive a %change in qty is to a %change in price\n",
    "- \\>1 means elastic: x% increase in price decreases units by greater than x%\n",
    "- <1 means inelastic: x% increase in price decreases units by less than x%"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How much to decrease discounting and how to target it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cust_id</th>\n",
       "      <th>X_units</th>\n",
       "      <th>Y_units</th>\n",
       "      <th>Z_units</th>\n",
       "      <th>X_price</th>\n",
       "      <th>Y-price</th>\n",
       "      <th>Z_price</th>\n",
       "      <th>dm</th>\n",
       "      <th>em</th>\n",
       "      <th>sms</th>\n",
       "      <th>income</th>\n",
       "      <th>size_hh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>1249</td>\n",
       "      <td>179.110779</td>\n",
       "      <td>263.915369</td>\n",
       "      <td>248.757024</td>\n",
       "      <td>512.123305</td>\n",
       "      <td>94.5</td>\n",
       "      <td>9.134586</td>\n",
       "      <td>143.062571</td>\n",
       "      <td>294</td>\n",
       "      <td>17.778363</td>\n",
       "      <td>99366.333908</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>151</th>\n",
       "      <td>1252</td>\n",
       "      <td>264.884108</td>\n",
       "      <td>418.513822</td>\n",
       "      <td>329.834006</td>\n",
       "      <td>318.672356</td>\n",
       "      <td>99.5</td>\n",
       "      <td>4.750000</td>\n",
       "      <td>90.666488</td>\n",
       "      <td>333</td>\n",
       "      <td>52.126345</td>\n",
       "      <td>102215.120369</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     cust_id     X_units     Y_units     Z_units     X_price  Y-price  \\\n",
       "150     1249  179.110779  263.915369  248.757024  512.123305     94.5   \n",
       "151     1252  264.884108  418.513822  329.834006  318.672356     99.5   \n",
       "\n",
       "      Z_price          dm   em        sms         income  size_hh  \n",
       "150  9.134586  143.062571  294  17.778363   99366.333908        4  \n",
       "151  4.750000   90.666488  333  52.126345  102215.120369        5  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "df = pd.read_excel('ch-16-dataset-quant-complexity-9780749477158.xlsx')\n",
    "df.tail(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's consider units and price of product X\n",
    "# sns.pairplot(df, kind='reg', height=8, x_vars=['X_units'], y_vars=['X_price']);\n",
    "plt.figure(figsize=(12, 5))\n",
    "sns.regplot(x=df[\"X_units\"], y=df[\"X_price\"], data=df);\n",
    "# chart total revenue and units\n",
    "plt.figure(figsize=(12, 5))\n",
    "df['X_revenue'] = df.apply(lambda x: x.X_units * x.X_price, axis=1)\n",
    "sns.regplot(x=df[\"X_units\"], y=df[\"X_revenue\"], data=df);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cust_id</th>\n",
       "      <th>X_units</th>\n",
       "      <th>Y_units</th>\n",
       "      <th>Z_units</th>\n",
       "      <th>X_price</th>\n",
       "      <th>Y-price</th>\n",
       "      <th>Z_price</th>\n",
       "      <th>dm</th>\n",
       "      <th>em</th>\n",
       "      <th>sms</th>\n",
       "      <th>income</th>\n",
       "      <th>size_hh</th>\n",
       "      <th>X_revenue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>151</th>\n",
       "      <td>1252</td>\n",
       "      <td>264.884108</td>\n",
       "      <td>418.513822</td>\n",
       "      <td>329.834006</td>\n",
       "      <td>318.672356</td>\n",
       "      <td>99.5</td>\n",
       "      <td>4.75</td>\n",
       "      <td>90.666488</td>\n",
       "      <td>333</td>\n",
       "      <td>52.126345</td>\n",
       "      <td>102215.120369</td>\n",
       "      <td>5</td>\n",
       "      <td>84411.243027</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     cust_id     X_units     Y_units     Z_units     X_price  Y-price  \\\n",
       "151     1252  264.884108  418.513822  329.834006  318.672356     99.5   \n",
       "\n",
       "     Z_price         dm   em        sms         income  size_hh     X_revenue  \n",
       "151     4.75  90.666488  333  52.126345  102215.120369        5  84411.243027  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['cust_id',\n",
       " 'X_units',\n",
       " 'Y_units',\n",
       " 'Z_units',\n",
       " 'X_price',\n",
       " 'Y-price',\n",
       " 'Z_price',\n",
       " 'dm',\n",
       " 'em',\n",
       " 'sms',\n",
       " 'income',\n",
       " 'size_hh',\n",
       " 'X_revenue']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept    342.575747\n",
      "X_price       -0.267804\n",
      "dm            -0.285631\n",
      "em            -0.140346\n",
      "sms            0.503214\n",
      "income         0.000404\n",
      "size_hh        1.533921\n",
      "dtype: float64\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                X_units   R-squared:                       0.973\n",
      "Model:                            OLS   Adj. R-squared:                  0.972\n",
      "Method:                 Least Squares   F-statistic:                     878.3\n",
      "Date:                Mon, 09 Sep 2019   Prob (F-statistic):          2.68e-111\n",
      "Time:                        13:28:09   Log-Likelihood:                -593.52\n",
      "No. Observations:                 152   AIC:                             1201.\n",
      "Df Residuals:                     145   BIC:                             1222.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept    342.5757     20.967     16.338      0.000     301.135     384.017\n",
      "X_price       -0.2678      0.017    -15.487      0.000      -0.302      -0.234\n",
      "dm            -0.2856      0.063     -4.568      0.000      -0.409      -0.162\n",
      "em            -0.1403      0.037     -3.835      0.000      -0.213      -0.068\n",
      "sms            0.5032      0.109      4.611      0.000       0.288       0.719\n",
      "income         0.0004   8.95e-05      4.510      0.000       0.000       0.001\n",
      "size_hh        1.5339      0.692      2.216      0.028       0.166       2.902\n",
      "==============================================================================\n",
      "Omnibus:                        0.164   Durbin-Watson:                   1.882\n",
      "Prob(Omnibus):                  0.921   Jarque-Bera (JB):                0.244\n",
      "Skew:                          -0.076   Prob(JB):                        0.885\n",
      "Kurtosis:                       2.875   Cond. No.                     2.17e+06\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 2.17e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.formula.api as sm\n",
    "\n",
    "# Fit regression model\n",
    "\n",
    "abt = df[['X_price', 'dm', 'em', 'sms', 'income', 'size_hh', 'X_units']]\n",
    "\n",
    "lm_model = sm.ols(formula='X_units ~ X_price + dm + em + sms + income + size_hh', data=abt).fit()\n",
    "\n",
    "print(lm_model.params)\n",
    "print(lm_model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>X_units</td>     <th>  R-squared:         </th> <td>   0.973</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.972</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   878.3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 09 Sep 2019</td> <th>  Prob (F-statistic):</th> <td>2.68e-111</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:28:09</td>     <th>  Log-Likelihood:    </th> <td> -593.52</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   152</td>      <th>  AIC:               </th> <td>   1201.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   145</td>      <th>  BIC:               </th> <td>   1222.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</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>  342.5757</td> <td>   20.967</td> <td>   16.338</td> <td> 0.000</td> <td>  301.135</td> <td>  384.017</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X_price</th> <td>   -0.2678</td> <td>    0.017</td> <td>  -15.487</td> <td> 0.000</td> <td>   -0.302</td> <td>   -0.234</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dm</th>      <td>   -0.2856</td> <td>    0.063</td> <td>   -4.568</td> <td> 0.000</td> <td>   -0.409</td> <td>   -0.162</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>em</th>      <td>   -0.1403</td> <td>    0.037</td> <td>   -3.835</td> <td> 0.000</td> <td>   -0.213</td> <td>   -0.068</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sms</th>     <td>    0.5032</td> <td>    0.109</td> <td>    4.611</td> <td> 0.000</td> <td>    0.288</td> <td>    0.719</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>income</th>  <td>    0.0004</td> <td> 8.95e-05</td> <td>    4.510</td> <td> 0.000</td> <td>    0.000</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>size_hh</th> <td>    1.5339</td> <td>    0.692</td> <td>    2.216</td> <td> 0.028</td> <td>    0.166</td> <td>    2.902</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.164</td> <th>  Durbin-Watson:     </th> <td>   1.882</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.921</td> <th>  Jarque-Bera (JB):  </th> <td>   0.244</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.076</td> <th>  Prob(JB):          </th> <td>   0.885</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.875</td> <th>  Cond. No.          </th> <td>2.17e+06</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.17e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                X_units   R-squared:                       0.973\n",
       "Model:                            OLS   Adj. R-squared:                  0.972\n",
       "Method:                 Least Squares   F-statistic:                     878.3\n",
       "Date:                Mon, 09 Sep 2019   Prob (F-statistic):          2.68e-111\n",
       "Time:                        13:28:09   Log-Likelihood:                -593.52\n",
       "No. Observations:                 152   AIC:                             1201.\n",
       "Df Residuals:                     145   BIC:                             1222.\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        342.5757     20.967     16.338      0.000     301.135     384.017\n",
       "X_price       -0.2678      0.017    -15.487      0.000      -0.302      -0.234\n",
       "dm            -0.2856      0.063     -4.568      0.000      -0.409      -0.162\n",
       "em            -0.1403      0.037     -3.835      0.000      -0.213      -0.068\n",
       "sms            0.5032      0.109      4.611      0.000       0.288       0.719\n",
       "income         0.0004   8.95e-05      4.510      0.000       0.000       0.001\n",
       "size_hh        1.5339      0.692      2.216      0.028       0.166       2.902\n",
       "==============================================================================\n",
       "Omnibus:                        0.164   Durbin-Watson:                   1.882\n",
       "Prob(Omnibus):                  0.921   Jarque-Bera (JB):                0.244\n",
       "Skew:                          -0.076   Prob(JB):                        0.885\n",
       "Kurtosis:                       2.875   Cond. No.                     2.17e+06\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.17e+06. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "X = df[['X_price', 'dm', 'em', 'sms', 'income', 'size_hh']]\n",
    "y = df['X_units']\n",
    "# # leave behind one column as the \"reference value\" for that categorical variable\n",
    "# X = pd.get_dummies(X, columns=['MONTH', 'DAY_OF_WEEK', 'AIRLINE', 'ORIGIN_AIRPORT', 'DESTINATION_AIRPORT'], drop_first=True)\n",
    "\n",
    "# build linear regressors to find the intercept and coefficient\n",
    "X = sm.add_constant(X)\n",
    "results = sm.OLS(y, X).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Factor analysis on all independent variables except price\n",
    "- removes collinearity, calculate price elasticity, price should have negative coefficient\n",
    "- elasticity = coef on price * (avg price/avg quantity)\n",
    "> Factors that affect qty: dm, em, sms, q2, q3, q4, advert, events, avg price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>X_price</th>\n",
       "      <th>dm</th>\n",
       "      <th>em</th>\n",
       "      <th>sms</th>\n",
       "      <th>income</th>\n",
       "      <th>size_hh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>702.744247</td>\n",
       "      <td>101.999799</td>\n",
       "      <td>219</td>\n",
       "      <td>20.114253</td>\n",
       "      <td>58732.004995</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>439.560000</td>\n",
       "      <td>132.772370</td>\n",
       "      <td>237</td>\n",
       "      <td>10.939556</td>\n",
       "      <td>126133.271105</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>753.964568</td>\n",
       "      <td>230.096669</td>\n",
       "      <td>198</td>\n",
       "      <td>14.294824</td>\n",
       "      <td>134320.600634</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   const     X_price          dm   em        sms         income  size_hh\n",
       "0    1.0  702.744247  101.999799  219  20.114253   58732.004995        3\n",
       "1    1.0  439.560000  132.772370  237  10.939556  126133.271105        7\n",
       "2    1.0  753.964568  230.096669  198  14.294824  134320.600634        2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dm</th>\n",
       "      <th>em</th>\n",
       "      <th>sms</th>\n",
       "      <th>income</th>\n",
       "      <th>size_hh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.211726</td>\n",
       "      <td>-0.438809</td>\n",
       "      <td>0.060303</td>\n",
       "      <td>-1.293731</td>\n",
       "      <td>-0.633670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.356458</td>\n",
       "      <td>-0.164516</td>\n",
       "      <td>-0.509369</td>\n",
       "      <td>0.893729</td>\n",
       "      <td>1.322023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.348495</td>\n",
       "      <td>-0.758818</td>\n",
       "      <td>-0.301035</td>\n",
       "      <td>1.159443</td>\n",
       "      <td>-1.122594</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         dm        em       sms    income   size_hh\n",
       "0 -1.211726 -0.438809  0.060303 -1.293731 -0.633670\n",
       "1 -0.356458 -0.164516 -0.509369  0.893729  1.322023\n",
       "2  2.348495 -0.758818 -0.301035  1.159443 -1.122594"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# svd\n",
    "X = df[['dm', 'em', 'sms', 'income', 'size_hh']]\n",
    "X_scaled = (X-X.mean())/X.std()\n",
    "X_scaled.head(n=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(152, 152) (5,) (5, 5)\n"
     ]
    }
   ],
   "source": [
    "u, s, v = np.linalg.svd(X_scaled, full_matrices=True)\n",
    "print(u.shape, s.shape, v.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "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": [
    "var_explained = np.round(s**2/np.sum(s**2), decimals=3)\n",
    "var_explained\n",
    " \n",
    "sns.barplot(x=list(range(1,len(var_explained)+1)),\n",
    "            y=var_explained, color=\"limegreen\")\n",
    "plt.xlabel('SVs', fontsize=16)\n",
    "plt.ylabel('Percent Variance Explained', fontsize=16)\n",
    "plt.savefig('svd_scree_plot.png',dpi=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SV1</th>\n",
       "      <th>SV2</th>\n",
       "      <th>SV3</th>\n",
       "      <th>SV4</th>\n",
       "      <th>SV5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.017577</td>\n",
       "      <td>0.131900</td>\n",
       "      <td>-0.008472</td>\n",
       "      <td>0.069669</td>\n",
       "      <td>-0.074073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.027475</td>\n",
       "      <td>-0.064828</td>\n",
       "      <td>-0.112458</td>\n",
       "      <td>0.018815</td>\n",
       "      <td>-0.100733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.083129</td>\n",
       "      <td>-0.143679</td>\n",
       "      <td>0.128151</td>\n",
       "      <td>-0.019931</td>\n",
       "      <td>0.025477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.029675</td>\n",
       "      <td>-0.005917</td>\n",
       "      <td>-0.014116</td>\n",
       "      <td>-0.094325</td>\n",
       "      <td>0.056003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.034851</td>\n",
       "      <td>-0.073039</td>\n",
       "      <td>-0.149259</td>\n",
       "      <td>0.041863</td>\n",
       "      <td>-0.070051</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        SV1       SV2       SV3       SV4       SV5\n",
       "0  0.017577  0.131900 -0.008472  0.069669 -0.074073\n",
       "1 -0.027475 -0.064828 -0.112458  0.018815 -0.100733\n",
       "2  0.083129 -0.143679  0.128151 -0.019931  0.025477\n",
       "3 -0.029675 -0.005917 -0.014116 -0.094325  0.056003\n",
       "4 -0.034851 -0.073039 -0.149259  0.041863 -0.070051"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let us create a data frame containing the first two singular vectors (PCs) and the meta data for the data.\n",
    "n = len(X.columns)\n",
    "labels= ['SV'+str(i) for i in range(1,n+1)]\n",
    "svd_df = pd.DataFrame(u[:,0:n], columns=labels)\n",
    "# svd_df=svd_df.reset_index()\n",
    "# svd_df.rename(columns={'index':'Continent'}, inplace=True)\n",
    "svd_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>X_units</td>     <th>  R-squared:         </th> <td>   0.973</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.972</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   878.3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 09 Sep 2019</td> <th>  Prob (F-statistic):</th> <td>2.68e-111</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:28:10</td>     <th>  Log-Likelihood:    </th> <td> -593.52</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   152</td>      <th>  AIC:               </th> <td>   1201.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   145</td>      <th>  BIC:               </th> <td>   1222.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</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>  322.2215</td> <td>   10.645</td> <td>   30.271</td> <td> 0.000</td> <td>  301.183</td> <td>  343.260</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV1</th>     <td> -155.8640</td> <td>   45.048</td> <td>   -3.460</td> <td> 0.001</td> <td> -244.900</td> <td>  -66.828</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV2</th>     <td>  -58.1531</td> <td>   16.095</td> <td>   -3.613</td> <td> 0.000</td> <td>  -89.964</td> <td>  -26.342</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV3</th>     <td>   -9.3398</td> <td>   12.470</td> <td>   -0.749</td> <td> 0.455</td> <td>  -33.987</td> <td>   15.308</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV4</th>     <td>   70.5491</td> <td>   13.064</td> <td>    5.400</td> <td> 0.000</td> <td>   44.729</td> <td>   96.369</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV5</th>     <td>  -58.3802</td> <td>   14.191</td> <td>   -4.114</td> <td> 0.000</td> <td>  -86.428</td> <td>  -30.332</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X_price</th> <td>   -0.2678</td> <td>    0.017</td> <td>  -15.487</td> <td> 0.000</td> <td>   -0.302</td> <td>   -0.234</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.164</td> <th>  Durbin-Watson:     </th> <td>   1.882</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.921</td> <th>  Jarque-Bera (JB):  </th> <td>   0.244</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.076</td> <th>  Prob(JB):          </th> <td>   0.885</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.875</td> <th>  Cond. No.          </th> <td>3.14e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.14e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                X_units   R-squared:                       0.973\n",
       "Model:                            OLS   Adj. R-squared:                  0.972\n",
       "Method:                 Least Squares   F-statistic:                     878.3\n",
       "Date:                Mon, 09 Sep 2019   Prob (F-statistic):          2.68e-111\n",
       "Time:                        13:28:10   Log-Likelihood:                -593.52\n",
       "No. Observations:                 152   AIC:                             1201.\n",
       "Df Residuals:                     145   BIC:                             1222.\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        322.2215     10.645     30.271      0.000     301.183     343.260\n",
       "SV1         -155.8640     45.048     -3.460      0.001    -244.900     -66.828\n",
       "SV2          -58.1531     16.095     -3.613      0.000     -89.964     -26.342\n",
       "SV3           -9.3398     12.470     -0.749      0.455     -33.987      15.308\n",
       "SV4           70.5491     13.064      5.400      0.000      44.729      96.369\n",
       "SV5          -58.3802     14.191     -4.114      0.000     -86.428     -30.332\n",
       "X_price       -0.2678      0.017    -15.487      0.000      -0.302      -0.234\n",
       "==============================================================================\n",
       "Omnibus:                        0.164   Durbin-Watson:                   1.882\n",
       "Prob(Omnibus):                  0.921   Jarque-Bera (JB):                0.244\n",
       "Skew:                          -0.076   Prob(JB):                        0.885\n",
       "Kurtosis:                       2.875   Cond. No.                     3.14e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.14e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svd_df['X_price'] = df['X_price']\n",
    "X = svd_df\n",
    "y = df['X_units']\n",
    "# # leave behind one column as the \"reference value\" for that categorical variable\n",
    "# X = pd.get_dummies(X, columns=['MONTH', 'DAY_OF_WEEK', 'AIRLINE', 'ORIGIN_AIRPORT', 'DESTINATION_AIRPORT'], drop_first=True)\n",
    "\n",
    "# build linear regressors to find the intercept and coefficient\n",
    "X = sm.add_constant(X)\n",
    "results = sm.OLS(y, X).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'_results': <statsmodels.regression.linear_model.OLSResults at 0x1c1938ef60>,\n",
       " '__doc__': '\\n    Results class for for an OLS model.\\n\\n    Most of the methods and attributes are inherited from RegressionResults.\\n    The special methods that are only available for OLS are:\\n\\n    - get_influence\\n    - outlier_test\\n    - el_test\\n    - conf_int_el\\n\\n    See Also\\n    --------\\n    RegressionResults\\n\\n    '}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vars(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VIF Factor</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>113.9</td>\n",
       "      <td>const</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14.6</td>\n",
       "      <td>X_price</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.4</td>\n",
       "      <td>SV1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.7</td>\n",
       "      <td>SV2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.3</td>\n",
       "      <td>SV5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.1</td>\n",
       "      <td>SV4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>SV3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   VIF Factor features\n",
       "0       113.9    const\n",
       "6        14.6  X_price\n",
       "1        13.4      SV1\n",
       "2         1.7      SV2\n",
       "5         1.3      SV5\n",
       "4         1.1      SV4\n",
       "3         1.0      SV3"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "# For each X, calculate VIF and save in dataframe\n",
    "vif = pd.DataFrame()\n",
    "vif[\"VIF Factor\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
    "vif[\"features\"] = X.columns\n",
    "vif.round(1).sort_values(by='VIF Factor', ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## try getting the price coefficient, but this time with price and units both normalized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['SV1', 'SV2', 'SV3', 'SV4', 'SV5', 'X_price']"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svd_df.columns.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>X_units</td>     <th>  R-squared:         </th> <td>   0.973</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.972</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   878.3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 09 Sep 2019</td> <th>  Prob (F-statistic):</th> <td>2.68e-111</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:28:10</td>     <th>  Log-Likelihood:    </th> <td> -593.52</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   152</td>      <th>  AIC:               </th> <td>   1201.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   145</td>      <th>  BIC:               </th> <td>   1222.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</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>  322.2215</td> <td>   10.645</td> <td>   30.271</td> <td> 0.000</td> <td>  301.183</td> <td>  343.260</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV1</th>     <td> -155.8640</td> <td>   45.048</td> <td>   -3.460</td> <td> 0.001</td> <td> -244.900</td> <td>  -66.828</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV2</th>     <td>  -58.1531</td> <td>   16.095</td> <td>   -3.613</td> <td> 0.000</td> <td>  -89.964</td> <td>  -26.342</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV3</th>     <td>   -9.3398</td> <td>   12.470</td> <td>   -0.749</td> <td> 0.455</td> <td>  -33.987</td> <td>   15.308</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV4</th>     <td>   70.5491</td> <td>   13.064</td> <td>    5.400</td> <td> 0.000</td> <td>   44.729</td> <td>   96.369</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SV5</th>     <td>  -58.3802</td> <td>   14.191</td> <td>   -4.114</td> <td> 0.000</td> <td>  -86.428</td> <td>  -30.332</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X_price</th> <td>   -0.2678</td> <td>    0.017</td> <td>  -15.487</td> <td> 0.000</td> <td>   -0.302</td> <td>   -0.234</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.164</td> <th>  Durbin-Watson:     </th> <td>   1.882</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.921</td> <th>  Jarque-Bera (JB):  </th> <td>   0.244</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.076</td> <th>  Prob(JB):          </th> <td>   0.885</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.875</td> <th>  Cond. No.          </th> <td>3.14e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.14e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                X_units   R-squared:                       0.973\n",
       "Model:                            OLS   Adj. R-squared:                  0.972\n",
       "Method:                 Least Squares   F-statistic:                     878.3\n",
       "Date:                Mon, 09 Sep 2019   Prob (F-statistic):          2.68e-111\n",
       "Time:                        13:28:10   Log-Likelihood:                -593.52\n",
       "No. Observations:                 152   AIC:                             1201.\n",
       "Df Residuals:                     145   BIC:                             1222.\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        322.2215     10.645     30.271      0.000     301.183     343.260\n",
       "SV1         -155.8640     45.048     -3.460      0.001    -244.900     -66.828\n",
       "SV2          -58.1531     16.095     -3.613      0.000     -89.964     -26.342\n",
       "SV3           -9.3398     12.470     -0.749      0.455     -33.987      15.308\n",
       "SV4           70.5491     13.064      5.400      0.000      44.729      96.369\n",
       "SV5          -58.3802     14.191     -4.114      0.000     -86.428     -30.332\n",
       "X_price       -0.2678      0.017    -15.487      0.000      -0.302      -0.234\n",
       "==============================================================================\n",
       "Omnibus:                        0.164   Durbin-Watson:                   1.882\n",
       "Prob(Omnibus):                  0.921   Jarque-Bera (JB):                0.244\n",
       "Skew:                          -0.076   Prob(JB):                        0.885\n",
       "Kurtosis:                       2.875   Cond. No.                     3.14e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.14e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (X-X.mean())/X.std()\n",
    "# svd_df['X_price_norm'] = (df['X_price'] - df['X_price'].mean()) / df['X_price'].std()\n",
    "# svd_df['X_units_norm'] = (df['X_units'] - df['X_units'].mean()) / df['X_units'].std()\n",
    "X = svd_df[['SV1', 'SV2', 'SV3', 'SV4', 'SV5', 'X_price']]\n",
    "y = df['X_units']\n",
    "# # leave behind one column as the \"reference value\" for that categorical variable\n",
    "# X = pd.get_dummies(X, columns=['MONTH', 'DAY_OF_WEEK', 'AIRLINE', 'ORIGIN_AIRPORT', 'DESTINATION_AIRPORT'], drop_first=True)\n",
    "\n",
    "# build linear regressors to find the intercept and coefficient\n",
    "X = sm.add_constant(X)\n",
    "results = sm.OLS(y, X).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "price_coefficient = results.params['X_price']\n",
    "average_price = X['X_price'].mean()\n",
    "average_quantity = df['X_units'].mean()\n",
    "elasticity = abs(price_coefficient * (average_price / average_quantity))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.31669692017833"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# when elasticity > 1, we're on the elastic portion of the demand curve, so revenue follows price.\n",
    "\n",
    "def total_revenue(prices, units, elasticity, percent_adjustment):\n",
    "    \"\"\"\n",
    "    :param: price_adjustment is the percent increase in price, e.g. 10.  If decreasing price 10%, put -10.\n",
    "    \"\"\"\n",
    "    if elasticity > 1:  # elastic, revenue follows price, so discount\n",
    "        estimated_prices = prices * (1 + (percent_adjustment/100))\n",
    "        units_decrease_percentage = percent_adjustment * elasticity\n",
    "        estimated_units = units * (1 - (units_decrease_percentage/100))\n",
    "        estimated_revenue = estimated_prices * estimated_units\n",
    "    return sum(estimated_revenue)/10**6\n",
    "        \n",
    "\n",
    "total_revenue(prices=X['X_price'], units=df['X_units'], elasticity=elasticity, percent_adjustment=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " (5.722208593969703, 70.0),\n",
       " (5.630031979034247, 70.5),\n",
       " (5.537216028965574, 71.0),\n",
       " (5.443760743763699, 71.5),\n",
       " (5.349666123428618, 72.0),\n",
       " (5.2549321679603285, 72.5),\n",
       " (5.159558877358827, 73.0),\n",
       " (5.063546251624123, 73.5),\n",
       " (4.96689429075621, 74.0),\n",
       " (4.86960299475509, 74.5),\n",
       " (4.771672363620769, 75.0),\n",
       " (4.673102397353231, 75.5),\n",
       " (4.573893095952491, 76.0),\n",
       " (4.474044459418542, 76.5),\n",
       " (4.373556487751388, 77.0),\n",
       " (4.272429180951021, 77.5),\n",
       " (4.170662539017454, 78.0),\n",
       " (4.0682565619506725, 78.5),\n",
       " (3.96521124975069, 79.0),\n",
       " (3.861526602417496, 79.5),\n",
       " (3.7572026199510993, 80.0),\n",
       " (3.6522393023514885, 80.5),\n",
       " (3.5466366496186765, 81.0),\n",
       " (3.4403946617526513, 81.5),\n",
       " (3.3335133387534266, 82.0),\n",
       " (3.2259926806209873, 82.5),\n",
       " (3.1178326873553437, 83.0),\n",
       " (3.009033358956493, 83.5),\n",
       " (2.899594695424439, 84.0),\n",
       " (2.7895166967591702, 84.5),\n",
       " (2.6787993629607003, 85.0),\n",
       " (2.567442694029023, 85.5),\n",
       " (2.455446689964133, 86.0),\n",
       " (2.342811350766041, 86.5),\n",
       " (2.229536676434736, 87.0),\n",
       " (2.1156226669702303, 87.5),\n",
       " (2.0010693223725116, 88.0),\n",
       " (1.8858766426415905, 88.5),\n",
       " (1.7700446277774569, 89.0),\n",
       " (1.6535732777801206, 89.5),\n",
       " (1.5364625926495725, 90.0),\n",
       " (1.4187125723858225, 90.5),\n",
       " (1.30032321698886, 91.0),\n",
       " (1.1812945264586956, 91.5),\n",
       " (1.0616265007953178, 92.0),\n",
       " (0.9413191399987386, 92.5),\n",
       " (0.8203724440689473, 93.0),\n",
       " (0.6987864130059527, 93.5),\n",
       " (0.5765610468097466, 94.0),\n",
       " (0.45369634548033816, 94.5),\n",
       " (0.33019230901771707, 95.0),\n",
       " (0.20604893742189415, 95.5),\n",
       " (0.08126623069285846, 96.0),\n",
       " (-0.0441558111693791, 96.5),\n",
       " (-0.17021718816482662, 97.0),\n",
       " (-0.2969179002934814, 97.5),\n",
       " (-0.4242579475553435, 98.0),\n",
       " (-0.5522373299504129, 98.5),\n",
       " (-0.6808560474786897, 99.0),\n",
       " (-0.8101141001401738, 99.5),\n",
       " (-0.9400114879348647, 100.0),\n",
       " (-1.0705482108627637, 100.5)]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[(total_revenue(prices=X['X_price'], units=df['X_units'], elasticity=elasticity, percent_adjustment=i), i) for i in np.arange(-101, 101, .5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12316696.92017833"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(X['X_price']*df['X_units'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inventory Forecasts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Behavioural Segmentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elasticity for each segment and for each major product category\n",
    "- different model for each product category"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- simultaneous equations can be used for optimal pricing and understanding cannibalization between products, brands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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