S05a_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Execute before using this notebook if using google colab\n",
    "\n",
    "kernel = str(get_ipython())\n",
    "\n",
    "if 'google.colab' in kernel:    \n",
    "    !wget https://raw.githubusercontent.com/fredzett/rmqa/master/utils.py -P local_modules -nc \n",
    "    !npx degit fredzett/rmqa/data data\n",
    "    import sys\n",
    "    sys.path.append('local_modules')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import Datasets, make_y_X\n",
    "from patsy import dmatrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following chapter is based on [*Backhaus et al (2017)*](https://www.springer.com/de/book/9783662460764)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear regresssion is one of the most flexibel and widely used statistical methods used in research. It is used for analysing the relationship between a **dependent** and one or more **independent** variables. Linear regression is used for \n",
    "\n",
    "1. **inference**, i.e. to test a prior developed hypothesis about the relationship between variables of interest\n",
    "\n",
    "2. **prediction**, i.e. to estimate the value of a dependent variable given values of independent variables\n",
    "\n",
    "Primary use case for linear regression analysis is the analysis of **causal relations**. This relation can be expressed as \n",
    "\n",
    "$$Y = f(X)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Simple (linear) regresssion:**  \n",
    "\n",
    "\n",
    "If we want to express that there we believe in a relation between *revenues* and *price* we may state this as\n",
    "\n",
    "$$\\text{revenues} = f(\\text{price})$$\n",
    "\n",
    "Using linear regression this **relation can be quantified**, i.e. we can determine how much *revenue* will change if we change *price*. \n",
    "\n",
    "\n",
    "**Stochastic model:**    \n",
    "It is very unlikely that the the relation between the above variables is entirely deterministic (as assumed in the above formula). We, therefore, need to introduce uncertainty to the model. The resulting **stochastic model** is commonly used in regression analysis and is described as:\n",
    "\n",
    "$$Y = f(X) + \\epsilon$$\n",
    "\n",
    "Here $\\epsilon$ is a **random variable** (called error term / residual) which cannot be observed and is assumed to follow a standard normal distribution (i.e. $\\epsilon \\sim N(0,1)$). The stochastic model will be required to **evaluate the regression models using statistical tests**.\n",
    "\n",
    "\n",
    "**Multiple (linear) regression:**  \n",
    "In many (if not most) research questions we may not assume a monocausal relationship. Instead $Y$, our variable we want to analyse, is influenced by numerous factors. In our above example *revenues* may also depend on advertising spent but also from other factor such as the state of the economy, the price, behaviour of competitors etc. \n",
    "\n",
    "For such a relationship we use a **multiple regression analysis** which may be expressed as:\n",
    "\n",
    "$$Y = f(X_1, X_2, \\ldots, X_J)$$\n",
    "\n",
    "\n",
    "**Causality vs. correlation:**  \n",
    "It is important to state that while we attempt to model a causal relationship between $Y$ and $X$, in practice we cannot determine whether or not the relationship is actually causal. Instead all we do is we approximate causality be assessing correlation. \n",
    "\n",
    "**Typical hypotheses modelled with linear regression**\n",
    "\n",
    " | # | Hypothesis                                                                                                | Dependent variable                    | Independent variable                                    |\n",
    "|---|-----------------------------------------------------------------------------------------------------------|---------------------------------------|---------------------------------------------------------|\n",
    "| 1 | Is revenue by salesperson dependent on number of customer visits?                                         | Revenue per sales person (per period) | Number of customer visits per sales person (per period) |\n",
    "| 2 | Will sales change if advertising spent is doubled                                                         | Sales per period                      | Spent on advertisment per period                        |\n",
    "| 3 | How does a price increase of x% impact sales if advertisment spent is   increased by 10% at the same time | Sales per period                      | Advertisment spent, price, …                            |\n",
    "|4|...|...|...|\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model formulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A model is a simplified representation of reality. Models are very useful but it is always a fine line between simplification and complexity. If we want to model reality as close as possible our model may become to complex. If our model is to simple it may not describe reality good enough for our purposes. There is no such thing as a good or a bad model. It is more helpful to think of a model as suitable or not suitable for our problem at hand. It turns out the linear regression models are quite simple yet very suitable for many research and practical problems which is why they are heavily relied on in all social sciences. \n",
    "\n",
    "> **Dataset**: In the following we will be using the advertising dataset from [Introduction to Statistical Learning](http://faculty.marshall.usc.edu/gareth-james/ISL/index.html) for the following examples. The dataset contains   \n",
    "> - sales in thousands units\n",
    "> - advertising budgets in thousand of dollars for TV, radio and newspaper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  radio  newspaper  sales\n",
       "0  230.1   37.8       69.2   22.1\n",
       "1   44.5   39.3       45.1   10.4\n",
       "2   17.2   45.9       69.3    9.3\n",
       "3  151.5   41.3       58.5   18.5\n",
       "4  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = Datasets.advertising(\"pandas\", col=\"all\") # load advertisment data\n",
    "df.head(5) # show first 5 rows of data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Sales vs. TV advertisment spent:**  \n",
    "Let us assume that we believe in a simple linear relation between **sales** and **TV** advertisment spent. We can describe this as  \n",
    "\n",
    "$$\\text{sales} = f(\\text{TV})$$\n",
    "\n",
    "This implies that we believe in a causal relationship between both variables. Specifically we believe that *TV* advertisment spent drives or influences *sales*. \n",
    "\n",
    "**Regression function:** \n",
    "\n",
    "A simple linear regression model of the above formulations could be:\n",
    "\n",
    "$$\\hat{Y} = \\hat{\\beta}_0 + \\hat{\\beta}_1X $$\n",
    "\n",
    "where $\\hat{Y}$ denotes the prediction of the dependent variable $Y$ given $X$. $\\hat{\\beta}_0$ and $\\hat{\\beta}_1$ are the coefficient estimates. \n",
    "\n",
    "For our example the regression function looks as follows:\n",
    "\n",
    "$$\\text{sales} = \\hat{\\beta}_0 + \\hat{\\beta}_1\\text{TV}$$\n",
    "\n",
    "Given the mathematical formulation implies a line in a 2D field, $\\beta_0$ represents the intercept of the line with the y-axis and $\\beta_1$ represents the slope of the line. \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "<img src=\"https://www.dropbox.com/s/g8smbktpeqgl90u/regressionmodel.png?dl=1\" alt=\"regression_model\" width=\"50%\" align=\"center\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's assume that $\\beta_0$ is $20$ and $\\beta_1$ is $0.5$. This would mean that our regression model becomes:\n",
    "\n",
    "$$\\text{sales} = 20+ 0.5\\text{TV}$$\n",
    "\n",
    "This would mean we could insert X and calculate $\\hat{Y}$. \n",
    "\n",
    "For example, if we assume we spent 100 in TV advertisment we would expect sales of \n",
    "\n",
    "$$\\text{sales} = 20 + 0.5\\times100 = 70$$\n",
    "\n",
    "Spending 100.000 USD in TV advertisment would yield in 70.000 Units of sales according to our model. \n",
    "\n",
    "(Note: sales and TV spent both in in units of thousands)\n",
    "\n",
    "**How do you determine coefficients?**  \n",
    "In our example we have just assumed values for $\\beta_0$ and $\\beta_1$. In practice we need to determine both coefficients. In order to derive how we do this it is helpful to look at the following interactive example:\n",
    "\n",
    "[Interactive example](https://share.streamlit.io/fredzett/rmqa/regression.py)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimation of regression function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to find coefficients that specify a line which describes the true relationship as best as possible. \n",
    "\n",
    "This is achieved by minimizing the *least squares* criterion, i.e. we want to minimize the resdiual sum of squares (RSS; sometimes SSR)\n",
    "\n",
    "$$\n",
    "\\text{RSS} = \\sum_{i=1}^n e_i^2\n",
    "$$\n",
    "\n",
    "where $e_i$ is defined as \n",
    "\n",
    "$$\n",
    "e_i = y_i - \\hat{y}_i\n",
    "$$\n",
    "\n",
    "The **least squares criterion** avoids that positive and negative deviations cancel each other out and weighs more heavily on large deviations (which may also be a disadvantage if we find to have outlier in our data). \n",
    "\n",
    "\n",
    "Analytically we can then derive $\\beta_0$ and $\\beta_1$ that minimizes the RSS:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\hat{\\beta}_1 & = \\frac{\\sum_{i=1}^n (x_i - \\bar{x})(y_i - \\bar{y})}{\\sum_{i=1}^n (x_i - \\bar{x})^2} \\\\[10pt]\n",
    "\\hat{\\beta}_0 & = \\bar{y} - \\hat{\\beta}_1\\bar{x}\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "We write $\\hat{\\beta}_i$ to indicate that it is an estimator. We omit if this is clear from the context. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily implement the above formulas in python and calculate the correct values for both coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write functions for b0, b1\n",
    "def beta1(x,y):\n",
    "    ________ # insert function\n",
    "\n",
    "def beta0(x,y):\n",
    "    ________ # insert function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df[\"sales\"] # column \"sales\"\n",
    "x = df[\"TV\"] # column \"TV\"\n",
    "\n",
    "#beta0(x,y), beta1(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimal regression line can therefore be described as:\n",
    "\n",
    "$$\\text{sales} = 7.03 + 0.048\\times\\text{TV}$$\n",
    "\n",
    "meaning that increasing TV spent by 1.000 USD will increase sales units by 48 (remember that both are in units of thoushands)\n",
    "\n",
    "Looking at our [interactive chart](https://share.streamlit.io/fredzett/rmqa/regression.py) we see that the line does not perfectly describe the relationship given most of the data points are not on the line described by the regression model. This is due to the fact that there are other factors influencing *sales*. We distinguish between two types of factors:\n",
    "\n",
    "1. **systematic factors**, i.e. other explanatory variables (e.g. price, newspaper ad spent, ...) which may drive sales but have not been incorporated into the model\n",
    "\n",
    "2. **unsystematic factors**, i.e. other factors which cannot be included because they are unknown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For most research question it is required that we have more than one indepenent variable. If this is the case the regression model has the following form:\n",
    "\n",
    "$$\\hat{Y} = \\beta_0 + \\beta_1x_1 + \\beta_2x_2 + \\ldots + \\beta_Jx_J$$\n",
    "\n",
    "**Example:**  \n",
    "We could describe the relationship between *sales* and advertising spent using all three media types, *TV*, *Newspaper* and *radio*. This would then be described as:\n",
    "\n",
    "$$\\text{sales} = \\beta_0 + \\beta_1\\text{TV} + \\beta_2\\text{newspaper} + \\beta_3\\text{radio}$$\n",
    "\n",
    "\n",
    "In order to solve for $\\beta_j$ we, in principal, follow the same route than in the simple regression case. However, solving the system of equations is somewhat more complex. It involves solving a system of linear equations of the following form:\n",
    "\n",
    "$$Y = X\\beta + \\epsilon$$\n",
    "\n",
    "where:\n",
    "\n",
    "\\begin{equation}\n",
    "Y = \\begin{pmatrix} y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n \\end{pmatrix}, \n",
    "X = \\begin{pmatrix} 1 & x_{11} & x_{12} & \\ldots & x_{1p} \\\\ 1 & x_{21} & x_{22} & \\ldots & x_{2p} \\\\ \\vdots & \\vdots &  \\vdots  & \\vdots & \\vdots \\\\ 1 & x_{n1} & x_{n2} & \\ldots & x_{np} \\end{pmatrix},\n",
    "\\beta = \\begin{pmatrix} \\beta_0 \\\\ \\vdots \\\\ \\beta_p  \\end{pmatrix}, \n",
    "\\epsilon = \\begin{pmatrix} \\epsilon_0 \\\\ \\epsilon_1  \\\\ \\vdots \\\\ \\epsilon_n  \\end{pmatrix}, \n",
    "\\end{equation}\n",
    "\n",
    "Without covering the details of the math this equation can be solved as follows:\n",
    "\n",
    "$$\n",
    "\\hat{\\beta} = (X^TX)^{-1}X^Ty\n",
    "$$\n",
    "\n",
    "What is important here is that there exists an analytical solution for the linear regression problem. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implementation in python is easy yet not intuitive. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_ols_multiple(X,y):\n",
    "    return np.linalg.inv(X.T@X)@X.T@y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also note that in the multiple regression part is it necessary to assume one factor to be consisting of $1$s in order to calculate $\\beta_0$ (i.e. the intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
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       "      <th>0</th>\n",
       "      <td>0.045765</td>\n",
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       "      <th>1</th>\n",
       "      <td>-0.001037</td>\n",
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       "      <th>2</th>\n",
       "      <td>0.188530</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.938889</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "      sales\n",
       "0  0.045765\n",
       "1 -0.001037\n",
       "2  0.188530\n",
       "3  2.938889"
      ]
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     "execution_count": 87,
     "metadata": {},
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   ],
   "source": [
    "X = df[[\"TV\",\"newspaper\",\"radio\"]] # Define X to be all three variables\n",
    "X[\"Intercept\"] = np.ones(len(X)) # add a variable consisting of ones\n",
    "coefs = fit_ols_multiple(X,y) # calculate coefficients\n",
    "coefs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sales</th>\n",
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       "      <th>TV</th>\n",
       "      <td>0.045765</td>\n",
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       "      <th>newspaper</th>\n",
       "      <td>-0.001037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>radio</th>\n",
       "      <td>0.188530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>2.938889</td>\n",
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      "text/plain": [
       "              sales\n",
       "TV         0.045765\n",
       "newspaper -0.001037\n",
       "radio      0.188530\n",
       "Intercept  2.938889"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefs.index = X.columns # assign names of X\n",
    "coefs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Implementation in python**:  \n",
    "It is tedious and verbose to implement regression from scratch. We will therefore use existing modules to achieve this. In doing so we can also make use of many statistical tests that are calculated on the fly. \n",
    "\n",
    "We will use:\n",
    "\n",
    "- `patsy.dmatrices`: this produces X and y based on a model specification (use model `patsy`)\n",
    "- `statsmodels.OLS`: calculates an ordinary least squares regression (use model `statsmodels`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "from patsy import dmatrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    2.938889\n",
       "TV           0.045765\n",
       "newspaper   -0.001037\n",
       "radio        0.188530\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"sales ~ TV + newspaper + radio\", df, return_type=\"dataframe\") # y = df[\"sales\"], X = [Intercept, TV, Newspaper, radio]\n",
    "model = sm.OLS(y,X) # define model\n",
    "ols = model.fit() # optimize model, i.e. calculate coefficients\n",
    "ols.params # print regression parameters (i.e. coefficients)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is very helpful as we can also use the optimized model (i.e. variable `ols`) to print summary statistics for the entire  regression model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the combination of both modules / functions to make our lives much easier and be able to explore models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Meaning of regression coefficients:**  \n",
    "We have now seen how to calculate the regression coefficients that minimize the residual sum of squares (RSS). Let's now focus on how to interpret these coefficients:\n",
    "\n",
    "The coeffiecients give the **marginal effect of change** of an independent variable on the dependent variable. For example, a coefficient of `0.18` for `radio` means that increasing radio spent by a $1.000$ USD - and keeping all other variables constant - the sales increase by $180$.\n",
    "\n",
    "It is, however, important to understand that the **size of the coefficient does not indicate importance** and should not be interpreted directly. For example, it cannot be concluded from the above estimation that the effect of *TV* is less than the effect of *radio* if we do not know the scale of the variables. More specifically, the scales of the variables need to be of the same size to make such a statement valid. In the above case it is actually valid to make such a statement because all independent (i.e. explanatory) variables are measures in '000 USD. \n",
    "\n",
    "For most models, the scale between different independent variables differs, however. \n",
    "\n",
    "Let's look at a different dataset containing information about different car models. The dataset has the following variables:\n",
    "\n",
    "- `mpg` = miles per gallon\n",
    "- `cylinders` = number of cylinders \n",
    "- `displacement` = overall volume in the engine as a factor of cylinder circumfrance, depth and total number of cylinders. This metric gives a good proxy for the total amount of power the engine can generate.\n",
    "- `horsepower` = gross horsepower\n",
    "- `weight` = weight of the car in lbs\n",
    "- `acceleration`= time in seconds to 100mph\n",
    "- `year` = year model was produced\n",
    "- `origin` = region (1=US, 2=Europe, 3=Asia)\n",
    "- `name` = name of model\n",
    "\n",
    "Just be looking at the descriptions it becomes apparent that the units of each variable are not comparable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration  year  \\\n",
       "0  18.0          8         307.0         130    3504          12.0    70   \n",
       "1  15.0          8         350.0         165    3693          11.5    70   \n",
       "2  18.0          8         318.0         150    3436          11.0    70   \n",
       "3  16.0          8         304.0         150    3433          12.0    70   \n",
       "4  17.0          8         302.0         140    3449          10.5    70   \n",
       "\n",
       "   origin                       name  \n",
       "0       1  chevrolet chevelle malibu  \n",
       "1       1          buick skylark 320  \n",
       "2       1         plymouth satellite  \n",
       "3       1              amc rebel sst  \n",
       "4       1                ford torino  "
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars = Datasets.cars(\"pandas\", col=\"all\") # Load cars dataset\n",
    "cars.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's assume we want to understand the drivers for `mpg`, i.e. what are factors influencing mileage per gallon. We hypothesize about a model that looks as follows:\n",
    "\n",
    "$$\\text{mpg} = \\beta_0 + \\beta_1\\text{horsepower} + \\beta_2\\text{weight} + \\beta_3\\text{year}$$\n",
    "\n",
    "Intuitively we would assume that `mpg`:\n",
    "- decreases with more `horsepower` and `weight` (as big and/or heavy cars usually are less efficient)\n",
    "- increases with `year` (as newer cars are more efficient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    -13.719360\n",
       "horsepower    -0.005000\n",
       "weight        -0.006448\n",
       "year           0.748705\n",
       "dtype: float64"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"mpg ~ horsepower + weight + year\", cars, return_type=\"dataframe\") # define y and X (including intercept)\n",
    "ols = sm.OLS(y,X).fit() # optimize model\n",
    "ols.params # print parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our initial intuition was confirmed given the negative signs of coefficients for `horsepower` and `weight` and the positive coefficient for `year`.\n",
    "\n",
    "We can now make a statement that $100$ horsepower extra decreases mileage per gallon by $5$. \n",
    "\n",
    "We may, however, be interested in the **most influential factor**. What is driving `mpg` the most? In this example we cannot state that `year` is driving horsepower the most given the units and scales of all three variables are not comparable.\n",
    "\n",
    "**Standardized coefficients**  \n",
    "In order to answer the question with of the $X$s is most important for determining $Y$ we need to make our $\\beta$s comparable. We can do this following two ways:\n",
    "\n",
    "1. Standardize variables using *z score*\n",
    "\n",
    "2. Standardize coefficients "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Z-Score approach**\n",
    "\n",
    "- standardize the variables using a z-score (i.e. mean of 0 and standard deviation of 1 for each variable)\n",
    "- run ols regression and receive standardized coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [],
   "source": [
    "y, X = dmatrices(\"mpg ~ horsepower + weight + year\", cars, return_type=\"dataframe\") # define y and X (including intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [],
   "source": [
    "def zscore(x):\n",
    "    return (x - np.mean(x)) / np.std(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [],
   "source": [
    "for col in [\"horsepower\", \"weight\", \"year\"]:\n",
    "    X[col] = zscore(X[col])\n",
    "y = zscore(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    -3.096481e-16\n",
       "horsepower   -2.465684e-02\n",
       "weight       -7.016947e-01\n",
       "year          3.533670e-01\n",
       "dtype: float64"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols = sm.OLS(y,X).fit() # optimize model\n",
    "ols.params # print parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the optimal parameters have changed. We can now compare the coefficients and say that \n",
    "\n",
    "- horsepower has the least impact\n",
    "- year has the second least impact\n",
    "- weight has the most impact and it's impact is 2x as high as the impact for year"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is recommended to use the below approach as it avoids\n",
    "\n",
    "- rerunning the entire model with new variables\n",
    "- leaves $X$s unchanged"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Standardized coefficients approach**\n",
    "\n",
    "- run ols regression using nominal (i.e. original) values for variables\n",
    "- convert nominal coefficients using $$\\beta_{j,std} = \\beta_j \\cdot \\frac{s_{X_j}}{s_Y}$$\n",
    "\n",
    "where\n",
    "\n",
    "$\\beta_{j,std}$ = standardized coefficient for variable $X_j$  \n",
    "$\\beta_j$ = unstandardized / nominal coefficient for variable $X_j$  \n",
    "$s_{X_j}$ = standard deviation of $X_j$  \n",
    "$s_Y$ = standard deviation of $Y$\n",
    "\n",
    "Let's do this in python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    -13.719360\n",
       "horsepower    -0.005000\n",
       "weight        -0.006448\n",
       "year           0.748705\n",
       "dtype: float64"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"mpg ~ horsepower + weight + year\", cars, return_type=\"dataframe\") # define y and X (including intercept)\n",
    "ols = sm.OLS(y,X).fit() # optimize model\n",
    "ols.params # print parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.02465684]\n",
      "[-0.70169467]\n",
      "[0.35336703]\n"
     ]
    }
   ],
   "source": [
    "for p, col in zip(ols.params[1:], [\"horsepower\", \"weight\", \"year\"]):\n",
    "    bstd = p * (np.std(X[col])/np.std(y))\n",
    "    print(bstd.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the resulting coefficients are different from the z-score approach. However, the interpretation yields exactly the same conclusion:\n",
    "\n",
    "- horsepower has the least impact\n",
    "- year has the second least impact\n",
    "- weight has the most impact and it's impact is 2x as high as the impact for year"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation of standardized coefficients**  \n",
    "We can say that changing $X_j$ bei $1$ standard deviation changes $Y$ bei $\\beta_{j, std}$ standard deviations.\n",
    "\n",
    "Example: changing `year` by $1$ standard deviation changes `mpg` by $0.35\\ldots$ standard deviations. This means "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg    2.754512\n",
       "dtype: float64"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bjstd = 0.35336703\n",
    "std_mpg = np.std(y)\n",
    "std_mpg * bjstd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can confirm this is true by comparing to the original parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.7545118245163795"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bj = 0.748705\n",
    "std_year = np.std(X[\"year\"])\n",
    "std_year*bj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summarizing:\n",
    "\n",
    "- nominal coefficients: use to show \"real unit\" effect of $X$ on $y$\n",
    "- standardized coefficients: use to compare effect size of $X$s on $y$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of regression function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have esimtated our regression function. However, we don't know how good the model. We have used a model to approximate reality and we need to understand how good our model is in doing so. We therefore need to evaluate our model. This consists of two types of evaluation:\n",
    "\n",
    "1. **Global assessment**, i.e. how good can $Y$ be explained by $X$ \n",
    "\n",
    "2. **Coefficient assemssment**, i.e. if and how individual $X$s contribute to explaining $Y$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true,
    "toc-nb-collapsed": true
   },
   "source": [
    "### Global assessment of regression model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The global assessment, i.e. the goodness of fit, can be done using two different metrics:\n",
    "\n",
    "1. $R^2$\n",
    "\n",
    "2. $F$-Statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen that we optimize our regression model by minimizing\n",
    "\n",
    "$$\n",
    "\\text{RSS} = \\sum_{i=1}^n e_i^2\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unfortunately, we cannot use RSS as an indicator of how good our model is as it is dependents on the size of the dataset. The larger the dataset the higher the RSS. \n",
    "\n",
    "However, we can disassemble the RSS in \n",
    "\n",
    "- explained deviation and\n",
    "- unexplained deviation\n",
    "\n",
    "Let's look at the deviations in the simple linear regression case with one explanatory variable $X$ and the dependent variable $Y$.\n",
    "\n",
    "<img src=\"https://www.dropbox.com/s/rz386z8fvl43o6o/regression_deviation.png?dl=1\" alt=\"regression_model\" width=\"50%\" align=\"center\"/>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's analyse one single observation $x_i$ with its corresponding observation $y_i$. The point $(x_i, y_i)$ is above the mean $\\bar{y}$. We treat $y_i - \\bar{y}$ as the total deviation. This deviation can be separated into:\n",
    "\n",
    "- explained deviation: $\\hat{y}_i - \\bar{y}$; given $x_i$ is higher than $\\bar{x}$ we expect $\\hat{y}_i$ to be higher than $\\bar{y}$\n",
    "\n",
    "- unexplained deviation: $\\epsilon_i$; cannot be exlained by the above argument\n",
    "\n",
    "We can therefore say that: *total deviation = explained deviation + residuum*\n",
    "\n",
    "Which can trivially be written as:\n",
    "\n",
    "$$y_i - \\bar{y} = (\\hat{y}_i - \\bar{y}) + (y_i - \\hat{y}_i)$$\n",
    "\n",
    "This equation also holds for multiple regressions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition of $R^2$**  \n",
    "Is derived from this relationship and is defined as \n",
    "\n",
    "$$R^2 = \\frac{\\text{explained deviation}}{\\text{total deviation}} = \\frac{\\sum_{i=1}^I (\\hat{y}_i - \\bar{y})^2}{\\sum_{i=1}^I (y_i - \\bar{y})^2}$$\n",
    "\n",
    "The $R^2$ score can be interpreted as how much % can be explained by the specified model. (Note: altenatively, the $R^2$ can also be calculated as the square of the correlation between $Y$ and $\\hat{Y}$).\n",
    "\n",
    "Let's look at our original advertisment model and see how good the model actually is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.611875050850071"
      ]
     },
     "execution_count": 328,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"sales ~ TV\", df, return_type=\"dataframe\") # y = df[\"sales\"], X = [Intercept, TV]\n",
    "model = sm.OLS(y,X) # define model\n",
    "ols = model.fit() # optimize model, i.e. calculate coefficients\n",
    "ols.rsquared # print regression parameters (i.e. coefficients)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively we can calcualte it as the square of correlation between $Y$ and $\\hat{Y}$,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "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>sales</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sales</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.611875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.611875</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          sales         0\n",
       "sales  1.000000  0.611875\n",
       "0      0.611875  1.000000"
      ]
     },
     "execution_count": 329,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = ols.predict(X)\n",
    "ys = pd.concat((y,yhat), axis=1)\n",
    "ys.corr()**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Either way, this means that $\\approx 60\\%$ of sales deviation can be explained by spent in TV advertisment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the $R^2$ is a good metric it has some drawbacks, mostly:\n",
    "\n",
    "- does not account for size of dataset: for example the $R^2$ of two data points is always 1 given we can always connect them using a line\n",
    "- does not account for number of $X$s: complex models with many variables always have a higher $R^2$ (all other things being equal)\n",
    "\n",
    "To compensate for these drawbacks we can use \n",
    "\n",
    "- adjusted $R^2$\n",
    "- $F$-statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Adjusted $R^2$**  \n",
    "Takes the number of variables into account and adjusts for it by \n",
    "\n",
    "$$R^2_{adj} = R^2 - \\frac{J \\cdot (1 - R^2}{N- J - 1}$$\n",
    "\n",
    "where:\n",
    "\n",
    "$N$ = number of observations (i.e. elements in dataset)  \n",
    "$J$ = number of coefficients (i.e. variables in datatset)  \n",
    "$N - J - 1$ = number of degrees of freedom\n",
    "\n",
    "Comparison of $R^2$ and $R^2_{adj}$ using our advertisment dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**F-Statistic**\n",
    "\n",
    "The $R^2$ measures how much of $Y$ can be explained by the model. Given in most research (and practical) context our data is based on a sample and not a population we have to understand to what extend the model - based on the sample data - is valid for the population. Therefore, we need to **understand the statistical significance of the model**. This is what the $F$-statistic is used for. \n",
    "\n",
    "The $F$-statistic includes\n",
    "\n",
    "- the deviations explained above\n",
    "- the number of observations\n",
    "- the number of coefficients \n",
    "\n",
    "Given the estimated regression function (of a sample)\n",
    "\n",
    "$$\\hat{Y} = \\beta_0 + \\beta_1x_1 + \\beta_2x_2 + \\ldots + \\beta_Jx_J + \\epsilon$$\n",
    "\n",
    "can be interpreted as \"true\" function with unknown parameters $\\beta_0, \\beta_1, \\beta_2, \\ldots,\\beta_J$ which describes the causal realtionship of the population. This function includes an error term ($\\epsilon$). Therefore, the regression function can be regarded as a **stochastic model**.\n",
    "\n",
    "As discussed $\\epsilon$ includes all random factors which drive the dependent variable $Y$. This variable cannot be observed directly (given we don't know which unsystematic factors influence $Y$ or else we would have included them) but is measured by the **residuals**. \n",
    "\n",
    "It follows from the above statement that $Y$ is also a random variable and the the coefficients (i.e. $\\beta$s) are also realisation of random variables. Therefore with different samples these coefficients will vary around the true value of $\\beta$.\n",
    "\n",
    "If a causal relationship exists betwenn $Y$ and $X$ then the true regression coefficients must be different from zero. \n",
    "\n",
    "To this end, for testing the significance of the regression model the following **null hypotheses must be tested**:\n",
    "\n",
    "$$H_0 : \\beta_0 = \\beta_1 = \\ldots = \\beta_J = 0$$\n",
    "\n",
    "For testing this hypothesis we conduct the $F$-Test using the $F$-distribution doing the following:\n",
    "\n",
    "- calculate the empirical $F$-value from the model \n",
    "- provide significance level\n",
    "- compare to the theoretical $F$-value given the $F$-distribution / calculate p-values\n",
    "\n",
    "**Calculation of empirical $F$-value**:\n",
    "\n",
    "$$F_emp = \\frac{\\sum_{i=1}^I(\\hat{y}_i - \\bar{y})^2/J}{\\sum_{i=1}^I(y_i - \\hat{y}_i)^2/(I - J - 1)} = \\frac{\\text{explained deviation}/J}{\\text{unexplained deviation}/(I - J - 1)} = \\frac{R^2/J}{(1 - R^2)/(I - J - 1)}$$\n",
    "\n",
    "where:\n",
    "\n",
    "$I$ = number of observations  \n",
    "$J$ = number of parameters (coefficients)\n",
    "\n",
    "\n",
    "Example using the `car dataset`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. calcualte empirical f-value**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 473,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "545.3985163061409"
      ]
     },
     "execution_count": 473,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Caluclate model\n",
    "y, X = dmatrices(\"mpg ~ horsepower + weight + year\", cars, return_type=\"dataframe\") \n",
    "ols = sm.OLS(y, X).fit()\n",
    "f_emp = ols.fvalue\n",
    "f_emp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the function from our model. However, let's check if the value can actually be recalculated using the above formula:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 474,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fvalue(y,X):\n",
    "    y = y.iloc[:,0] \n",
    "    yhat = ols.fittedvalues\n",
    "    ybar = np.mean(yhat)\n",
    "    J = X.shape[1]-1 # exclude intercept\n",
    "    I = X.shape[0]\n",
    "    fvalue = (np.sum((yhat - ybar)**2)/J)/(np.sum((y - yhat)**2)/(I-J-1))\n",
    "    return fvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 475,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "545.3985163061416"
      ]
     },
     "execution_count": 475,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate empirical F-value\n",
    "fvalue(y,X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the function from statsmodels from now on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. determine significance level**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 476,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. compare to theoretical f-value**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 477,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null hypothesis can be rejected\n"
     ]
    }
   ],
   "source": [
    "dfj = X.shape[1] - 1 # three independent variables\n",
    "dfn = len(X) - dfj - 1 # degrees of freedom\n",
    "f = stats.f(dfj, dfn)\n",
    "pvalue = 1 - f.cdf(f_emp)\n",
    "if pvalue < alpha:\n",
    "    print(\"Null hypothesis can be rejected\")\n",
    "else: \n",
    "    print(\"Null hypothesis cannot be rejected\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interpretation: our model yields an empirical $F$-value that is very unlikely under the theoretical $F$-distribuation. Therefore, we can conclude that at least one of the parameters ($\\beta$s) is not equal to zero. This means that we actually can be quite certain that we have specified a model that found a (statistical) realtion between $Y$ and $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true,
    "toc-nb-collapsed": true
   },
   "source": [
    "### Assessment of regression coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have so far \"only\" tested the significance of the entire model. However, we have not tested the individual coefficients. \n",
    "\n",
    "The common hypothesis we need to evaluate is:\n",
    "\n",
    "$$H_0 : \\beta_j = 0$$\n",
    "\n",
    "(note that we could in principal also conduct other hypotheses)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$t$-statistic**\n",
    "\n",
    "We have seen in previous chapter how to conduct the $t$-test. The steps are the same as with the $F$-test.\n",
    "\n",
    "1. we calculate the emprical $t$-value\n",
    "2. we provide significance level\n",
    "3. we compare to the theoretical $t$-value given the $t$-distribution / calculate p-values\n",
    "\n",
    "If we test the null hypothesis as described above the emprical $t$-value can be determined using:\n",
    "\n",
    "$$t_\\text{emp} = \\frac{\\beta_j}{s_{\\beta_j}}$$\n",
    "\n",
    "where:\n",
    "\n",
    "$s_{\\beta_j}$ = the standard error of $\\beta_j$.\n",
    "\n",
    "The calculation of the standard error in the multiple regression case is somewhat more complex and will not be covered here. This is due to the fact that\n",
    "\n",
    "1. most statistical packages yield the standard errors\n",
    "2. we could calculate it using a bootstrap approach\n",
    "\n",
    "For further information on the calculation of standard errors see, e.g., [*Backhaus et al (2017), p. 122ff*](https://www.springer.com/de/book/9783662460764)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: using the above model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 491,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept     -3.280764\n",
       "horsepower    -0.529690\n",
       "weight       -15.767548\n",
       "year          14.365022\n",
       "dtype: float64"
      ]
     },
     "execution_count": 491,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_emp = ols.tvalues\n",
    "t_emp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 492,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null hypothesis for Intercept can be rejected\n",
      "Null hypothesis for horsepower cannot be rejected\n",
      "Null hypothesis for weight can be rejected\n",
      "Null hypothesis for year can be rejected\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "pvalues = 1 - stats.t(dfn).cdf(abs(t_emp))\n",
    "for pvalue, col in zip(pvalues, X.columns):\n",
    "    if pvalue < alpha:\n",
    "        print(f\"Null hypothesis for {col} can be rejected\")\n",
    "    else: \n",
    "        print(f\"Null hypothesis for {col} cannot be rejected\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Confidence intervals using bootstrap approach**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 506,
   "metadata": {},
   "outputs": [],
   "source": [
    "sims = 10_000\n",
    "params = np.empty((sims,X.shape[1]))\n",
    "for i in range(sims):\n",
    "    idx = np.random.choice(range(len(X)),replace=True, size=len(X))\n",
    "    params[i,:] = sm.OLS(y.iloc[idx],X.iloc[idx,:]).fit().params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 510,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept [-21.37340957  -6.05244358]\n",
      "horsepower [-0.02480722  0.01476044]\n",
      "weight [-0.00730325 -0.00564262]\n",
      "year [0.65134201 0.84715418]\n"
     ]
    }
   ],
   "source": [
    "for i, col in zip(range(params.shape[1]), X.columns):\n",
    "    print(col, np.quantile(params[:,i], [0.025,0.975]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `summary` function we can, however, make this analysis less verbose. We also get other statistics such as "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 493,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.808</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.807</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   545.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 12 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>9.37e-139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:58:38</td>     <th>  Log-Likelihood:    </th> <td> -1037.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   392</td>      <th>  AIC:               </th> <td>   2083.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   388</td>      <th>  BIC:               </th> <td>   2099.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</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>Intercept</th>  <td>  -13.7194</td> <td>    4.182</td> <td>   -3.281</td> <td> 0.001</td> <td>  -21.941</td> <td>   -5.498</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>horsepower</th> <td>   -0.0050</td> <td>    0.009</td> <td>   -0.530</td> <td> 0.597</td> <td>   -0.024</td> <td>    0.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th>     <td>   -0.0064</td> <td>    0.000</td> <td>  -15.768</td> <td> 0.000</td> <td>   -0.007</td> <td>   -0.006</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>year</th>       <td>    0.7487</td> <td>    0.052</td> <td>   14.365</td> <td> 0.000</td> <td>    0.646</td> <td>    0.851</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>41.952</td> <th>  Durbin-Watson:     </th> <td>   1.227</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  69.490</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.671</td> <th>  Prob(JB):          </th> <td>8.14e-16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.566</td> <th>  Cond. No.          </th> <td>7.48e+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, 7.48e+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:                    mpg   R-squared:                       0.808\n",
       "Model:                            OLS   Adj. R-squared:                  0.807\n",
       "Method:                 Least Squares   F-statistic:                     545.4\n",
       "Date:                Thu, 12 Nov 2020   Prob (F-statistic):          9.37e-139\n",
       "Time:                        20:58:38   Log-Likelihood:                -1037.4\n",
       "No. Observations:                 392   AIC:                             2083.\n",
       "Df Residuals:                     388   BIC:                             2099.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    -13.7194      4.182     -3.281      0.001     -21.941      -5.498\n",
       "horsepower    -0.0050      0.009     -0.530      0.597      -0.024       0.014\n",
       "weight        -0.0064      0.000    -15.768      0.000      -0.007      -0.006\n",
       "year           0.7487      0.052     14.365      0.000       0.646       0.851\n",
       "==============================================================================\n",
       "Omnibus:                       41.952   Durbin-Watson:                   1.227\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               69.490\n",
       "Skew:                           0.671   Prob(JB):                     8.14e-16\n",
       "Kurtosis:                       4.566   Cond. No.                     7.48e+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, 7.48e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 493,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true,
    "toc-nb-collapsed": true
   },
   "source": [
    "## Validating model assumptions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have so far not discussed the assumptions that we depend on when calculating test statistics etc. For calculating these statistics we mainly rely on the residual which is stochastic. We introduced this term to incorporate uncertainty into our model which must be included given that we are estimating a model (and its parameters) based on a sample (see last chapter). When conducting the regression analysis we make multiple assumptions regarding the stochastic component. \n",
    "\n",
    "**Assumptions**:\n",
    "\n",
    "1. the model is correctly specified\n",
    "    - it is linear for the parameters ($\\beta$s)\n",
    "    - it includes the relevant explanatory variables\n",
    "    - the number of estimated parameters (J + 1) is smaller than the number of observations (I)\n",
    "\n",
    "2. the expected value of $\\epsilon$ is zero\n",
    "3. the correlation between the explanatory variables and $\\epsilon$ is zero\n",
    "4. the variance of $\\epsilon$ is constant (called *homoscedasticity*)\n",
    "5. there is no autocorrelation in $\\epsilon$\n",
    "6. there is no linear dependency between the explanatory variables $X$\n",
    "7. the residuals are normally distributed\n",
    "\n",
    "If assumptions 1 to 6 hold the linear regression model yields unbiased estimates (best linear unbiased estimator, BLUE).\n",
    "\n",
    "For conducting the significance tests ($F$- and $t$-test) assumption 7 needs to hold. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please refer to [*Backhaus et al (2017), p. 89ff*] for furter details on testing model assumptions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true,
    "toc-nb-collapsed": true
   },
   "source": [
    "## Non-linearity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A common misconception with linear regression is that the relation between $Y$ and $X$ needs to be linear. This is actually not the case. Assumption A1 only stipulates for linearity in the parameters. It is possible in many cases to transform non-linear relationships into linear relationships. \n",
    "\n",
    "Given the model \n",
    "\n",
    "$$Y = \\beta_0 + \\beta_1X + \\epsilon$$\n",
    "\n",
    "we can replace $X$ with $X' = f(X)$, where $f$ is a nonlinear function. The resulting model:\n",
    "\n",
    "$$Y = \\beta_0 + \\beta_1X' + \\epsilon$$\n",
    "\n",
    "is still linear in its parameters.\n",
    "\n",
    "The most common nonlinear transformations in using linear regression is the log-transformation. \n",
    "\n",
    "Remember that $$log(a) = b \\leftrightarrow a = e^b$$ \n",
    "\n",
    "\n",
    "We can distinguish between four model types:\n",
    "\n",
    "1. level-level model: $Y = \\beta_0 + \\beta_1X + \\epsilon$\n",
    "\n",
    "2. log-level model: $log_e(y) = \\beta_0 + \\beta_1X + \\epsilon$\n",
    "\n",
    "3. level-log model: $Y = \\beta_0 + \\beta_1log_e(X) + \\epsilon$\n",
    "\n",
    "4. log-log model: $log_e(y) = \\beta_0 + \\beta_1log_e(X) + \\epsilon$\n",
    "\n",
    "When using models 2 to 4 it is important that the interpretation of the coefficients differs from the *level-level* model. Interpretations are as follows:\n",
    "\n",
    "- log-level: increasing $X$ by one unit changes $Y$(on average and approximately) by $100 \\cdot \\beta_1\\%$\n",
    "\n",
    "- level-log: increasing $X$ by one percent, changes $Y$ (on average) by $\\beta_1/100$ units\n",
    "\n",
    "- log-log: increasing $X$ by one percent, changes $Y$ (on average) by $\\beta_1\\%$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to determine if it is helpful to transform data we should **inspect it visually**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 606,
   "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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration  year  \\\n",
       "0  18.0          8         307.0         130    3504          12.0    70   \n",
       "1  15.0          8         350.0         165    3693          11.5    70   \n",
       "2  18.0          8         318.0         150    3436          11.0    70   \n",
       "3  16.0          8         304.0         150    3433          12.0    70   \n",
       "4  17.0          8         302.0         140    3449          10.5    70   \n",
       "\n",
       "   origin                       name  \n",
       "0       1  chevrolet chevelle malibu  \n",
       "1       1          buick skylark 320  \n",
       "2       1         plymouth satellite  \n",
       "3       1              amc rebel sst  \n",
       "4       1                ford torino  "
      ]
     },
     "execution_count": 606,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 633,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 582.375x540 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = cars[[\"mpg\", \"horsepower\",\"acceleration\", \"origin\" ]] # let's take four variables and inspect them\n",
    "sns.pairplot(data,hue=\"origin\"); # show pair by pair plot for all variables, color indicates origin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that `mpg` and `horsepower` seems to be non-linear. \n",
    "\n",
    "We could therefore decide (and test) to transform one or both of the variables. \n",
    "\n",
    "Let's see how that works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 638,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = data[\"mpg\"], data[\"horsepower\"]\n",
    "fig, axes = plt.subplots(ncols=2, figsize=(9,7))\n",
    "ax1, ax2 = axes\n",
    "ax1.scatter(x,y), ax1.set_title(\"mpg vs. horsepower\")\n",
    "ax2.scatter(np.log(x), np.log(y)), ax2.set_title(\"log(mpg) vs. log(horsepower)\")\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run a regression analysis on both models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 639,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.606</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.605</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   599.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 12 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>7.03e-81</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>22:11:49</td>     <th>  Log-Likelihood:    </th> <td> -1178.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   392</td>      <th>  AIC:               </th> <td>   2361.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   390</td>      <th>  BIC:               </th> <td>   2369.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>  <td>   39.9359</td> <td>    0.717</td> <td>   55.660</td> <td> 0.000</td> <td>   38.525</td> <td>   41.347</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>horsepower</th> <td>   -0.1578</td> <td>    0.006</td> <td>  -24.489</td> <td> 0.000</td> <td>   -0.171</td> <td>   -0.145</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>16.432</td> <th>  Durbin-Watson:     </th> <td>   0.920</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  17.305</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.492</td> <th>  Prob(JB):          </th> <td>0.000175</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.299</td> <th>  Cond. No.          </th> <td>    322.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                    mpg   R-squared:                       0.606\n",
       "Model:                            OLS   Adj. R-squared:                  0.605\n",
       "Method:                 Least Squares   F-statistic:                     599.7\n",
       "Date:                Thu, 12 Nov 2020   Prob (F-statistic):           7.03e-81\n",
       "Time:                        22:11:49   Log-Likelihood:                -1178.7\n",
       "No. Observations:                 392   AIC:                             2361.\n",
       "Df Residuals:                     390   BIC:                             2369.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     39.9359      0.717     55.660      0.000      38.525      41.347\n",
       "horsepower    -0.1578      0.006    -24.489      0.000      -0.171      -0.145\n",
       "==============================================================================\n",
       "Omnibus:                       16.432   Durbin-Watson:                   0.920\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.305\n",
       "Skew:                           0.492   Prob(JB):                     0.000175\n",
       "Kurtosis:                       3.299   Cond. No.                         322.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 639,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"mpg ~ horsepower\", cars)\n",
    "ols1 = sm.OLS(y,X).fit()\n",
    "ols1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 640,
   "metadata": {},
   "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": [
    "yhat = ols1.fittedvalues\n",
    "plt.scatter(X[:,1],y)\n",
    "plt.plot(X[:,1],yhat, color=\"red\")\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 663,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>np.log(mpg)</td>   <th>  R-squared:         </th> <td>   0.723</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.722</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1016.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 12 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>1.13e-110</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>22:46:35</td>     <th>  Log-Likelihood:    </th> <td>  118.52</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   392</td>      <th>  AIC:               </th> <td>  -233.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   390</td>      <th>  BIC:               </th> <td>  -225.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>          <td>    6.9606</td> <td>    0.121</td> <td>   57.296</td> <td> 0.000</td> <td>    6.722</td> <td>    7.199</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>np.log(horsepower)</th> <td>   -0.8418</td> <td>    0.026</td> <td>  -31.881</td> <td> 0.000</td> <td>   -0.894</td> <td>   -0.790</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 6.244</td> <th>  Durbin-Watson:     </th> <td>   1.094</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.044</td> <th>  Jarque-Bera (JB):  </th> <td>   8.144</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.122</td> <th>  Prob(JB):          </th> <td>  0.0170</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.663</td> <th>  Cond. No.          </th> <td>    64.6</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:            np.log(mpg)   R-squared:                       0.723\n",
       "Model:                            OLS   Adj. R-squared:                  0.722\n",
       "Method:                 Least Squares   F-statistic:                     1016.\n",
       "Date:                Thu, 12 Nov 2020   Prob (F-statistic):          1.13e-110\n",
       "Time:                        22:46:35   Log-Likelihood:                 118.52\n",
       "No. Observations:                 392   AIC:                            -233.0\n",
       "Df Residuals:                     390   BIC:                            -225.1\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================\n",
       "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "Intercept              6.9606      0.121     57.296      0.000       6.722       7.199\n",
       "np.log(horsepower)    -0.8418      0.026    -31.881      0.000      -0.894      -0.790\n",
       "==============================================================================\n",
       "Omnibus:                        6.244   Durbin-Watson:                   1.094\n",
       "Prob(Omnibus):                  0.044   Jarque-Bera (JB):                8.144\n",
       "Skew:                          -0.122   Prob(JB):                       0.0170\n",
       "Kurtosis:                       3.663   Cond. No.                         64.6\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 663,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"np.log(mpg) ~ np.log(horsepower)\", cars)\n",
    "ols2 = sm.OLS(y,X).fit()\n",
    "ols2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 632,
   "metadata": {},
   "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": [
    "yhat = ols2.fittedvalues\n",
    "plt.scatter(X[:,1],y)\n",
    "plt.plot(X[:,1],yhat, color=\"red\")\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just looking at the two graphs we can see that the second model (log-log) seems to be better and capturing / explaining the deviation. We can also confirm this when looking at the $R^2$ value which is $72$% vs. $61$%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true,
    "toc-nb-collapsed": true
   },
   "source": [
    "## Interaction effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A special case of non-linearity occurs when we combine two or more variables multiplicatively. This may be necessary or feasible if one effect depends (or is conditional) on another effect. \n",
    "\n",
    "Let's return to our `advertisment` data set where we analyzed the causal relationship between `sales` and advertisment spent on `TV`,  `newspaper` and `radio`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 665,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>sales</td>      <th>  R-squared:         </th> <td>   0.897</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.896</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   859.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 12 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>4.83e-98</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>22:46:42</td>     <th>  Log-Likelihood:    </th> <td> -386.20</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>   778.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   197</td>      <th>  BIC:               </th> <td>   788.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>Intercept</th> <td>    2.9211</td> <td>    0.294</td> <td>    9.919</td> <td> 0.000</td> <td>    2.340</td> <td>    3.502</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TV</th>        <td>    0.0458</td> <td>    0.001</td> <td>   32.909</td> <td> 0.000</td> <td>    0.043</td> <td>    0.048</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>radio</th>     <td>    0.1880</td> <td>    0.008</td> <td>   23.382</td> <td> 0.000</td> <td>    0.172</td> <td>    0.204</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>60.022</td> <th>  Durbin-Watson:     </th> <td>   2.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 148.679</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.323</td> <th>  Prob(JB):          </th> <td>5.19e-33</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.292</td> <th>  Cond. No.          </th> <td>    425.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  sales   R-squared:                       0.897\n",
       "Model:                            OLS   Adj. R-squared:                  0.896\n",
       "Method:                 Least Squares   F-statistic:                     859.6\n",
       "Date:                Thu, 12 Nov 2020   Prob (F-statistic):           4.83e-98\n",
       "Time:                        22:46:42   Log-Likelihood:                -386.20\n",
       "No. Observations:                 200   AIC:                             778.4\n",
       "Df Residuals:                     197   BIC:                             788.3\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      2.9211      0.294      9.919      0.000       2.340       3.502\n",
       "TV             0.0458      0.001     32.909      0.000       0.043       0.048\n",
       "radio          0.1880      0.008     23.382      0.000       0.172       0.204\n",
       "==============================================================================\n",
       "Omnibus:                       60.022   Durbin-Watson:                   2.081\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              148.679\n",
       "Skew:                          -1.323   Prob(JB):                     5.19e-33\n",
       "Kurtosis:                       6.292   Cond. No.                         425.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 665,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = Datasets.advertising(dtype=\"pandas\", col=\"all\")\n",
    "y, X = dmatrices(\"sales ~ TV  + radio\", df)\n",
    "sales_model = sm.OLS(y,X).fit()\n",
    "sales_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model assumes that the effect of increasing advertisment spent in one medium (e.g. TV) is independent of the amount spent on the other media. The effect on `sales` of spending one additional unit on `TV` is always $\\beta_{tv}$ irrespective of the amount spent on e.g. `radio`. \n",
    "\n",
    "This assumption may be wrong and therefore the specified model may be incorrect.  For example, the amount spent on `radio` may actually  increase the effectiveness of `TV` advertisment. \n",
    "\n",
    "This synergy (or dysynergy) effect is referred to as **interaction effect** in statistics.  \n",
    "\n",
    "One way of incorporating this interaction effect into a regression model is to combine variables multiplicatively such that \n",
    "\n",
    "$$Y = \\beta_0 + \\beta_1X_1 + \\beta_2X_2 + \\beta_3X_1X_2 + \\epsilon$$\n",
    "\n",
    "This can be rearranged such that:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "Y &= \\beta_0 + (\\beta_1+\\beta_3X_2)X_1 + \\beta_2X_2 + \\epsilon \\\\ \n",
    "& =  \\beta_0 + \\tilde{\\beta}X_1 + \\beta_2X_2 + \\epsilon\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "In this case $\\tilde{\\beta}$ changes with $X_2$. Therefore, the effect of $X_1$ on $Y$ is no longer constant given that adjusting $X_2$ changes $X_1$ and $Y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at our dataset and include the interaction effect of `TV`x`radio`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 656,
   "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>Intercept</th>\n",
       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>TV:radio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>8697.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>1748.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>789.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>6256.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>1952.64</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Intercept     TV  radio  TV:radio\n",
       "0        1.0  230.1   37.8   8697.78\n",
       "1        1.0   44.5   39.3   1748.85\n",
       "2        1.0   17.2   45.9    789.48\n",
       "3        1.0  151.5   41.3   6256.95\n",
       "4        1.0  180.8   10.8   1952.64"
      ]
     },
     "execution_count": 656,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"sales ~ TV + radio + TV:radio\", df, return_type=\"dataframe\") # Note: TV:radio indicates that we want the interaction term\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 666,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>sales</td>      <th>  R-squared:         </th> <td>   0.897</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.896</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   859.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 12 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>4.83e-98</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>22:46:46</td>     <th>  Log-Likelihood:    </th> <td> -386.20</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>   778.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   197</td>      <th>  BIC:               </th> <td>   788.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>Intercept</th> <td>    2.9211</td> <td>    0.294</td> <td>    9.919</td> <td> 0.000</td> <td>    2.340</td> <td>    3.502</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TV</th>        <td>    0.0458</td> <td>    0.001</td> <td>   32.909</td> <td> 0.000</td> <td>    0.043</td> <td>    0.048</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>radio</th>     <td>    0.1880</td> <td>    0.008</td> <td>   23.382</td> <td> 0.000</td> <td>    0.172</td> <td>    0.204</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>60.022</td> <th>  Durbin-Watson:     </th> <td>   2.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 148.679</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.323</td> <th>  Prob(JB):          </th> <td>5.19e-33</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.292</td> <th>  Cond. No.          </th> <td>    425.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  sales   R-squared:                       0.897\n",
       "Model:                            OLS   Adj. R-squared:                  0.896\n",
       "Method:                 Least Squares   F-statistic:                     859.6\n",
       "Date:                Thu, 12 Nov 2020   Prob (F-statistic):           4.83e-98\n",
       "Time:                        22:46:46   Log-Likelihood:                -386.20\n",
       "No. Observations:                 200   AIC:                             778.4\n",
       "Df Residuals:                     197   BIC:                             788.3\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      2.9211      0.294      9.919      0.000       2.340       3.502\n",
       "TV             0.0458      0.001     32.909      0.000       0.043       0.048\n",
       "radio          0.1880      0.008     23.382      0.000       0.172       0.204\n",
       "==============================================================================\n",
       "Omnibus:                       60.022   Durbin-Watson:                   2.081\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              148.679\n",
       "Skew:                          -1.323   Prob(JB):                     5.19e-33\n",
       "Kurtosis:                       6.292   Cond. No.                         425.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 666,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.OLS(y,X).fit().summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the inclusion of the effedt increased $R^2_\\text{adj}$ significantly. Also the coefficient `TV:radio` ($\\beta_3$) is highly significant. \n",
    "\n",
    "Interpretation of $\\beta_3$: increase in effectiveness of TV advertisment on radio advertisment (or the other way around)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dealing with qualitative data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Up until now we have only worked with quantitative data, i.e. all variables in our models where numerical. However, this is not always the case. Explanatory variables can, of course, be qualitative. \n",
    "\n",
    "For example, in our cars dataset we have a variable `origin`. The variable stores the information from which region the car is (US = 1, Europe = 2, Asia = 3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 672,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 2])"
      ]
     },
     "execution_count": 672,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars[\"origin\"].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the data is already encoded to be numerical the information it stores is still qualitative. For example, we cannot compare the data similar to numerial data. There is no numerical order and the distances between the values do not mean anything, i.e. 3 is not bigger than 1 in this case or a statement such as Asia is two more than US does not make sense. \n",
    "\n",
    "**How do we deal with this kind of data in our regression model?**\n",
    "\n",
    "If we deal with two categories (male/female) we can simply create a *dummy variable* (0/1) of the form:\n",
    "\n",
    "\\begin{equation}\n",
    "  x_i =\\begin{cases}\n",
    "    1, & \\text{if $i$th person is female}\\\\\n",
    "    0, & \\text{if $i$th person is male}\n",
    "  \\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "This results in the model:\n",
    "\n",
    "\\begin{equation}\n",
    "  y_i = \\beta_0 + \\beta_1x_i + \\epsilon =\\begin{cases}\n",
    "    \\beta_0 + \\beta_1 + \\epsilon, & \\text{if $i$th person is female}\\\\\n",
    "    \\beta_0 + \\epsilon & \\text{if $i$th person is male}\n",
    "  \\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "If we deal with more than two categories we need to create additional *dummy variables*. For example in our case we need two variables of the form:\n",
    "\n",
    "\\begin{equation}\n",
    "  x_{i1} =\\begin{cases}\n",
    "    1, & \\text{if $i$th car is from US}\\\\\n",
    "    0, & \\text{if $i$th car is not from US}\n",
    "  \\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "and\\begin{equation}\n",
    "  x_{i2} =\\begin{cases}\n",
    "    1, & \\text{if $i$th car is from Asia}\\\\\n",
    "    0, & \\text{if $i$th car is not from Asia}\n",
    "  \\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "If we then use both variables in our model we can describe it as:\n",
    "\n",
    "\\begin{equation}\n",
    "  y_i = \\beta_0 + \\beta_1x_{i2} + \\beta_2x_{i2} + \\epsilon =\\begin{cases}\n",
    "    \\beta_0 + \\beta_1 + \\epsilon, & \\text{if $i$th car is from US }\\\\\n",
    "    \\beta_0 + \\beta_2 + \\epsilon & \\text{if $i$th car is from Asia}\\\\\n",
    "        \\beta_0  + \\epsilon & \\text{if $i$th car is from Europe}\n",
    "  \\end{cases}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at an example using our car dataset. \n",
    "\n",
    "If we treat the variable `origin` just as a regular numerial value, the regression model will not yield sensical results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 677,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.319</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.318</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   183.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 12 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>1.81e-34</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:10:02</td>     <th>  Log-Likelihood:    </th> <td> -1285.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   392</td>      <th>  AIC:               </th> <td>   2576.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   390</td>      <th>  BIC:               </th> <td>   2583.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   14.8120</td> <td>    0.716</td> <td>   20.676</td> <td> 0.000</td> <td>   13.404</td> <td>   16.220</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>origin</th>    <td>    5.4765</td> <td>    0.405</td> <td>   13.531</td> <td> 0.000</td> <td>    4.681</td> <td>    6.272</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>26.546</td> <th>  Durbin-Watson:     </th> <td>   0.829</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  30.323</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.678</td> <th>  Prob(JB):          </th> <td>2.60e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.138</td> <th>  Cond. No.          </th> <td>    4.93</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                    mpg   R-squared:                       0.319\n",
       "Model:                            OLS   Adj. R-squared:                  0.318\n",
       "Method:                 Least Squares   F-statistic:                     183.1\n",
       "Date:                Thu, 12 Nov 2020   Prob (F-statistic):           1.81e-34\n",
       "Time:                        23:10:02   Log-Likelihood:                -1285.8\n",
       "No. Observations:                 392   AIC:                             2576.\n",
       "Df Residuals:                     390   BIC:                             2583.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     14.8120      0.716     20.676      0.000      13.404      16.220\n",
       "origin         5.4765      0.405     13.531      0.000       4.681       6.272\n",
       "==============================================================================\n",
       "Omnibus:                       26.546   Durbin-Watson:                   0.829\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               30.323\n",
       "Skew:                           0.678   Prob(JB):                     2.60e-07\n",
       "Kurtosis:                       3.138   Cond. No.                         4.93\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 677,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"mpg ~ origin\", cars, return_type=\"dataframe\") # origin NOT encoded categorically using dummy variables\n",
    "sm.OLS(y,X).fit().summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It does not make sense to say that asian cars (encoded as 3) have an impact of $3\\times5.4765$ on mpg, whereas as US cars only have an impact of $1\\times5.4765$\n",
    "\n",
    "However, when encoding the variable as *dummy variable* the model itself is correctly specified and the interpretation is intuitive. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 686,
   "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>Intercept</th>\n",
       "      <th>C(origin)[T.2]</th>\n",
       "      <th>C(origin)[T.3]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Intercept  C(origin)[T.2]  C(origin)[T.3]\n",
       "0        1.0             0.0             0.0\n",
       "1        1.0             0.0             0.0\n",
       "2        1.0             0.0             0.0\n",
       "3        1.0             0.0             0.0\n",
       "4        1.0             0.0             0.0"
      ]
     },
     "execution_count": 686,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, X = dmatrices(\"mpg ~ C(origin)\", cars, return_type=\"dataframe\") # origin encoded categorically using C(origin) \n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 678,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.332</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.328</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   96.60</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 12 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>8.67e-35</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:12:38</td>     <th>  Log-Likelihood:    </th> <td> -1282.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   392</td>      <th>  AIC:               </th> <td>   2570.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   389</td>      <th>  BIC:               </th> <td>   2582.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>Intercept</th>      <td>   20.0335</td> <td>    0.409</td> <td>   49.025</td> <td> 0.000</td> <td>   19.230</td> <td>   20.837</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(origin)[T.2]</th> <td>    7.5695</td> <td>    0.877</td> <td>    8.634</td> <td> 0.000</td> <td>    5.846</td> <td>    9.293</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(origin)[T.3]</th> <td>   10.4172</td> <td>    0.828</td> <td>   12.588</td> <td> 0.000</td> <td>    8.790</td> <td>   12.044</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>26.330</td> <th>  Durbin-Watson:     </th> <td>   0.763</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  30.217</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.679</td> <th>  Prob(JB):          </th> <td>2.74e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.066</td> <th>  Cond. No.          </th> <td>    3.16</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                    mpg   R-squared:                       0.332\n",
       "Model:                            OLS   Adj. R-squared:                  0.328\n",
       "Method:                 Least Squares   F-statistic:                     96.60\n",
       "Date:                Thu, 12 Nov 2020   Prob (F-statistic):           8.67e-35\n",
       "Time:                        23:12:38   Log-Likelihood:                -1282.2\n",
       "No. Observations:                 392   AIC:                             2570.\n",
       "Df Residuals:                     389   BIC:                             2582.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==================================================================================\n",
       "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------\n",
       "Intercept         20.0335      0.409     49.025      0.000      19.230      20.837\n",
       "C(origin)[T.2]     7.5695      0.877      8.634      0.000       5.846       9.293\n",
       "C(origin)[T.3]    10.4172      0.828     12.588      0.000       8.790      12.044\n",
       "==============================================================================\n",
       "Omnibus:                       26.330   Durbin-Watson:                   0.763\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               30.217\n",
       "Skew:                           0.679   Prob(JB):                     2.74e-07\n",
       "Kurtosis:                       3.066   Cond. No.                         3.16\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 678,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.OLS(y,X).fit().summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How do we interpret the model results?** \n",
    "\n",
    "The model yields two coefficients (besides the intercept):\n",
    "\n",
    "- coefficient for `origin=2` is $7.57$\n",
    "- coefficient for `origin=3` is $10.42$\n",
    "\n",
    "They can be interpreted as follows. \n",
    "\n",
    "- the fact that the car is European (ceteris paribus) increases mpg by $7.57$\n",
    "- the fact that the car is Asian (ceteris paribus) increases mpg by $10.42$\n",
    "- the US case is not modelled explicitly but we can deduct that the mpg for US cars is $7.57$ lower compared to European cars and $10.42$ lower compared to Asian cars (on average)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Creating dummy variables**\n",
    "\n",
    "We have created dummy variables using `C(origin)` (C stands for categorical data). We can also do this (i) manually or (ii) using pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 685,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Intercept</th>\n",
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       "      <th>387</th>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>388</th>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>392 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Intercept  European  Asia\n",
       "0          1.0         0     0\n",
       "1          1.0         0     0\n",
       "2          1.0         0     0\n",
       "3          1.0         0     0\n",
       "4          1.0         0     0\n",
       "..         ...       ...   ...\n",
       "387        1.0         0     0\n",
       "388        1.0         1     0\n",
       "389        1.0         0     0\n",
       "390        1.0         0     0\n",
       "391        1.0         0     0\n",
       "\n",
       "[392 rows x 3 columns]"
      ]
     },
     "execution_count": 685,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# manually:\n",
    "y, X = dmatrices(\"mpg ~ origin\", cars, return_type=\"dataframe\")\n",
    "origin = X[\"origin\"]\n",
    "X[\"European\"] = np.where(origin == 2, 1, 0)\n",
    "X[\"Asia\"] = np.where(origin == 3, 1, 0)\n",
    "X = X.drop(labels=\"origin\", axis=1)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 689,
   "metadata": {},
   "outputs": [
    {
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       "      <th>2.0</th>\n",
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       "  </thead>\n",
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       "      <th>2</th>\n",
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       "      <th>4</th>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>389</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <th>390</th>\n",
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       "      <td>0</td>\n",
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       "      <th>391</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>392 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     2.0  3.0\n",
       "0      0    0\n",
       "1      0    0\n",
       "2      0    0\n",
       "3      0    0\n",
       "4      0    0\n",
       "..   ...  ...\n",
       "387    0    0\n",
       "388    1    0\n",
       "389    0    0\n",
       "390    0    0\n",
       "391    0    0\n",
       "\n",
       "[392 rows x 2 columns]"
      ]
     },
     "execution_count": 689,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using pandas\n",
    "pd.get_dummies(origin, drop_first=True)"
   ]
  }
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