14-LinearModels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "Linear (regression) modelling is a method of predicting the value of an output value as a linear combination of weighted input values.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Models - Overview\n",
    "\n",
    "In the simplest case, we are trying to fit a line. In this case, our model is of the form:\n",
    "\n",
    "$$ y = ax + b $$\n",
    "\n",
    "In this equation above, we are trying to predict some data variable $y$, from some other data variable $x$, where $a$ and $b$ are parameters we need to figure out (learn), by fitting the model, and reflect the slope, and y-intercept, of the model (line) respectively.\n",
    "\n",
    "We need some procedure to go about finding $a$ and $b$. We will use OLS to do so - the values of $a$ and $b$ we want are those that fulfill the OLS solution - meaning the values that lead to the smallest distance between the predictions of the model, and our data. \n",
    "\n",
    "Note that to train this kind of model, you need data in which you know both $x$ and $y$ already, to train your model. This kind of model only applies to predicting values you have at least some information about. \n",
    "\n",
    "Having training data makes it a 'supervised' model, meaning that learning the prediction model is 'supervised' or guided by knowing some 'answers' to our prediction problem already, and the goal is to use this data to learn a model that can generalize to new data. \n",
    "\n",
    "This approach can also be generalized, including, for example, more features used to predict our output of interest. \n",
    "\n",
    "Therefore, we will rewrite our model, in the general form, as:\n",
    "\n",
    "$$ y = a_0 + a_1 x_1 + a_2 x_2 + ... + a_n x_n + \\epsilon $$\n",
    "\n",
    "In the equation above $a_0$ is the intercept (the same as $b$ from above), and $a_1$ to $a_n$ are $n$ parameters that we are trying to learn, as weights for data features $x_1$ to $x_n$. Our output variable (what we are trying to predict) is still $y$, and we've introduced $\\epsilon$, which is the error, which basically captures unexplained variance.\n",
    "\n",
    "### Linear Models Practice\n",
    "\n",
    "In the following, we will generate some data, with two features, that we'll call `d1` and `d2`. \n",
    "\n",
    "We will generate this data such that `d1` and `d2` are correlated. This means that they share some information, and so we can use this to property to try and predict values of `d2` from `d1`, using a linear model to do so. \n",
    "\n",
    "This model, using the second notation from above, will be of the form:\n",
    "\n",
    "$$ d2 = a_0 + a_1 * d1 $$\n",
    "\n",
    "Where `a_0` and `a_1` are parameters of the model that we are trying to learn, reflecting the intercept and slope, respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports \n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Statmodels & patsy\n",
    "import patsy\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, lets generate some example data to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set random seed, for consistency simulating data\n",
    "np.random.seed(21)\n",
    "\n",
    "# Settings\n",
    "corr = 0.75\n",
    "covs = [[1, corr], [corr, 1]]\n",
    "means = [0, 0]\n",
    "\n",
    "# Generate the data\n",
    "data = np.random.multivariate_normal(means, covs, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check out the data we generated\n",
    "plt.scatter(data[:, 0], data[:, 1], alpha=0.5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Put the data into a DataFrame\n",
    "df = pd.DataFrame(data, columns=['d1', 'd2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.087922</td>\n",
       "      <td>0.009294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-0.530187</td>\n",
       "      <td>-1.418836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>-0.092297</td>\n",
       "      <td>-1.302195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.275502</td>\n",
       "      <td>0.109635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>-1.050818</td>\n",
       "      <td>-1.059746</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         d1        d2\n",
       "0  0.087922  0.009294\n",
       "1 -0.530187 -1.418836\n",
       "2 -0.092297 -1.302195\n",
       "3  0.275502  0.109635\n",
       "4 -1.050818 -1.059746"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Have a quick look at the simualed data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>d1</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.773245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>d2</td>\n",
       "      <td>0.773245</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          d1        d2\n",
       "d1  1.000000  0.773245\n",
       "d2  0.773245  1.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check the correlation between d1 & d2 (that it matches what was synthesized)\n",
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Models with Statsmodels & Patsy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\">\n",
    "Statsmodels is a module for statistical analyses in Python. Patsy is a useful package for describing and applying statistical models.\n",
    "</div>\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "The official documentation for\n",
    "<a href=\"http://www.statsmodels.org/stable/index.html\" class=\"alert-link\">statsmodels</a>\n",
    "and\n",
    "<a href=\"https://patsy.readthedocs.io/en/latest/\" class=\"alert-link\">patsy</a>.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Patsy gives us an easy way to construct 'design matrices'. \n",
    "\n",
    "For our purpose, 'design matrices' are just organized matrices of our predictor and output variables. \n",
    "\n",
    "'Predictors' refers to the features we want to predict from, and 'outputs' refers to the variables we want to predict. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use patsy to organize our data into predictor and outputs\n",
    "#   The string `d2 ~ d1` indicates to predict d2 as a function of d1\n",
    "outcome, predictors = patsy.dmatrices('d2 ~ d1', df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you check the type of 'outcome' and 'predictors', you will find they are custom patsy objects, of type 'DesignMatrix'.\n",
    "\n",
    "If you print them out, you will see that they resemble pandas Series or DataFrames. \n",
    "\n",
    "You can think of them as customized dataframe-like objects for the specific purpose of being organized into matrices to be used for modeling.\n",
    "\n",
    "Next, we can use `statsmodels` to initialize an OLS model object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize an OLS model object\n",
    "#   Note: This initializes the model, and provides the data \n",
    "#         but does not actually compute the model yet\n",
    "model = sm.OLS(outcome, predictors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `statsmodels`, just like `sklearn` that we will encounter a bit later, uses an object-oriented approach. \n",
    "\n",
    "In this approach you initialize objects that store the data and methods together. This allows for an organized approach to storing and check data and parameters, and applying computations to them, such as fitting models. Outputs parameters of the model are also stored in the object, which can then also be used to make predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "statsmodels.regression.linear_model.OLS"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check the type of the model object we just created.\n",
    "#  You can also explore, with tab-complete, what is available from this object\n",
    "type(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Finally, fit the model\n",
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     d2   R-squared:                       0.598\n",
      "Model:                            OLS   Adj. R-squared:                  0.598\n",
      "Method:                 Least Squares   F-statistic:                     1484.\n",
      "Date:                Sun, 21 Jun 2020   Prob (F-statistic):          1.18e-199\n",
      "Time:                        16:14:06   Log-Likelihood:                -953.74\n",
      "No. Observations:                1000   AIC:                             1911.\n",
      "Df Residuals:                     998   BIC:                             1921.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0116      0.020     -0.582      0.561      -0.051       0.027\n",
      "d1             0.7396      0.019     38.523      0.000       0.702       0.777\n",
      "==============================================================================\n",
      "Omnibus:                        0.715   Durbin-Watson:                   2.008\n",
      "Prob(Omnibus):                  0.699   Jarque-Bera (JB):                0.787\n",
      "Skew:                          -0.014   Prob(JB):                        0.675\n",
      "Kurtosis:                       2.866   Cond. No.                         1.04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Check out the results\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpreting Outputs\n",
    "\n",
    "`statsmodels` gives us a lot of information!\n",
    "\n",
    "The top section is largely meta-data: it includes things like the model type, and time and date of us running it. \n",
    "\n",
    "It also includes the `R-squared`, which is an overall summary of the amount of variance the model is able to capture. R-squared values are bound between 0-1. An r-squared of ~0.5, that we have here, is quite a high value, suggesting a good model fit. \n",
    "\n",
    "The middle section is the actual model results. \n",
    "\n",
    "Each row reflects a parameter, and gives us it's value (`coef`), the error (`std err`), the results of a statistical test regarding whether this parameter is a significant predictor of the output variable (`t`, which associated p-value as `P>|t|`), and the confidence interval of the parameters value (`[0.025` - `0.975]`).\n",
    "\n",
    "The last section includes some other tests that are run on the data. These can be used to check some properties of the input data, and to check assumptions of the model are met. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking our Model\n",
    "\n",
    "In terms of the model itself, the most useful components are in the second row, in which the summary gives the parameter values, and p-values of our predictors, which in this case are 'Intercept', and 'd2'. \n",
    "\n",
    "From the results above, we can grab the values of the parameters, and obtain the following model:\n",
    "\n",
    "$$ d2 = -0.0116 + 0.7396 * d1 $$\n",
    "\n",
    "However, we should also keep in mind whether each parameter is significant. To check use, let's look at the statistical test that is reported that checks whether the parameter value is significant (as in, significantly different from zero). Using an alpha value of 0.05, in this case, the 'd2' parameter value is significant, but the 'Intercept' value is not. Since the parameter value for 'Intercept' is not significantly different from zero, we can decide not to include it in our final model. \n",
    "\n",
    "We therefore finish with the model:\n",
    "$$ d2 = 0.7396 * d1 $$\n",
    "\n",
    "With this model, it is promising that are value of $a_1$, of 0.7396, is very close to the correlation value of the data points, which we set at 0.75! This suggest our model is working well!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing our Model\n",
    "\n",
    "Next, we can visualize our model, with our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the orginal data (as before)\n",
    "plt.scatter(df['d1'], df['d2'], alpha=0.3, label='Data');\n",
    "\n",
    "# Generate and plot the model fit line\n",
    "xs = np.arange(df['d1'].min(), df['d1'].max())\n",
    "ys = 0.7185 * xs\n",
    "plt.plot(xs, ys, '--k', linewidth=4, label='Model')\n",
    "\n",
    "plt.xlabel('D1')\n",
    "plt.ylabel('D2')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using multiple predictors\n",
    "\n",
    "The model above used only one predictor, fitting a straight line to the data. This is similar to previous examples we've seen of and tried for fitting lines.\n",
    "\n",
    "We can also fit more than 1 predictor variable, and that is where the power and benefits of using `patsy` and `statsmodels` really comes through. We can use these tools to specify any models we want, including multiple predictors with different kinds of interactions between predictors, and these functions take care of fitting these models. \n",
    "\n",
    "To briefly explore this, let's now add a new variable to our dataframe, and fit an OLS model with two predictors. \n",
    "\n",
    "In this case, we will fit a model of the form:\n",
    "\n",
    "$$ d1 = a_0 + a_1 * d2 + a_1 * d3 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "      <th>d3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.087922</td>\n",
       "      <td>0.009294</td>\n",
       "      <td>-1.611758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-0.530187</td>\n",
       "      <td>-1.418836</td>\n",
       "      <td>1.933703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>-0.092297</td>\n",
       "      <td>-1.302195</td>\n",
       "      <td>0.334072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.275502</td>\n",
       "      <td>0.109635</td>\n",
       "      <td>-0.124464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>-1.050818</td>\n",
       "      <td>-1.059746</td>\n",
       "      <td>0.278050</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         d1        d2        d3\n",
       "0  0.087922  0.009294 -1.611758\n",
       "1 -0.530187 -1.418836  1.933703\n",
       "2 -0.092297 -1.302195  0.334072\n",
       "3  0.275502  0.109635 -0.124464\n",
       "4 -1.050818 -1.059746  0.278050"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a new column of data to df\n",
    "df['d3'] = pd.Series(np.random.randn(1000), index=df.index)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Predict d1 from d2 and d3\n",
    "outcome, predictors = patsy.dmatrices('d1 ~ d2 + d3', df)\n",
    "model = sm.OLS(outcome, predictors)\n",
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     d1   R-squared:                       0.599\n",
      "Model:                            OLS   Adj. R-squared:                  0.598\n",
      "Method:                 Least Squares   F-statistic:                     745.1\n",
      "Date:                Sun, 21 Jun 2020   Prob (F-statistic):          1.21e-198\n",
      "Time:                        16:14:06   Log-Likelihood:                -996.62\n",
      "No. Observations:                1000   AIC:                             1999.\n",
      "Df Residuals:                     997   BIC:                             2014.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0179      0.021      0.861      0.389      -0.023       0.059\n",
      "d2             0.8070      0.021     38.471      0.000       0.766       0.848\n",
      "d3            -0.0368      0.021     -1.763      0.078      -0.078       0.004\n",
      "==============================================================================\n",
      "Omnibus:                        0.703   Durbin-Watson:                   1.985\n",
      "Prob(Omnibus):                  0.704   Jarque-Bera (JB):                0.574\n",
      "Skew:                           0.015   Prob(JB):                        0.751\n",
      "Kurtosis:                       3.113   Cond. No.                         1.06\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Check the model fit summary\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that in this case, we simulated the `d3` column with no relation to the `d1` values we were trying to predict, so the `d3` predictor isn't significant, and overall this bigger model doesn't explain anymore variance of the data (the r-squared is no better). \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "\n",
    "`statsmodels` offers a powerful and general approach to fitting statistical models to data, investigating properties of these model fits, and comparing between models. You can further investigate how to include other features, such as interactions between input variables, and so on. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression with sklearn\n",
    "\n",
    "As we've already seen with the `OLS` tutorial, there are multiple ways to apply the same underlying computations. \n",
    "\n",
    "Another popular module that can be used for fitting models to data is `sklearn`. \n",
    "\n",
    "Here, for a quick demonstration and comparison, we will fit the `sklearn` implementation of Linear Regression models to our same data. The underlying computations are approximately the same, but as we can see, the API for using `sklearn` and the exact results are different."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "Linear regression in \n",
    "<a href=\"http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html\" class=\"alert-link\">sklearn</a>.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Linear Models with sklearn\n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert data into arrays for easier use with sklearn\n",
    "d1 = np.reshape(df.d1.values, [len(df.d1), 1])\n",
    "d2 = np.reshape(df.d2.values, [len(df.d2), 1])\n",
    "d3 = np.reshape(df.d3.values, [len(df.d3), 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize linear regression model\n",
    "reg = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the linear regression model\n",
    "reg.fit(d2, d1)  # d1 = a0 + a1*d2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The intercept value is: \t0.0164\n",
      "The coefficient value is: \t0.8084\n"
     ]
    }
   ],
   "source": [
    "# Check the results of this\n",
    "#  If you compare these to what we got with statsmodels above, they are indeed the same\n",
    "print('The intercept value is: \\t{:1.4f}'.format(reg.intercept_[0]))\n",
    "print('The coefficient value is: \\t{:1.4f}'.format(reg.coef_[0][0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using multiple predictors (in sklearn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initialize and fit linear model\n",
    "# d1 = a0 + a1*d2 + a2*d3\n",
    "reg = linear_model.LinearRegression()\n",
    "reg.fit(np.hstack([d2, d3]), d1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: \t +0.0179\n",
      "d2 value:\t +0.8070\n",
      "d2 value:\t -0.0368\n"
     ]
    }
   ],
   "source": [
    "# Check the results of this\n",
    "#  If you compare these to what we got with statsmodels above, they are indeed the same\n",
    "print('Intercept: \\t {:+1.4f}'.format(reg.intercept_[0]))\n",
    "print('d2 value:\\t {:+1.4f}'.format(reg.coef_[0][0]))\n",
    "print('d2 value:\\t {:+1.4f}'.format(reg.coef_[0][1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "\n",
    "The pattern of results with `sklearn` is about the same as before, though we can see there is some small differences in estimation. In general, if you have data organized into Dataframes, then `statsmodels` does offer a more direct way to apply statistical models, but `sklearn` does also offer a lot of useful functionality for model fitting & analysis. "
   ]
  }
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