interaction effect.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis of Sales Influenced by Season and Temperature\n",
    "\n",
    "This notebook aims to explore how different seasons and temperature levels affect sales through a synthetic dataset. We will generate data representing sales across different seasons and temperatures, hypothesizing that interactions between these factors can significantly impact sales outcomes.\n",
    "\n",
    "We will visually and statistically analyze the main effects of each factor and their interaction to understand their impacts better. The analysis will conclude with fitting linear models to quantify these effects."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate Synthetic Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Season Temperature       Sales\n",
      "0  Spring         low   93.781423\n",
      "1  Winter        high   82.393617\n",
      "2  Summer        high  119.745644\n",
      "3  Spring         low   92.509541\n",
      "4    Fall      medium   93.232105\n",
      "5  Winter         low  120.497193\n",
      "6    Fall        high   92.315245\n",
      "7  Winter         low  122.881046\n",
      "8  Spring         low   93.756572\n",
      "9  Winter      medium  104.004960\n"
     ]
    }
   ],
   "source": [
    "# Setting a random seed for reproducibility\n",
    "np.random.seed(2)\n",
    "\n",
    "# Generate categories\n",
    "season = np.random.choice(['Spring', 'Summer', 'Fall', 'Winter'], 1000, replace=True)\n",
    "temp = np.random.choice(['low', 'medium', 'high'], 1000, replace=True)\n",
    "\n",
    "# Define sales based on season and temperature with specific interactions\n",
    "sales = np.random.normal(100, 5, 1000) + \\\n",
    "        20 * ((season == 'Summer') & (temp == 'high')) - \\\n",
    "        20 * ((season == 'Summer') & (temp == 'low')) - \\\n",
    "        20 * ((season == 'Winter') & (temp == 'high')) + \\\n",
    "        20 * ((season == 'Winter') & (temp == 'low'))\n",
    "\n",
    "# Create DataFrame\n",
    "df = pd.DataFrame({'Season': season, 'Temperature': temp, 'Sales': sales})\n",
    "\n",
    "print(df.head(10))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exploratory Data Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the main effects of Temperature and Season on Sales side by side\n",
    "plt.figure(figsize=(16, 6))  # Set the figure size to be large enough for two subplots\n",
    "\n",
    "# Subplot 1: Main Effect of Temperature on Sales\n",
    "plt.subplot(1, 2, 1)  # 1 row, 2 columns, 1st subplot\n",
    "sns.barplot(x='Temperature', y='Sales', data=df, errorbar=None, palette='Set2')\n",
    "plt.title('Main Effect of Temperature on Sales')\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Sales')\n",
    "\n",
    "# Subplot 2: Main Effect of Season on Sales\n",
    "plt.subplot(1, 2, 2)  # 1 row, 2 columns, 2nd subplot\n",
    "sns.barplot(x='Season', y='Sales', data=df, errorbar=None, palette='Set2')\n",
    "plt.title('Main Effect of Season on Sales')\n",
    "plt.xlabel('Season')\n",
    "plt.ylabel('Sales')\n",
    "\n",
    "plt.tight_layout()  # Adjust subplots to fit into figure area.\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear Model without Interaction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.001\n",
      "Model:                            OLS   Adj. R-squared:                 -0.005\n",
      "Method:                 Least Squares   F-statistic:                    0.1009\n",
      "Date:                Thu, 30 May 2024   Prob (F-statistic):              0.992\n",
      "Time:                        12:09:59   Log-Likelihood:                -3940.1\n",
      "No. Observations:                1000   AIC:                             7892.\n",
      "Df Residuals:                     994   BIC:                             7922.\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "============================================================================================\n",
      "                               coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------------\n",
      "Intercept                   99.8946      0.934    106.938      0.000      98.062     101.728\n",
      "C(Season)[T.Spring]          0.3702      1.115      0.332      0.740      -1.817       2.558\n",
      "C(Season)[T.Summer]         -0.1617      1.100     -0.147      0.883      -2.320       1.996\n",
      "C(Season)[T.Winter]         -0.3876      1.097     -0.353      0.724      -2.540       1.765\n",
      "C(Temperature)[T.low]       -0.1639      0.981     -0.167      0.867      -2.088       1.761\n",
      "C(Temperature)[T.medium]    -0.0513      0.956     -0.054      0.957      -1.928       1.825\n",
      "==============================================================================\n",
      "Omnibus:                        1.812   Durbin-Watson:                   2.120\n",
      "Prob(Omnibus):                  0.404   Jarque-Bera (JB):                1.674\n",
      "Skew:                           0.088   Prob(JB):                        0.433\n",
      "Kurtosis:                       3.096   Cond. No.                         5.16\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Fit and summarize the linear model without interaction\n",
    "model = smf.ols('Sales ~ C(Season) + C(Temperature)', data=df).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualizing Interaction Effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the interaction effect between Season and Temperature\n",
    "plt.figure(figsize=(10, 6))\n",
    "sns.barplot(x='Season', y='Sales', hue='Temperature', data=df, errorbar=None, palette='Set2')\n",
    "plt.title('Sales by Season and Temperature Category')\n",
    "plt.xlabel('Season')\n",
    "plt.ylabel('Sales')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Model with Interaction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.854\n",
      "Model:                            OLS   Adj. R-squared:                  0.852\n",
      "Method:                 Least Squares   F-statistic:                     524.7\n",
      "Date:                Thu, 30 May 2024   Prob (F-statistic):               0.00\n",
      "Time:                        12:09:59   Log-Likelihood:                -2978.9\n",
      "No. Observations:                1000   AIC:                             5982.\n",
      "Df Residuals:                     988   BIC:                             6041.\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "================================================================================================================\n",
      "                                                   coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------------------------------\n",
      "Intercept                                       99.2961      0.491    202.163      0.000      98.332     100.260\n",
      "C(Season)[T.Spring]                              1.5990      0.722      2.216      0.027       0.183       3.015\n",
      "C(Season)[T.Summer]                             21.8045      0.739     29.486      0.000      20.353      23.256\n",
      "C(Season)[T.Winter]                            -19.7566      0.726    -27.196      0.000     -21.182     -18.331\n",
      "C(Temperature)[T.low]                            1.1454      0.715      1.602      0.109      -0.257       2.548\n",
      "C(Temperature)[T.medium]                         0.5077      0.704      0.721      0.471      -0.874       1.890\n",
      "C(Season)[T.Spring]:C(Temperature)[T.low]       -2.2087      1.053     -2.098      0.036      -4.275      -0.142\n",
      "C(Season)[T.Summer]:C(Temperature)[T.low]      -42.4804      1.045    -40.641      0.000     -44.532     -40.429\n",
      "C(Season)[T.Winter]:C(Temperature)[T.low]       39.4719      1.046     37.721      0.000      37.418      41.525\n",
      "C(Season)[T.Spring]:C(Temperature)[T.medium]    -1.5931      1.030     -1.546      0.122      -3.615       0.429\n",
      "C(Season)[T.Summer]:C(Temperature)[T.medium]   -21.4648      1.029    -20.858      0.000     -23.484     -19.445\n",
      "C(Season)[T.Winter]:C(Temperature)[T.medium]    19.3514      1.016     19.054      0.000      17.358      21.344\n",
      "==============================================================================\n",
      "Omnibus:                        0.035   Durbin-Watson:                   2.006\n",
      "Prob(Omnibus):                  0.983   Jarque-Bera (JB):                0.027\n",
      "Skew:                           0.013   Prob(JB):                        0.986\n",
      "Kurtosis:                       2.996   Cond. No.                         17.1\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Fit and summarize the linear model with interaction\n",
    "model_interaction = smf.ols('Sales ~ C(Season) + C(Temperature) + C(Season):C(Temperature)', data=df).fit()\n",
    "print(model_interaction.summary())"
   ]
  }
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