Introduction to Regression with statsmodels in Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regressions and Logistic Regressions\n",
    "\n",
    "> A Summary of lecture \"Linear Regressions & Logistic Regressions in Python\", via datacamp\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "\n",
    "For now, limited to 1 explanatory (independent) variable to explain the response (numeric or categorical/logical)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which one is the response variable?\n",
    "Regression lets you predict the values of a response variable from known values of explanatory variables. Which variable you use as the response variable depends on the question you are trying to answer, but in many datasets there will be an obvious choice for variables that would be interesting to predict. Over the next few exercises, you'll explore a Taiwan real estate dataset with four variables.\n",
    "\n",
    "Variable\tMeaning\n",
    "dist_to_mrt_station_m\tDistance to nearest MRT metro station, in meters.\n",
    "n_convenience\tNo. of convenience stores in walking distance.\n",
    "house_age_years\tThe age of the house, in years, in three groups.\n",
    "price_twd_msq\tHouse price per unit area, in New Taiwan dollars per meter squared.\n",
    "Print taiwan_real_estate in the console to view the dataset, and decide which variable would make a good response variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing two numeric variables\n",
    "Before you can run any statistical models, it's usually a good idea to visualize your dataset. Here, you'll look at the relationship between house price per area and the number of nearby convenience stores using the Taiwan real estate dataset.\n",
    "\n",
    "One challenge in this dataset is that the number of convenience stores contains integer data, causing points to overlap. To solve this, you will make the points transparent.\n",
    "\n",
    "taiwan_real_estate is available as a pandas DataFrame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Processing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   dist_to_mrt_m  n_convenience house_age_years  price_twd_msq\n",
      "0       84.87882             10        30 to 45      11.467474\n",
      "1      306.59470              9        15 to 30      12.768533\n",
      "2      561.98450              5         0 to 15      14.311649\n",
      "3      561.98450              5         0 to 15      16.580938\n",
      "4      390.56840              5         0 to 15      13.040847\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import sys, os\n",
    "import seaborn as sns\n",
    "from matplotlib import rcParams\n",
    "\n",
    "sns.set(rc = {'figure.figsize':(11.7,7.27)})\n",
    "rcParams['figure.figsize'] = 11.7,7.27\n",
    "sns.set_style(\"dark\")\n",
    "\n",
    "path = 'C:/Users/T0230575/source/repos/DataCamp__/Python/_data'\n",
    "os.chdir(path)\n",
    "taiwan_real_estate = pd.read_csv('taiwan_real_estate2.csv')\n",
    "print(taiwan_real_estate.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import seaborn with alias sns\n",
    "import seaborn as sns\n",
    "\n",
    "# Import matplotlib.pyplot with alias plt\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Draw the scatter plot\n",
    "sns.scatterplot(x=\"n_convenience\",\n",
    "                y=\"price_twd_msq\",\n",
    "                data=taiwan_real_estate)\n",
    "\n",
    "# Plot it\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing two numeric variables\n",
    "Before you can run any statistical models, it's usually a good idea to visualize your dataset. Here, you'll look at the relationship between house price per area and the number of nearby convenience stores using the Taiwan real estate dataset.\n",
    "\n",
    "One challenge in this dataset is that the number of convenience stores contains integer data, causing points to overlap. To solve this, you will make the points transparent.\n",
    "\n",
    "taiwan_real_estate is available as a pandas DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import seaborn with alias sns\n",
    "import seaborn as sns\n",
    "\n",
    "# Import matplotlib.pyplot with alias plt\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Draw the scatter plot\n",
    "sns.scatterplot(x=\"n_convenience\",\n",
    "                y=\"price_twd_msq\",\n",
    "                data=taiwan_real_estate)\n",
    "\n",
    "# Draw a trend line on the scatter plot of n_convenience vs. price_twd_msq\n",
    "sns.regplot(x=\"n_convenience\", \n",
    "y=\"price_twd_msq\",\n",
    "         data=taiwan_real_estate,\n",
    "         ci=False,\n",
    "         scatter_kws={'alpha': 0.5})\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scatter plots are the standard way to visualize the relationship between two numeric variables, and seaborn makes adding linear trend lines easy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear regression with ols()\n",
    "\n",
    "While sns.regplot() can display a linear regression trend line, it doesn't give you access to the intercept and slope as variables, or allow you to work with the model results as variables. That means that sometimes you'll need to run a linear regression yourself.\n",
    "\n",
    "Time to run your first model!\n",
    "\n",
    "taiwan_real_estate is available. TWD is an abbreviation for Taiwan dollars.\n",
    "\n",
    "In addition, for this exercise and the remainder of the course, the following packages will be imported and aliased if necessary: matplotlib.pyplot as plt, seaborn as sns, and pandas as pd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept        8.224237\n",
      "n_convenience    0.798080\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Import the ols function\n",
    "from statsmodels.formula.api import ols\n",
    "\n",
    "# Create the model object\n",
    "mdl_price_vs_conv = ols('price_twd_msq ~ n_convenience', data=taiwan_real_estate)\n",
    "\n",
    "# Fit the model\n",
    "mdl_price_vs_conv = mdl_price_vs_conv.fit()\n",
    "\n",
    "# Print the parameters of the fitted model\n",
    "print(mdl_price_vs_conv.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question\n",
    "The model had an Intercept coefficient of 8.2242. What does this mean?\n",
    "On average, a house with zero convenience stores nearby had a price of 8.2242 TWD per square meter.\n",
    "\n",
    "The model had an n_convenience coefficient of 0.7981. What does this mean?\n",
    "If you increase the number of nearby convenience stores by one, then the expected increase in house price is 0.7981 TWD per square meter.\n",
    "\n",
    "The intercept is positive, so a house with no convenience stores nearby still has a positive price. The coefficient for convenience stores is also positive, so as the number of nearby convenience stores increases, so does the price of the house."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing numeric vs. categorical\n",
    "\n",
    "If the explanatory variable is categorical, the scatter plot that you used before to visualize the data doesn't make sense. Instead, a good option is to draw a histogram for each category.\n",
    "\n",
    "The Taiwan real estate dataset has a categorical variable in the form of the age of each house. The ages have been split into 3 groups: 0 to 15 years, 15 to 30 years, and 30 to 45 years.\n",
    "\n",
    "taiwan_real_estate is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   dist_to_mrt_m  n_convenience house_age_years  price_twd_msq\n",
      "0       84.87882             10        30 to 45      11.467474\n",
      "1      306.59470              9        15 to 30      12.768533\n",
      "2      561.98450              5         0 to 15      14.311649\n",
      "3      561.98450              5         0 to 15      16.580938\n",
      "4      390.56840              5         0 to 15      13.040847\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histograms of price_twd_msq with 10 bins, split by the age of each house\n",
    "print(taiwan_real_estate.head())\n",
    "\n",
    "sns.distplot(taiwan_real_estate['price_twd_msq'],\n",
    "             color = None, #can insert here any categorical to facet~\n",
    "             bins = 10)\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " It appears that new houses are the most expensive on average, and the medium aged ones (15 to 30 years) are the cheapest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating means by category\n",
    "\n",
    "A good way to explore categorical variables further is to calculate summary statistics for each category. For example, you can calculate the mean and median of your response variable, grouped by a categorical variable. As such, you can compare each category in more detail.\n",
    "\n",
    "Here, you'll look at grouped means for the house prices in the Taiwan real estate dataset. This will help you understand the output of a linear regression with a categorical variable.\n",
    "\n",
    "taiwan_real_estate is available as a pandas DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "house_age_years\n",
      "0 to 15     12.637471\n",
      "15 to 30     9.876743\n",
      "30 to 45    11.393264\n",
      "Name: price_twd_msq, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Calculate the mean of price_twd_msq, grouped by house age\n",
    "mean_price_by_age = taiwan_real_estate.groupby('house_age_years')['price_twd_msq'].mean()\n",
    "\n",
    "# Print the result\n",
    "print(mean_price_by_age)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear regression with a categorical explanatory variable\n",
    "\n",
    "Great job calculating those grouped means! As mentioned in the last video, the means of each category will also be the coefficients of a linear regression model with one categorical variable. You'll prove that in this exercise.\n",
    "\n",
    "To run a linear regression model with categorical explanatory variables, you can just use the same code as with numeric explanatory variables. The coefficients returned by the model are different however. Here you'll run a linear regression on the Taiwan real estate dataset.\n",
    "\n",
    "taiwan_real_estate is available and the ols() function is also loaded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept                      12.637471\n",
      "house_age_years[T.15 to 30]    -2.760728\n",
      "house_age_years[T.30 to 45]    -1.244207\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Create the model, fit it\n",
    "mdl_price_vs_age = ols('price_twd_msq~house_age_years', data=taiwan_real_estate).fit()\n",
    "\n",
    "# Print the parameters of the fitted model\n",
    "print(mdl_price_vs_age.params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "house_age_years[0 to 15]     12.637471\n",
      "house_age_years[15 to 30]     9.876743\n",
      "house_age_years[30 to 45]    11.393264\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Update the model formula to remove the intercept\n",
    "mdl_price_vs_age0 = ols(\"price_twd_msq ~ house_age_years +0\", data=taiwan_real_estate).fit()\n",
    "\n",
    "# Print the parameters of the fitted model\n",
    "print(mdl_price_vs_age0.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients of the model are just the means of each category you calculated previously. Fantastic job!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting house prices\n",
    "\n",
    "Perhaps the most useful feature of statistical models like linear regression is that you can make predictions. That is, you specify values for each of the explanatory variables, feed them to the model, and you get a prediction for the corresponding response variable. The code flow is as follows.\n",
    "\n",
    "``\n",
    "explanatory_data = pd.DataFrame({\"explanatory_var\": list_of_values})\n",
    "predictions = model.predict(explanatory_data)\n",
    "prediction_data = explanatory_data.assign(response_var=predictions)\n",
    "``\n",
    "\n",
    "Here, you'll make predictions for the house prices in the Taiwan real estate dataset.\n",
    "\n",
    "taiwan_real_estate is available. The fitted linear regression model of house price versus number of convenience stores is available as mdl_price_vs_conv. For future exercises, when a model is available, it will also be fitted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    n_convenience  price_twd_msq\n",
      "0               0       8.224237\n",
      "1               1       9.022317\n",
      "2               2       9.820397\n",
      "3               3      10.618477\n",
      "4               4      11.416556\n",
      "5               5      12.214636\n",
      "6               6      13.012716\n",
      "7               7      13.810795\n",
      "8               8      14.608875\n",
      "9               9      15.406955\n",
      "10             10      16.205035\n"
     ]
    }
   ],
   "source": [
    "# Import numpy with alias np\n",
    "import numpy as np\n",
    "\n",
    "# Create explanatory_data \n",
    "explanatory_data = pd.DataFrame({'n_convenience': np.arange(0, 11)})\n",
    "\n",
    "# Use mdl_price_vs_conv to predict with explanatory_data, call it price_twd_msq\n",
    "price_twd_msq = mdl_price_vs_conv.predict(explanatory_data)\n",
    "\n",
    "# Create prediction_data\n",
    "prediction_data = explanatory_data.assign(\n",
    "    price_twd_msq = price_twd_msq)\n",
    "\n",
    "# Print the result\n",
    "print(prediction_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing predictions\n",
    "\n",
    "The prediction DataFrame you created contains a column of explanatory variable values and a column of response variable values. That means you can plot it on the same scatter plot of response versus explanatory data values.\n",
    "\n",
    "prediction_data is available. The code for the plot you created using sns.regplot() in Chapter 1 is shown."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a new figure, fig\n",
    "fig = plt.figure()\n",
    "\n",
    "sns.regplot(x=\"n_convenience\",\n",
    "            y=\"price_twd_msq\",\n",
    "            data=taiwan_real_estate,\n",
    "            ci=None)\n",
    "# Add a scatter plot layer to the regplot\n",
    "sns.scatterplot(x=\"n_convenience\", y=\"price_twd_msq\",data=prediction_data, color=\"yellow\", alpha=1)\n",
    "\n",
    "# Show the layered plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The limits of prediction\n",
    "\n",
    "In the last exercise, you made predictions on some sensible, could-happen-in-real-life, situations. That is, the cases when the number of nearby convenience stores were between zero and ten. To test the limits of the model's ability to predict, try some impossible situations.\n",
    "\n",
    "Use the console to try predicting house prices from mdl_price_vs_conv when there are -1 convenience stores. Do the same for 2.5 convenience stores. What happens in each case?\n",
    "\n",
    "mdl_price_vs_conv is available."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Processing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a DataFrame impossible\n",
    "impossible = pd.DataFrame({\"n_convenience\": [-1, 2.5]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question\n",
    "Try making predictions on your two impossible cases. What happens?\n",
    "The model successfully gives a prediction about cases that are impossible in real life.\n",
    "Linear models don't know what is possible or not in real life. That means that they can give you predictions that don't make any sense when applied to your data. You need to understand what your data means in order to determine whether a prediction is nonsense or not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extracting model elements\n",
    "\n",
    "The model object created by ols() contains many elements. In order to perform further analysis on the model results, you need to extract its useful bits. The model coefficients, the fitted values, and the residuals are perhaps the most important pieces of the linear model object.\n",
    "\n",
    "mdl_price_vs_conv is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<statsmodels.regression.linear_model.RegressionResultsWrapper object at 0x000001469C5652B0>\n",
      "Intercept        8.224237\n",
      "n_convenience    0.798080\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Print the model parameters of mdl_price_vs_conv\n",
    "print(mdl_price_vs_conv)\n",
    "print(mdl_price_vs_conv.params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    16.205035\n",
      "1    15.406955\n",
      "2    12.214636\n",
      "3    12.214636\n",
      "4    12.214636\n",
      "5    10.618477\n",
      "6    13.810795\n",
      "7    13.012716\n",
      "8     9.022317\n",
      "9    10.618477\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Print the fitted values of mdl_price_vs_conv\n",
    "# head(n=10)\n",
    "\n",
    "print(mdl_price_vs_conv.fittedvalues.head(n=10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0   -4.737561\n",
      "1   -2.638422\n",
      "2    2.097013\n",
      "3    4.366302\n",
      "4    0.826211\n",
      "5   -0.905920\n",
      "6   -1.617149\n",
      "7    1.117390\n",
      "8   -3.333966\n",
      "9   -3.931638\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Print the residuals of mdl_price_vs_conv\n",
    "# head(n=10)\n",
    "\n",
    "print(mdl_price_vs_conv.resid.head(n=10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:          price_twd_msq   R-squared:                       0.326\n",
      "Model:                            OLS   Adj. R-squared:                  0.324\n",
      "Method:                 Least Squares   F-statistic:                     199.3\n",
      "Date:                Thu, 15 Apr 2021   Prob (F-statistic):           3.41e-37\n",
      "Time:                        17:22:19   Log-Likelihood:                -1091.1\n",
      "No. Observations:                 414   AIC:                             2186.\n",
      "Df Residuals:                     412   BIC:                             2194.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=================================================================================\n",
      "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "Intercept         8.2242      0.285     28.857      0.000       7.664       8.784\n",
      "n_convenience     0.7981      0.057     14.118      0.000       0.687       0.909\n",
      "==============================================================================\n",
      "Omnibus:                      171.927   Durbin-Watson:                   1.993\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1417.242\n",
      "Skew:                           1.553   Prob(JB):                    1.78e-308\n",
      "Kurtosis:                      11.516   Cond. No.                         8.87\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Print a summary of mdl_price_vs_conv\n",
    "print(mdl_price_vs_conv.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Working with individual pieces of the model is often more useful than working with the whole model object at once."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Manually predicting house prices\n",
    "\n",
    "You can manually calculate the predictions from the model coefficients. When making predictions in real life, it is better to use .predict(), but doing this manually is helpful to reassure yourself that predictions aren't magic - they are simply arithmetic.\n",
    "\n",
    "In fact, for a simple linear regression, the predicted value is just the intercept plus the slope times the explanatory variable.\n",
    "\n",
    "```\n",
    "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\n",
    "  <mtext>response</mtext>\n",
    "  <mo>=</mo>\n",
    "  <mtext>intercept</mtext>\n",
    "  <mo>+</mo>\n",
    "  <mtext>slope</mtext>\n",
    "  <mo>&#x2217;</mo>\n",
    "  <mtext>explanatory</mtext>\n",
    "</math>\n",
    "```\n",
    "\n",
    "mdl_price_vs_conv and explanatory_data are available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    n_convenience\n",
      "0        8.224237\n",
      "1        9.022317\n",
      "2        9.820397\n",
      "3       10.618477\n",
      "4       11.416556\n",
      "5       12.214636\n",
      "6       13.012716\n",
      "7       13.810795\n",
      "8       14.608875\n",
      "9       15.406955\n",
      "10      16.205035\n",
      "    n_convenience  predictions_auto\n",
      "0        8.224237          8.224237\n",
      "1        9.022317          9.022317\n",
      "2        9.820397          9.820397\n",
      "3       10.618477         10.618477\n",
      "4       11.416556         11.416556\n",
      "5       12.214636         12.214636\n",
      "6       13.012716         13.012716\n",
      "7       13.810795         13.810795\n",
      "8       14.608875         14.608875\n",
      "9       15.406955         15.406955\n",
      "10      16.205035         16.205035\n"
     ]
    }
   ],
   "source": [
    "# Get the coefficients of mdl_price_vs_conv\n",
    "coeffs = mdl_price_vs_conv.params\n",
    "\n",
    "# Get the intercept\n",
    "intercept = coeffs[0]\n",
    "\n",
    "# Get the slope\n",
    "slope = coeffs[1]\n",
    "\n",
    "# Manually calculate the predictions\n",
    "price_twd_msq = intercept + slope * explanatory_data\n",
    "print(price_twd_msq)\n",
    "\n",
    "# Compare to the results from .predict()\n",
    "print(price_twd_msq.assign(predictions_auto=mdl_price_vs_conv.predict(explanatory_data)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that a response value is always a fitted value + a residual (stuff explained + stuff that we couldn't explain).\n",
    "Residuals exist because model is not perfect and there is randomness in data. Extreme responses are often due to luck, luck can run out, and extreme cases will look more like mean cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression to the mean (for extreme values)\n",
    "### Home run!\n",
    "\n",
    "Regression to the mean is an important concept in many areas, including sports.\n",
    "\n",
    "Here you can see a dataset of baseball batting data in 2017 and 2018. Each point represents a player, and more home runs are better. A naive prediction might be that the performance in 2018 would be that it is the same as the performance in 2017. That is, a linear regression would lie on the \"y equals x\" line.\n",
    "\n",
    "Explore the plot and make predictions. What does regression to the mean say about the number of home runs in 2018 for a player who was very successful in 2017?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to regression to the mean, it's common that one player or team that does really well one year, doesn't do as well the next. Likewise players or teams that perform very badly one year do better the next year."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting consecutive portfolio returns\n",
    "\n",
    "Regression to the mean is also an important concept in investing. Here you'll look at the annual returns from investing in companies in the Standard and Poor 500 index (S&P 500), in 2018 and 2019.\n",
    "\n",
    "The sp500_yearly_returns dataset contains three columns:\n",
    "A positive number for the return means the investment increased in value; negative means it lost value.\n",
    "\n",
    "Just as with baseball home runs, a naive prediction might be that the investment performance stays the same from year to year, lying on the y equals x line.\n",
    "\n",
    "sp500_yearly_returns is available as a pandas DataFrame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pre-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp500_yearly_returns = pd.read_csv('sp500_yearly_returns.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a new figure, fig\n",
    "from matplotlib import pyplot as plt\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure()\n",
    "# Plot the first layer: y = x\n",
    "plt.axhline(y=0, linewidth=2, color=\"green\")\n",
    "plt.axvline(x=0, linewidth=2, color=\"yellow\")\n",
    "\n",
    "# Add scatter plot with linear regression trend line\n",
    "sns.regplot(x=\"return_2018\", y=\"return_2019\", data=sp500_yearly_returns, ci=None)\n",
    "\n",
    "# Set the axes so that the distances along the x and y axes look the same\n",
    "plt.axis(\"equal\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regression trend line looks very different to the y equals x line. As the financial advisors say, \"Past performance is no guarantee of future results.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept      0.321321\n",
      "return_2018    0.020069\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Run a linear regression on return_2019 vs. return_2018\n",
    "# using sp500_yearly_returns\n",
    "mdl_returns = ols(\"return_2019 ~ return_2018\", data=sp500_yearly_returns).fit()\n",
    "\n",
    "# Print the parameters\n",
    "print(mdl_returns.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modeling consecutive returns\n",
    "\n",
    "Let's quantify the relationship between returns in 2019 and 2018 by running a linear regression and making predictions. By looking at companies with extremely high or extremely low returns in 2018, we can see if their performance was similar in 2019.\n",
    "\n",
    "sp500_yearly_returns is available and ols() is loaded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    0.301251\n",
      "1    0.321321\n",
      "2    0.341390\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# From previous step\n",
    "mdl_returns = ols(\"return_2019 ~ return_2018\", data=sp500_yearly_returns).fit()\n",
    "\n",
    "# Create a DataFrame with return_2018 at -1, 0, and 1 \n",
    "explanatory_data = pd.DataFrame({\"return_2018\": [-1, 0, 1]})\n",
    "\n",
    "# Use mdl_returns to predict with explanatory_data\n",
    "print(mdl_returns.predict(explanatory_data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Investments that gained a lot in value in 2018 on average gained only a small amount in 2019. Similarly, investments that lost a lot of value in 2018 on average also gained a small amount in 2019."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transforming variables before modeling\n",
    "\n",
    "A solution to model data better, before adapting the model, is often to better understand and transform the data first if necessary (cube, square, log, exp, etc)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transforming the explanatory variable\n",
    "\n",
    "If there is no straight line relationship between the response variable and the explanatory variable, it is sometimes possible to create one by transforming one or both of the variables. Here, you'll look at transforming the explanatory variable.\n",
    "\n",
    "You'll take another look at the Taiwan real estate dataset, this time using the distance to the nearest MRT (metro) station as the explanatory variable. You'll use code to make every commuter's dream come true: shortening the distance to the metro station by taking the square root. Take that, geography!\n",
    "\n",
    "taiwan_real_estate is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Clear the plot\n",
    "plt.figure()\n",
    "\n",
    "\n",
    "# Plot using the transformed variable\n",
    "sns.regplot(x='dist_to_mrt_m', y = 'price_twd_msq', data=taiwan_real_estate)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now we sqrt() the explanatory variable\n",
    "\n",
    "# Create sqrt_dist_to_mrt_m\n",
    "taiwan_real_estate[\"sqrt_dist_to_mrt_m\"] = np.sqrt(taiwan_real_estate[\"dist_to_mrt_m\"])\n",
    "\n",
    "# Clear the plot\n",
    "plt.figure()\n",
    "\n",
    "# Plot using the transformed variable\n",
    "sns.regplot(x='sqrt_dist_to_mrt_m', y = 'price_twd_msq', data=taiwan_real_estate)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept             16.709799\n",
      "sqrt_dist_to_mrt_m    -0.182843\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Create sqrt_dist_to_mrt_m\n",
    "taiwan_real_estate[\"sqrt_dist_to_mrt_m\"] = np.sqrt(taiwan_real_estate[\"dist_to_mrt_m\"])\n",
    "\n",
    "# Run a linear regression of price_twd_msq vs. \n",
    "# square root of dist_to_mrt_m using taiwan_real_estate\n",
    "mdl_price_vs_dist = ols('price_twd_msq ~ sqrt_dist_to_mrt_m', data=taiwan_real_estate).fit()\n",
    "\n",
    "# Print the parameters\n",
    "print(mdl_price_vs_dist.params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   sqrt_dist_to_mrt_m  dist_to_mrt_m  price_twd_msq\n",
      "0                 0.0              0      16.709799\n",
      "1                10.0            100      14.881370\n",
      "2                20.0            400      13.052942\n",
      "3                30.0            900      11.224513\n",
      "4                40.0           1600       9.396085\n",
      "5                50.0           2500       7.567656\n",
      "6                60.0           3600       5.739227\n",
      "7                70.0           4900       3.910799\n",
      "8                80.0           6400       2.082370\n"
     ]
    }
   ],
   "source": [
    "# Create sqrt_dist_to_mrt_m\n",
    "taiwan_real_estate[\"sqrt_dist_to_mrt_m\"] = np.sqrt(taiwan_real_estate[\"dist_to_mrt_m\"])\n",
    "\n",
    "# Run a linear regression of price_twd_msq vs. sqrt_dist_to_mrt_m\n",
    "mdl_price_vs_dist = ols(\"price_twd_msq ~ sqrt_dist_to_mrt_m\", data=taiwan_real_estate).fit()\n",
    "\n",
    "# Use this explanatory data\n",
    "explanatory_data = pd.DataFrame({\"sqrt_dist_to_mrt_m\": np.sqrt(np.arange(0, 81, 10) ** 2),\n",
    "                                \"dist_to_mrt_m\": np.arange(0, 81, 10) ** 2})\n",
    "\n",
    "# Use mdl_price_vs_dist to predict explanatory_data\n",
    "price_twd_msq = mdl_price_vs_dist.predict(explanatory_data)\n",
    "prediction_data = explanatory_data.assign(\n",
    "    price_twd_msq = price_twd_msq)\n",
    "# See the result\n",
    "print(prediction_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create sqrt_dist_to_mrt_m\n",
    "taiwan_real_estate[\"sqrt_dist_to_mrt_m\"] = np.sqrt(taiwan_real_estate[\"dist_to_mrt_m\"])\n",
    "\n",
    "# Run a linear regression of price_twd_msq vs. sqrt_dist_to_mrt_m\n",
    "mdl_price_vs_dist = ols(\"price_twd_msq ~ sqrt_dist_to_mrt_m\", data=taiwan_real_estate).fit()\n",
    "\n",
    "# Use this explanatory data\n",
    "explanatory_data = pd.DataFrame({\"sqrt_dist_to_mrt_m\": np.sqrt(np.arange(0, 81, 10) ** 2),\n",
    "                                \"dist_to_mrt_m\": np.arange(0, 81, 10) ** 2})\n",
    "\n",
    "# Use mdl_price_vs_dist to predict explanatory_data\n",
    "prediction_data = explanatory_data.assign(\n",
    "    price_twd_msq = mdl_price_vs_dist.predict(explanatory_data)\n",
    ")\n",
    "\n",
    "fig = plt.figure()\n",
    "sns.regplot(x=\"sqrt_dist_to_mrt_m\", y=\"price_twd_msq\", data=taiwan_real_estate, ci=None)\n",
    "\n",
    "# Add a layer of your prediction points\n",
    "sns.scatterplot(x='sqrt_dist_to_mrt_m', y='price_twd_msq', data=prediction_data, color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By transforming the explanatory variable, the relationship with the response variable became linear, and so a linear regression became an appropriate model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transforming the response variable too\n",
    "\n",
    "The response variable can be transformed too, but this means you need an extra step at the end to undo that transformation. That is, you \"back transform\" the predictions.\n",
    "\n",
    "In the video, you saw the first step of the digital advertising workflow: spending money to buy ads, and counting how many people see them (the \"impressions\"). The next step is determining how many people click on the advert after seeing it.\n",
    "\n",
    "ad_conversion is available as a pandas DataFrame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pre-processing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [],
   "source": [
    "ad_conversion = pd.read_csv('ad_conversion.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create qdrt_n_impressions and qdrt_n_clicks\n",
    "ad_conversion[\"qdrt_n_impressions\"] = ad_conversion['n_impressions'] ** 0.25\n",
    "ad_conversion[\"qdrt_n_clicks\"] = ad_conversion['n_clicks'] ** 0.25\n",
    "\n",
    "# Clear the previous plot\n",
    "plt.figure()\n",
    "\n",
    "# Plot using the transformed variables\n",
    "sns.regplot(x='qdrt_n_impressions', y='qdrt_n_clicks', data=ad_conversion)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:          qdrt_n_clicks   R-squared:                       0.945\n",
      "Model:                            OLS   Adj. R-squared:                  0.944\n",
      "Method:                 Least Squares   F-statistic:                 1.590e+04\n",
      "Date:                Thu, 15 Apr 2021   Prob (F-statistic):               0.00\n",
      "Time:                        17:22:22   Log-Likelihood:                 193.90\n",
      "No. Observations:                 936   AIC:                            -383.8\n",
      "Df Residuals:                     934   BIC:                            -374.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept              0.0717      0.017      4.171      0.000       0.038       0.106\n",
      "qdrt_n_impressions     0.1115      0.001    126.108      0.000       0.110       0.113\n",
      "==============================================================================\n",
      "Omnibus:                       11.447   Durbin-Watson:                   0.568\n",
      "Prob(Omnibus):                  0.003   Jarque-Bera (JB):               10.637\n",
      "Skew:                          -0.216   Prob(JB):                      0.00490\n",
      "Kurtosis:                       2.707   Cond. No.                         52.1\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# From previous step\n",
    "ad_conversion[\"qdrt_n_impressions\"] = ad_conversion[\"n_impressions\"] ** 0.25\n",
    "ad_conversion[\"qdrt_n_clicks\"] = ad_conversion[\"n_clicks\"] ** 0.25\n",
    "\n",
    "# Run a linear regression of your transformed variables\n",
    "mdl_click_vs_impression = ols('qdrt_n_clicks ~ qdrt_n_impressions', data=ad_conversion).fit()\n",
    "print(mdl_click_vs_impression.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   qdrt_n_impressions  n_impressions  qdrt_n_clicks\n",
      "0            0.000000            0.0       0.071748\n",
      "1           26.591479       500000.0       3.037576\n",
      "2           31.622777      1000000.0       3.598732\n",
      "3           34.996355      1500000.0       3.974998\n",
      "4           37.606031      2000000.0       4.266063\n",
      "5           39.763536      2500000.0       4.506696\n",
      "6           41.617915      3000000.0       4.713520\n"
     ]
    }
   ],
   "source": [
    "# From previous steps\n",
    "ad_conversion[\"qdrt_n_impressions\"] = ad_conversion[\"n_impressions\"] ** 0.25\n",
    "ad_conversion[\"qdrt_n_clicks\"] = ad_conversion[\"n_clicks\"] ** 0.25\n",
    "\n",
    "mdl_click_vs_impression = ols(\"qdrt_n_clicks ~ qdrt_n_impressions\", data=ad_conversion, ci=None).fit()\n",
    "\n",
    "# Use this explanatory data\n",
    "explanatory_data = pd.DataFrame({\"qdrt_n_impressions\": np.arange(0, 3e6+1, 5e5) ** .25,\n",
    "                                 \"n_impressions\": np.arange(0, 3e6+1, 5e5)})\n",
    "\n",
    "# Complete prediction_data\n",
    "prediction_data = explanatory_data.assign(\n",
    "    qdrt_n_clicks = mdl_click_vs_impression.predict(explanatory_data)\n",
    ")\n",
    "\n",
    "# Print the result\n",
    "print(prediction_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the response variable has been transformed, you'll now need to back-transform the predictions to correctly interpret your results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Back transformation\n",
    "\n",
    "In the previous exercise, you transformed the response variable, ran a regression, and made predictions. But you're not done yet! In order to correctly interpret and visualize your predictions, you'll need to do a back-transformation.\n",
    "\n",
    "prediction_data, which you created in the previous exercise, is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   qdrt_n_impressions  n_impressions  qdrt_n_clicks    n_clicks\n",
      "0            0.000000            0.0       0.071748    0.000026\n",
      "1           26.591479       500000.0       3.037576   85.135121\n",
      "2           31.622777      1000000.0       3.598732  167.725102\n",
      "3           34.996355      1500000.0       3.974998  249.659131\n",
      "4           37.606031      2000000.0       4.266063  331.214159\n",
      "5           39.763536      2500000.0       4.506696  412.508546\n",
      "6           41.617915      3000000.0       4.713520  493.607180\n"
     ]
    }
   ],
   "source": [
    "# Back transform qdrt_n_clicks\n",
    "prediction_data[\"n_clicks\"] = prediction_data[\"qdrt_n_clicks\"] ** 4\n",
    "print(prediction_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Back transform qdrt_n_clicks\n",
    "prediction_data[\"n_clicks\"] = prediction_data[\"qdrt_n_clicks\"] ** 4\n",
    "\n",
    "# Plot the transformed variables\n",
    "fig = plt.figure()\n",
    "sns.regplot(x=\"qdrt_n_impressions\", y=\"qdrt_n_clicks\", data=ad_conversion, ci=None)\n",
    "\n",
    "# Add a layer of your prediction points\n",
    "sns.scatterplot(x=\"qdrt_n_impressions\", y=\"qdrt_n_clicks\", data=prediction_data, color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that your back-transformed predictions nicely follow the trend line and allow you to make more accurate predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantifying model fit\n",
    "\n",
    "Understand & assess if model predictions are non-sense (how inaccurate it is).\n",
    "\n",
    "1. Coefficient of determination : R-squared (1 is best, 0 is as good as randomness).\n",
    "\n",
    "It can be defined as the proportion of variance in the response variable that is predictable (explainable) by the explanatory variable. It tells of the models at hand does a good or a poor job resuming our data.\n",
    "Recall that the interpretation of r-squared is heavily dependent of the data we model, the context, the way we transform our variables etc.\n",
    "\n",
    "Accessible inside .summary() or .rsquared\n",
    "\n",
    "2. Residual standard error (RSE)\n",
    "\n",
    "Residuals are the difference between a response predicted value VS an observed response value (the distance, or much the prediction is wrong).\n",
    "It has the same unit as the response.\n",
    "\n",
    "```\n",
    "MSE = RSE**2\n",
    "RSE = np.sqrt(MSE)\n",
    "```\n",
    "\n",
    "Accessible with .mse_resid()\n",
    "\n",
    "To calculate RSE manually, we take the square of each residual, then we sum them up. We then calculate the degrees of freedom (# of observations minus the # of model coefficients). Finally,\n",
    "we do the square root of the sum of square divided by the deg_freedom.\n",
    "\n",
    "3. Root mean square error\n",
    "\n",
    "The same as MSE except we do not remove the degrees of freedom (we divide only by the number of obs.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Coefficient of determination\n",
    "\n",
    "The coefficient of determination is a measure of how well the linear regression line fits the observed values. For simple linear regression, it is equal to the square of the correlation between the explanatory and response variables.\n",
    "\n",
    "Here, you'll take another look at the second stage of the advertising pipeline: modeling the click response to impressions. Two models are available: mdl_click_vs_impression_orig models n_clicks versus n_impressions. mdl_click_vs_impression_trans is the transformed model you saw in Chapter 2. It models n_clicks to the power of 0.25 versus n_impressions to the power of 0.25."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   spent_usd  n_impressions  n_clicks  qdrt_n_impressions  qdrt_n_clicks\n",
      "0       1.43           7350         1            9.259165       1.000000\n",
      "1       1.82          17861         2           11.560495       1.189207\n",
      "2       1.25           4259         1            8.078429       1.000000\n",
      "3       1.29           4133         1            8.018006       1.000000\n",
      "4       4.77          15615         3           11.178551       1.316074\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               n_clicks   R-squared:                       0.892\n",
      "Model:                            OLS   Adj. R-squared:                  0.891\n",
      "Method:                 Least Squares   F-statistic:                     7683.\n",
      "Date:                Thu, 15 Apr 2021   Prob (F-statistic):               0.00\n",
      "Time:                        17:22:23   Log-Likelihood:                -4126.7\n",
      "No. Observations:                 936   AIC:                             8257.\n",
      "Df Residuals:                     934   BIC:                             8267.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=================================================================================\n",
      "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "Intercept         1.6829      0.789      2.133      0.033       0.135       3.231\n",
      "n_impressions     0.0002   1.96e-06     87.654      0.000       0.000       0.000\n",
      "==============================================================================\n",
      "Omnibus:                      247.038   Durbin-Watson:                   0.870\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            13215.277\n",
      "Skew:                          -0.258   Prob(JB):                         0.00\n",
      "Kurtosis:                      21.401   Cond. No.                     4.88e+05\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, 4.88e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:          qdrt_n_clicks   R-squared:                       0.945\n",
      "Model:                            OLS   Adj. R-squared:                  0.944\n",
      "Method:                 Least Squares   F-statistic:                 1.590e+04\n",
      "Date:                Thu, 15 Apr 2021   Prob (F-statistic):               0.00\n",
      "Time:                        17:22:23   Log-Likelihood:                 193.90\n",
      "No. Observations:                 936   AIC:                            -383.8\n",
      "Df Residuals:                     934   BIC:                            -374.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept              0.0717      0.017      4.171      0.000       0.038       0.106\n",
      "qdrt_n_impressions     0.1115      0.001    126.108      0.000       0.110       0.113\n",
      "==============================================================================\n",
      "Omnibus:                       11.447   Durbin-Watson:                   0.568\n",
      "Prob(Omnibus):                  0.003   Jarque-Bera (JB):               10.637\n",
      "Skew:                          -0.216   Prob(JB):                      0.00490\n",
      "Kurtosis:                       2.707   Cond. No.                         52.1\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(ad_conversion.head())\n",
    "\n",
    "mdl_click_vs_impression_orig = ols('n_clicks ~ n_impressions' , data = ad_conversion).fit()\n",
    "\n",
    "# Print a summary of mdl_click_vs_impression_orig\n",
    "print(mdl_click_vs_impression_orig.summary())\n",
    "\n",
    "\n",
    "mdl_click_vs_impression_trans = ols('qdrt_n_clicks ~ qdrt_n_impressions  ' , data = ad_conversion).fit()\n",
    "\n",
    "# Print a summary of mdl_click_vs_impression_trans\n",
    "print(mdl_click_vs_impression_trans.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8916134973508041\n",
      "0.9445272817143905\n"
     ]
    }
   ],
   "source": [
    "# Print the coeff of determination for mdl_click_vs_impression_orig\n",
    "print(mdl_click_vs_impression_orig.rsquared)\n",
    "\n",
    "# Print the coeff of determination for mdl_click_vs_impression_trans\n",
    "print(mdl_click_vs_impression_trans.rsquared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question\n",
    "mdl_click_vs_impression_orig has a coefficient of determination of 0.89. Which statement about the model is true?\n",
    "\n",
    "The number of impressions explains 89% of the variability in the number of clicks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Residual standard error\n",
    "Residual standard error (RSE) is a measure of the typical size of the residuals. Equivalently, it's a measure of how wrong you can expect predictions to be. Smaller numbers are better, with zero being a perfect fit to the data.\n",
    "\n",
    "Again, you'll look at the models from the advertising pipeline, mdl_click_vs_impression_orig and mdl_click_vs_impression_trans."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RSE of original model:  19.905838862478138\n",
      "RSE of transformed model:  0.19690640896875727\n"
     ]
    }
   ],
   "source": [
    "# Calculate mse_orig for mdl_click_vs_impression_orig\n",
    "mse_orig = mdl_click_vs_impression_orig.mse_resid\n",
    "\n",
    "# Calculate rse_orig for mdl_click_vs_impression_orig and print it\n",
    "rse_orig = np.sqrt(mse_orig)\n",
    "print(\"RSE of original model: \", rse_orig)\n",
    "\n",
    "# Calculate mse_trans for mdl_click_vs_impression_trans\n",
    "mse_trans = mdl_click_vs_impression_trans.mse_resid\n",
    "\n",
    "# Calculate rse_trans for mdl_click_vs_impression_trans and print it\n",
    "rse_trans = np.sqrt(mse_trans)\n",
    "print(\"RSE of transformed model: \", rse_trans)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question\n",
    "mdl_click_vs_impression_orig has an RSE of about 20. Which statement is true?\n",
    "\n",
    "The typical difference between observed number of clicks and predicted number of clicks is 20.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question\n",
    "Which model does the RSE suggest gives more accurate predictions? mdl_click_vs_impression_orig has an RSE of about 20, mdl_click_vs_impression_trans has an RSE of about 0.2.\n",
    "\n",
    "mdl_click_vs_impression_trans.\n",
    "RSE is a measure of accuracy for regression models. It even works on other other statistical model types like regression trees, so you can compare accuracy across different classes of models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing model fit\n",
    "\n",
    "If a model is a good fit, normally, the residuals should be normally distributed along the model line/curve, and their mean should be 0.\n",
    "It also shows when the fitted residuals go positive or negative (above/below the straight line).\n",
    "\n",
    "1. Residual VS fitted values chart\n",
    "\n",
    "Useful for visualizing trends. A curve following the y=0 line is the best accuracy possible. If the curve goes all over the place = bad accuracy.\n",
    "\n",
    "sns.residplot()\n",
    "\n",
    "2. Q-Q Plot\n",
    "\n",
    "If the points trek along the straight line, then they are normally distributed and validate the best conditions. If not, they aren't.\n",
    "\n",
    "qqplot() (from statsmodels.api import qqplot)\n",
    "\n",
    "3. Square root of Standardized Residuals VS fitted values, Scale-location plot\n",
    "\n",
    "This shows the sizes of the residuals and whether they get smaller or bigger as the fitted values change. Again it has to be stable, if it bounces all over or is irregular, it means residuals tend to vary randomly or in an inconsistent way as fitted values change = poor fit.\n",
    "\n",
    "Requires more pre-processing.\n",
    "See exercise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Drawing diagnostic plots\n",
    "It's time for you to draw these diagnostic plots yourself using the Taiwan real estate dataset and the model of house prices versus number of convenience stores.\n",
    "\n",
    "taiwan_real_estate is available as a pandas DataFrame and mdl_price_vs_conv is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the residuals vs. fitted values\n",
    "sns.residplot(x='n_convenience', y='price_twd_msq', data=taiwan_real_estate, lowess=True)\n",
    "plt.xlabel(\"Fitted values\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import qqplot\n",
    "from statsmodels.api import qqplot\n",
    "\n",
    "# Create the Q-Q plot of the residuals\n",
    "qqplot(data=mdl_price_vs_conv.resid, fit=True, line=\"45\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Preprocessing steps\n",
    "model_norm_residuals = mdl_price_vs_conv.get_influence().resid_studentized_internal\n",
    "model_norm_residuals_abs_sqrt = np.sqrt(np.abs(model_norm_residuals))\n",
    "\n",
    "# Create the scale-location plot\n",
    "sns.regplot(x=mdl_price_vs_conv.fittedvalues, y=model_norm_residuals_abs_sqrt, ci=None, lowess=True)\n",
    "plt.xlabel(\"Fitted values\")\n",
    "plt.ylabel(\"Sqrt of abs val of stdized residuals\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Outliers, leverage & influence\n",
    "\n",
    "Some special values can have strong effects on our models.\n",
    "Removing 1 or 2 extreme datapoints can completly change the slope of the fit.\n",
    "\n",
    "1. Unusual datapoints, outliers, data is extreme\n",
    "\n",
    "Easy to visualize them, it can either be far away from the model fit, or far away from the datapoint along the fit (horizontally / vertically).\n",
    "\n",
    "2. Leverage & influence\n",
    "\n",
    "Leverage and influence are important concepts for determining whether your model is overly affected by some unusual data points.\n",
    "\n",
    "Leverage is a measure of how extreme the explanatory variables values are.\n",
    "Observations with a large distance to the nearest MRT station have the highest leverage, because most of the observations have a short distance, so long distances are more extreme.\n",
    "Highly leveraged points are the ones with explanatory variables that are furthest away from the others.\n",
    "\n",
    "Influence measures how much the model would change if you left the observation out of the dataset when modeling.\n",
    "Observations far away from the trend line have high influence, because they have large residuals and are far away from other observations.\n",
    "The majority of the influential houses were those with prices that were much higher than the model predicted (and one with a price that was much lower).\n",
    "\n",
    "\n",
    ".get_influence()\n",
    ".summary_frame()\n",
    "\n",
    "Influence is based on Cook's distance, accessible in summary()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   dfb_Intercept  dfb_sqrt_dist_to_mrt_m       cooks_d  standard_resid  \\\n",
      "0      -0.094893                0.073542  4.648246e-03       -1.266363   \n",
      "1      -0.013981                0.008690  1.216711e-04       -0.262996   \n",
      "2       0.025510               -0.009963  6.231096e-04        0.688143   \n",
      "3       0.055525               -0.021686  2.939394e-03        1.494602   \n",
      "4      -0.000932                0.000518  6.055123e-07       -0.019716   \n",
      "5      -0.012257                0.029560  7.976174e-04        0.544490   \n",
      "6       0.000592               -0.000187  3.896928e-07        0.017531   \n",
      "7       0.010115               -0.006428  6.232088e-05        0.185284   \n",
      "8      -0.087118                0.126666  9.060428e-03        0.915959   \n",
      "9       0.009041               -0.033610  1.378024e-03       -0.818660   \n",
      "\n",
      "   hat_diag  dffits_internal  student_resid    dffits  \n",
      "0  0.005764        -0.096418      -1.267294 -0.096489  \n",
      "1  0.003506        -0.015599      -0.262699 -0.015582  \n",
      "2  0.002625         0.035302       0.687703  0.035279  \n",
      "3  0.002625         0.076673       1.496850  0.076789  \n",
      "4  0.003106        -0.001100      -0.019692 -0.001099  \n",
      "5  0.005352         0.039940       0.544024  0.039906  \n",
      "6  0.002530         0.000883       0.017509  0.000882  \n",
      "7  0.003618         0.011164       0.185067  0.011151  \n",
      "8  0.021142         0.134614       0.915780  0.134587  \n",
      "9  0.004095        -0.052498      -0.818332 -0.052477  \n"
     ]
    }
   ],
   "source": [
    "# Create summary_info\n",
    "summary_info = mdl_price_vs_dist.get_influence().summary_frame()\n",
    "print(summary_info.head(n=10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     dist_to_mrt_m  n_convenience house_age_years  price_twd_msq  \\\n",
      "347       6488.021              1        15 to 30       3.388805   \n",
      "116       6396.283              1        30 to 45       3.691377   \n",
      "249       6306.153              1        15 to 30       4.538578   \n",
      "255       5512.038              1        30 to 45       5.264750   \n",
      "8         5512.038              1        30 to 45       5.688351   \n",
      "\n",
      "     sqrt_dist_to_mrt_m  leverage  \n",
      "347           80.548253  0.026665  \n",
      "116           79.976765  0.026135  \n",
      "249           79.411290  0.025617  \n",
      "255           74.243101  0.021142  \n",
      "8             74.243101  0.021142  \n"
     ]
    }
   ],
   "source": [
    "# Create summary_info\n",
    "summary_info = mdl_price_vs_dist.get_influence().summary_frame()\n",
    "\n",
    "# Add the hat_diag column to taiwan_real_estate, name it leverage\n",
    "taiwan_real_estate[\"leverage\"] = summary_info['hat_diag']\n",
    "\n",
    "# Sort taiwan_real_estate by leverage in descending order and print the head\n",
    "print(taiwan_real_estate.sort_values(by='leverage', ascending=False).head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     dist_to_mrt_m  n_convenience house_age_years  price_twd_msq  \\\n",
      "270       252.5822              1         0 to 15      35.552194   \n",
      "148      3780.5900              0        15 to 30      13.645991   \n",
      "228      3171.3290              0         0 to 15      14.099849   \n",
      "220       186.5101              9        30 to 45      23.691377   \n",
      "113       393.2606              6         0 to 15       2.299546   \n",
      "\n",
      "     sqrt_dist_to_mrt_m  leverage  cooks_dist  \n",
      "270           15.892835  0.003849    0.115549  \n",
      "148           61.486503  0.012147    0.052440  \n",
      "228           56.314554  0.009332    0.035384  \n",
      "220           13.656870  0.004401    0.025123  \n",
      "113           19.830799  0.003095    0.022813  \n"
     ]
    }
   ],
   "source": [
    "# Create summary_info\n",
    "summary_info = mdl_price_vs_dist.get_influence().summary_frame()\n",
    "\n",
    "# Add the hat_diag column to taiwan_real_estate, name it leverage\n",
    "taiwan_real_estate[\"leverage\"] = summary_info[\"hat_diag\"]\n",
    "\n",
    "# Add the cooks_d column to taiwan_real_estate, name it cooks_dist\n",
    "taiwan_real_estate[\"cooks_dist\"] = summary_info[\"cooks_d\"]\n",
    "\n",
    "# Sort taiwan_real_estate by cooks_dist in descending order and print the head.\n",
    "print(taiwan_real_estate.sort_values(\"cooks_dist\", ascending=False).head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic Regression\n",
    "\n",
    "What if the response variable is binary/logical ?\n",
    "-Yes/no, 1/0, Blue/Red, etc.\n",
    "\n",
    "Logistic Regression is another type of generalized linear model for categorical responses.\n",
    "\n",
    "The response follow a logistic S curve.\n",
    "We can think about the fitted values between 0 & 1 as probabilities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring the explanatory variables\n",
    "When the response variable is logical, all the points lie on the y equals zero and y equals one lines, making it difficult to see what is happening. In the video, until you saw the trend line, it wasn't clear how the explanatory variable was distributed on each line. This can be solved with a histogram of the explanatory variable, grouped by the response.\n",
    "\n",
    "You will use these histograms to get to know the financial services churn dataset seen in the video.\n",
    "\n",
    "churn is available as a pandas DataFrame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pre-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   has_churned  time_since_first_purchase  time_since_last_purchase\n",
      "0            0                  -1.089221                 -0.721322\n",
      "1            0                   1.182983                  3.634435\n",
      "2            0                  -0.846156                 -0.427582\n",
      "3            0                   0.086942                 -0.535672\n",
      "4            0                  -1.166642                 -0.672640\n"
     ]
    }
   ],
   "source": [
    "churn = pd.read_csv('churn.csv')\n",
    "print(churn.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 499.675x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the histograms of time_since_last_purchase split by has_churned\n",
    "sns.distplot(churn['time_since_last_purchase'])\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n",
    "\n",
    "print(churn['has_churned'].unique())\n",
    "\n",
    "for x in churn['has_churned'].unique():\n",
    "    values = churn.time_since_last_purchase[churn['has_churned'] == x]\n",
    "    sns.distplot(values, hist=False, rug=False)\n",
    "    \n",
    "g = sns.FacetGrid(churn, col='has_churned', hue='has_churned')\n",
    "p1 = g.map(sns.distplot, 'time_since_last_purchase', hist=True, rug=True).add_legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 499.675x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the histograms of time_since_last_purchase split by has_churned\n",
    "sns.distplot(churn['time_since_first_purchase'])\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n",
    "\n",
    "print(churn['has_churned'].unique())\n",
    "\n",
    "for x in churn['has_churned'].unique():\n",
    "    values = churn.time_since_last_purchase[churn['has_churned'] == x]\n",
    "    sns.distplot(values, hist=False, rug=False)\n",
    "    \n",
    "g = sns.FacetGrid(churn, col='has_churned', hue='has_churned')\n",
    "p1 = g.map(sns.distplot, 'time_since_first_purchase', hist=True, rug=True).add_legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the time_since_last_purchase plot, the distribution of churned customers was further right than the distribution of non-churned customers (churners typically have longer times since their last purchase). For time_since_first_purchase the opposite is true: churners have a shorter length of relationship."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing linear and logistic models\n",
    "As with linear regressions, regplot() will draw model predictions for a logistic regression without you having to worry about the modeling code yourself. To see how the predictions differ for linear and logistic regressions, try drawing both trend lines side by side. Spoiler: you should see a linear (straight line) trend from the linear model, and a logistic (S-shaped) trend from the logistic model.\n",
    "\n",
    "churn is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw a linear regression trend line and a scatter plot of time_since_first_purchase vs. has_churned\n",
    "sns.regplot(data = churn, x='time_since_first_purchase',y='has_churned',\n",
    "            line_kws={\"color\": \"red\"})\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw a linear regression trend line and a scatter plot of time_since_first_purchase vs. has_churned\n",
    "sns.regplot(x=\"time_since_first_purchase\",\n",
    "            y=\"has_churned\",\n",
    "            data=churn,\n",
    "            ci=None,\n",
    "            line_kws={\"color\": \"red\"})\n",
    "\n",
    "# Draw a logistic regression trend line and a scatter plot of time_since_first_purchase vs. has_churned\n",
    "sns.regplot(x=\"time_since_first_purchase\",\n",
    "            y=\"has_churned\",\n",
    "            data=churn,\n",
    "            ci=None,\n",
    "            logistic=True,\n",
    "            line_kws={\"color\": \"blue\"})\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two models give similar predictions in some places, but notice the slight curve in the logistic model trend."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic regression with logit()\n",
    "Logistic regression requires another function from statsmodels.formula.api: logit(). It takes the same arguments as ols(): a formula and data argument. You then use .fit() to fit the model to the data.\n",
    "\n",
    "Here, you'll model how the length of relationship with a customer affects churn.\n",
    "\n",
    "churn is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.679663\n",
      "         Iterations 4\n",
      "Intercept                   -0.015185\n",
      "time_since_first_purchase   -0.354795\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Import logit\n",
    "from statsmodels.formula.api import logit\n",
    "\n",
    "# Fit a logistic regression of churn vs. \n",
    "# length of relationship using the churn dataset\n",
    "mdl_churn_vs_relationship = logit('has_churned~time_since_first_purchase', data=churn).fit()\n",
    "\n",
    "# Print the parameters of the fitted model\n",
    "print(mdl_churn_vs_relationship.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The code to run a logistic regression is a simple change from the code to run a linear regression. Now we can make some predictions with the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction & Odds ratios\n",
    "\n",
    "1. Odds ratios\n",
    "\n",
    "The probability of something happening divided by the probability that it doesn't. (P / (1-P)). Prob For / Prob Against.\n",
    "It cannot be compared to the original data but can be plotted with a special chart instead.\n",
    "The units is the chance for ... happening (3 = 3 times the chance for...).\n",
    "Easy to interpret, not easy to change data, precise.\n",
    "\n",
    "2. Log odds ratio\n",
    "\n",
    "A nice property of odds ratios, is passing them into a log() = linear regression. Changes in data easy to interpret, precise.\n",
    "\n",
    "3. Most likely Outcome\n",
    "\n",
    "In logistic regression, we speak about the rounded most likely outcome (response > 0.5 chance of churning, of ...) as response value can be interpreted a probabilities. Very easy to interpret, easy to change data, not precise (rounded).\n",
    "\n",
    "4. Probability\n",
    "\n",
    "The original data. easy to interpret, not easy to change data on-the-go, precise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probabilities\n",
    "There are four main ways of expressing the prediction from a logistic regression model – we'll look at each of them over the next four exercises. Firstly, since the response variable is either \"yes\" or \"no\", you can make a prediction of the probability of a \"yes\". Here, you'll calculate and visualize these probabilities.\n",
    "\n",
    "Two variables are available:\n",
    "\n",
    "mdl_churn_vs_relationship is the fitted logistic regression model of has_churned versus time_since_first_purchase.\n",
    "explanatory_data is a DataFrame of explanatory values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   time_since_first_purchase  has_churned\n",
      "0                      -1.50     0.626448\n",
      "1                      -1.15     0.596964\n",
      "2                      -0.80     0.566762\n",
      "3                      -0.45     0.536056\n",
      "4                      -0.10     0.505074\n"
     ]
    }
   ],
   "source": [
    "explanatory_data = pd.DataFrame({'time_since_first_purchase': np.arange(-1.5, 4, .35)})\n",
    "\n",
    "# Create prediction_data\n",
    "prediction_data = explanatory_data.assign(\n",
    "  has_churned = mdl_churn_vs_relationship.predict(explanatory_data)\n",
    ")\n",
    "\n",
    "# Print the head\n",
    "print(prediction_data.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create prediction_data\n",
    "prediction_data = explanatory_data.assign(\n",
    "    has_churned = mdl_churn_vs_relationship.predict(explanatory_data)\n",
    ")\n",
    "\n",
    "# Create a new figure\n",
    "fig = plt.figure()\n",
    "\n",
    "# Create a scatter plot with logistic trend line\n",
    "sns.regplot(x=\"time_since_first_purchase\",\n",
    "            y=\"has_churned\",\n",
    "            data=churn,\n",
    "            ci=None,\n",
    "            logistic=True)\n",
    "\n",
    "# Overlay with prediction_data, colored red\n",
    "sns.scatterplot(x=\"time_since_first_purchase\",\n",
    "                y=\"has_churned\",\n",
    "                data=prediction_data,\n",
    "                color=\"darkred\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability of a positive response is a natural way of thinking about predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Most likely outcome\n",
    "When explaining your results to a non-technical audience, you may wish to side-step talking about probabilities and simply explain the most likely outcome. That is, rather than saying there is a 60% chance of a customer churning, you say that the most likely outcome is that the customer will churn. The trade-off here is easier interpretation at the cost of nuance.\n",
    "\n",
    "mdl_churn_vs_relationship, explanatory_data, and prediction_data are available from the previous exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   time_since_first_purchase  has_churned  most_likely_outcome\n",
      "0                      -1.50     0.626448                  1.0\n",
      "1                      -1.15     0.596964                  1.0\n",
      "2                      -0.80     0.566762                  1.0\n",
      "3                      -0.45     0.536056                  1.0\n",
      "4                      -0.10     0.505074                  1.0\n"
     ]
    }
   ],
   "source": [
    "# Update prediction data by adding most_likely_outcome\n",
    "prediction_data[\"most_likely_outcome\"] = np.round(prediction_data[\"has_churned\"])\n",
    "\n",
    "# Print the head\n",
    "print(prediction_data.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Update prediction data by adding most_likely_outcome\n",
    "prediction_data[\"most_likely_outcome\"] = np.round(prediction_data[\"has_churned\"])\n",
    "\n",
    "# Create a new figure\n",
    "fig = plt.figure()\n",
    "\n",
    "# Create a scatter plot with logistic trend line (from previous exercise)\n",
    "sns.regplot(x=\"time_since_first_purchase\",\n",
    "            y=\"has_churned\",\n",
    "            data=churn,\n",
    "            ci=None,\n",
    "            logistic=True)\n",
    "\n",
    "# Overlay with prediction_data, colored red\n",
    "sns.scatterplot(x=\"time_since_first_purchase\",\n",
    "                y=\"most_likely_outcome\",\n",
    "                data=prediction_data,\n",
    "                color=\"red\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most likely outcome is that you will master logistic regression! Providing the most likely response is a great way to share the model results with a non-technical audience."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Odds ratio\n",
    "Odds ratios compare the probability of something happening with the probability of it not happening. This is sometimes easier to reason about than probabilities, particularly when you want to make decisions about choices. For example, if a customer has a 20% chance of churning, it may be more intuitive to say \"the chance of them not churning is four times higher than the chance of them churning\".\n",
    "\n",
    "mdl_churn_vs_relationship, explanatory_data and prediction_data are available from the previous exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   time_since_first_purchase  has_churned  most_likely_outcome  odds_ratio\n",
      "0                      -1.50     0.626448                  1.0    1.677003\n",
      "1                      -1.15     0.596964                  1.0    1.481166\n",
      "2                      -0.80     0.566762                  1.0    1.308199\n",
      "3                      -0.45     0.536056                  1.0    1.155431\n",
      "4                      -0.10     0.505074                  1.0    1.020502\n"
     ]
    }
   ],
   "source": [
    "# Update prediction data with odds_ratio\n",
    "prediction_data[\"odds_ratio\"] = prediction_data[\"has_churned\"] / (1 - prediction_data[\"has_churned\"])\n",
    "\n",
    "# Print the head\n",
    "print(prediction_data.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Update prediction data with odds_ratio\n",
    "prediction_data[\"odds_ratio\"] = prediction_data[\"has_churned\"] / (1 - prediction_data[\"has_churned\"])\n",
    "\n",
    "# Create a new figure\n",
    "fig = plt.figure()\n",
    "\n",
    "# Create a line plot of odds_ratio vs time_since_first_purchase\n",
    "sns.lineplot(x='time_since_first_purchase', y='odds_ratio', data = prediction_data)\n",
    "\n",
    "# Add a dotted horizontal line at odds_ratio = 1\n",
    "plt.axhline(y=1, linestyle=\"dotted\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Odds ratios provide an alternative to probabilities that make it easier to compare positive and negative responses."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Log odds ratio\n",
    "One downside to probabilities and odds ratios for logistic regression predictions is that the prediction lines for each are curved. This makes it harder to reason about what happens to the prediction when you make a change to the explanatory variable. The logarithm of the odds ratio (the \"log odds ratio\" or \"logit\") does have a linear relationship between predicted response and explanatory variable. That means that as the explanatory variable changes, you don't see dramatic changes in the response metric - only linear changes.\n",
    "\n",
    "Since the actual values of log odds ratio are less intuitive than (linear) odds ratio, for visualization purposes it's usually better to plot the odds ratio and apply a log transformation to the y-axis scale.\n",
    "\n",
    "mdl_churn_vs_relationship, explanatory_data and prediction_data are available from the previous exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   time_since_first_purchase  has_churned  most_likely_outcome  odds_ratio  \\\n",
      "0                      -1.50     0.626448                  1.0    1.677003   \n",
      "1                      -1.15     0.596964                  1.0    1.481166   \n",
      "2                      -0.80     0.566762                  1.0    1.308199   \n",
      "3                      -0.45     0.536056                  1.0    1.155431   \n",
      "4                      -0.10     0.505074                  1.0    1.020502   \n",
      "\n",
      "   log_odds_ratio  \n",
      "0        0.517008  \n",
      "1        0.392830  \n",
      "2        0.268651  \n",
      "3        0.144473  \n",
      "4        0.020295  \n"
     ]
    }
   ],
   "source": [
    "# Update prediction data with log_odds_ratio\n",
    "prediction_data[\"log_odds_ratio\"] = np.log(prediction_data['odds_ratio'])\n",
    "\n",
    "# Print the head\n",
    "print(prediction_data.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Update prediction data with log_odds_ratio\n",
    "prediction_data[\"log_odds_ratio\"] = np.log(prediction_data[\"odds_ratio\"])\n",
    "\n",
    "# Create a new figure\n",
    "fig = plt.figure()\n",
    "\n",
    "# Update the line plot: log_odds_ratio vs time_since_first_purchase\n",
    "sns.lineplot(x=\"time_since_first_purchase\",\n",
    "             y=\"log_odds_ratio\",\n",
    "             data=prediction_data)\n",
    "\n",
    "# Add a dotted horizontal line at log_odds_ratio = 0\n",
    "plt.axhline(y=0, linestyle=\"dotted\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linear relationship between predicted log odds ratio and the explanatory variable makes changes easier to reason about."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantifying logistic regression fit\n",
    "\n",
    "Resid plot, QQplot & Scale location plot are less useful in the case of logistic regression. Instead, we can use confusion matrices to analyze the fit performance. With True/False positive & negative outcomes.\n",
    "We can also compute metrics based on various ratios.\n",
    "\n",
    "1. Accuracy : proportion of correct predictions. Higher better.\n",
    "\n",
    "TN+TP / (TN+FN+FP+TP)\n",
    "\n",
    "2. Sensitivity : proportions of observations where the actual response was true and where the model also predicted it was true. Higher better.\n",
    "\n",
    "TP / (FN + TP)\n",
    "\n",
    "3. Specificity : proportions of observations where the actual was false and where the model also predicted it was false. Higher better.\n",
    "\n",
    "TN / (TN + FP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the confusion matrix\n",
    "A confusion matrix (occasionally called a confusion table) is the basis of all performance metrics for models with a categorical response (such as a logistic regression). It contains the counts of each actual response-predicted response pair. In this case, where there are two possible responses (churn or not churn), there are four overall outcomes.\n",
    "\n",
    "1. True positive: The customer churned and the model predicted they would.\n",
    "2. False positive: The customer didn't churn, but the model predicted they would.\n",
    "3. True negative: The customer didn't churn and the model predicted they wouldn't.\n",
    "4. False negative: The customer churned, but the model predicted they wouldn't."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index(['actual_response', 'predicted_response'], dtype='object')\n",
      "Predicted  0.0  1.0\n",
      "Actual             \n",
      "0          112   88\n",
      "1           76  124\n"
     ]
    }
   ],
   "source": [
    "# Get the actual responses\n",
    "actual_response = churn[\"has_churned\"]\n",
    "\n",
    "# Get the predicted responses\n",
    "predicted_response = np.round(mdl_churn_vs_relationship.predict())\n",
    "\n",
    "# Create outcomes as a DataFrame of both Series\n",
    "outcomes = pd.DataFrame({\"actual_response\": actual_response,\n",
    "                         \"predicted_response\": predicted_response})\n",
    "\n",
    "print(type(outcomes))\n",
    "print(outcomes.columns)\n",
    "# Print the outcomes\n",
    "# print(outcomes.value_counts(sort = False))\n",
    "# print(pd.value_counts(outcomes.values.flatten()))\n",
    "conf_matrix = pd.crosstab(outcomes['actual_response'], outcomes['predicted_response'], rownames=['Actual'], colnames=['Predicted'])\n",
    "print(conf_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Drawing a mosaic plot of the confusion matrix\n",
    "While calculating the performance matrix might be fun, it would become tedious if you needed multiple confusion matrices of different models. Luckily, the .pred_table() method can calculate the confusion matrix for you.\n",
    "\n",
    "Additionally, you can use the output from the .pred_table() method to visualize the confusion matrix, using the mosaic() function.\n",
    "\n",
    "churn and mdl_churn_vs_relationship are available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[112.  88.]\n",
      " [ 76. 124.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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PRcAysK5evVoHDhyoycnJ2rFjR83OztaVK1e6Hgugc5cuXarTp0/X9PR016PAY+l1PQBslTt37tTU1NTa8fT0dN24caPDiQC2hzNnznQ9AjwRK7AMrNXV1WqaZu24bdt1xwBAJgHLwNq7d2/Nz8+vHc/Pz/vvMgAYAAKWgXXw4MG6du1a3b17t+7fv19zc3N16NChrscCAJ6Qe2AZWHv27KlTp07ViRMnanl5uY4fP1779u3reiwA4AnZShYAgChuIQAAIIqABQAgioAFACCKgAUAIIqABQAgioAFACCKgAUAIIqABQAgyn8DWUb/aiHb7AgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 842.4x523.44 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import mosaic from statsmodels.graphics.mosaicplot\n",
    "from statsmodels.graphics.mosaicplot import mosaic\n",
    "\n",
    "# Calculate the confusion matrix conf_matrix\n",
    "conf_matrix = mdl_churn_vs_relationship.pred_table()\n",
    "\n",
    "# Print it\n",
    "print(conf_matrix)\n",
    "\n",
    "# Draw a mosaic plot of conf_matrix\n",
    "mosaic(conf_matrix)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accuracy, sensitivity, and specificity are the most important performance metrics for logistic regression models. In the last exercise, you'll learn how to calculate them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy:  0.59\n",
      "sensitivity:  0.62\n",
      "specificity:  0.56\n"
     ]
    }
   ],
   "source": [
    "# Extract TN, TP, FN and FP from conf_matrix\n",
    "TN = conf_matrix[0,0]\n",
    "TP = conf_matrix[1,1]\n",
    "FN = conf_matrix[1,0]\n",
    "FP = conf_matrix[0,1]\n",
    "\n",
    "# Calculate and print the accuracy\n",
    "accuracy = (TN + TP) / (TN + FN + FP + TP)\n",
    "print(\"accuracy: \", accuracy)\n",
    "\n",
    "# Calculate and print the sensitivity\n",
    "sensitivity = TP / (TP + FN)\n",
    "print(\"sensitivity: \", sensitivity)\n",
    "\n",
    "# Calculate and print the specificity\n",
    "specificity = TN / (TN + FP)\n",
    "print(\"specificity: \", specificity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using these metrics, it becomes much easier to interpret and compare logistic regression models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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