Ch03-linreg-lab.ipynb

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    "# Linear Regression\n",
    "\n",
    "<a target=\"_blank\" href=\"https://colab.research.google.com/github/intro-stat-learning/ISLP_labs/blob/v2.2/Ch03-linreg-lab.ipynb\">\n",
    "<img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
    "</a>\n",
    "\n",
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/intro-stat-learning/ISLP_labs/v2.2?labpath=Ch03-linreg-lab.ipynb)\n"
   ]
  },
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   "source": [
    "## Importing packages\n",
    "We import our standard libraries at this top\n",
    "level."
   ]
  },
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib.pyplot import subplots\n"
   ]
  },
  {
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    "### New imports\n",
    "Throughout this lab we will introduce new functions and libraries. However,\n",
    "we will import them here to emphasize these are the new\n",
    "code objects in this lab. Keeping imports near the top\n",
    "of a notebook makes the code more readable, since scanning the first few\n",
    "lines tells us what libraries are used."
   ]
  },
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   "source": [
    "import statsmodels.api as sm\n"
   ]
  },
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   "source": [
    " We will provide relevant details about the\n",
    "functions below as they are needed.\n",
    "\n",
    "Besides importing whole modules, it is also possible\n",
    "to import only a few items from a given module. This\n",
    "will help keep the  *namespace* clean.\n",
    "We will use a few specific objects from the `statsmodels` package\n",
    "which we import here."
   ]
  },
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   "source": [
    "from statsmodels.stats.outliers_influence \\\n",
    "     import variance_inflation_factor as VIF\n",
    "from statsmodels.stats.anova import anova_lm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4713b12",
   "metadata": {},
   "source": [
    "As one of the import statements above is quite a long line, we inserted a line break `\\` to\n",
    "ease readability.\n",
    "\n",
    "We will also use some functions written for the labs in this book in the `ISLP`\n",
    "package."
   ]
  },
  {
   "cell_type": "code",
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   "id": "307b7e22",
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   "source": [
    "from ISLP import load_data\n",
    "from ISLP.models import (ModelSpec as MS,\n",
    "                         summarize,\n",
    "                         poly)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81d778fb",
   "metadata": {},
   "source": [
    "### Inspecting Objects and Namespaces\n",
    "The\n",
    "function  `dir()`\n",
    "provides a list of\n",
    "objects in a namespace."
   ]
  },
  {
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       "['In',\n",
       " 'MS',\n",
       " 'Out',\n",
       " 'VIF',\n",
       " '_',\n",
       " '__',\n",
       " '___',\n",
       " '__builtin__',\n",
       " '__builtins__',\n",
       " '__doc__',\n",
       " '__loader__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__spec__',\n",
       " '_dh',\n",
       " '_i',\n",
       " '_i1',\n",
       " '_i2',\n",
       " '_i3',\n",
       " '_i4',\n",
       " '_i5',\n",
       " '_ih',\n",
       " '_ii',\n",
       " '_iii',\n",
       " '_oh',\n",
       " 'anova_lm',\n",
       " 'exit',\n",
       " 'get_ipython',\n",
       " 'load_data',\n",
       " 'np',\n",
       " 'open',\n",
       " 'pd',\n",
       " 'poly',\n",
       " 'quit',\n",
       " 'sm',\n",
       " 'subplots',\n",
       " 'summarize']"
      ]
     },
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   "source": [
    "dir()\n"
   ]
  },
  {
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    " This shows you everything that `Python` can find at the top level.\n",
    "There are certain objects like `__builtins__` that contain references to built-in\n",
    "functions like `print()`.\n",
    "\n",
    "Every python object has its own notion of\n",
    "namespace, also accessible with `dir()`. This will include\n",
    "both the attributes of the object\n",
    "as well as any methods associated with it. For instance, we see `'sum'` in the listing for an\n",
    "array."
   ]
  },
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       "['T',\n",
       " '__abs__',\n",
       " '__add__',\n",
       " '__and__',\n",
       " '__array__',\n",
       " '__array_finalize__',\n",
       " '__array_function__',\n",
       " '__array_interface__',\n",
       " '__array_prepare__',\n",
       " '__array_priority__',\n",
       " '__array_struct__',\n",
       " '__array_ufunc__',\n",
       " '__array_wrap__',\n",
       " '__bool__',\n",
       " '__class__',\n",
       " '__class_getitem__',\n",
       " '__complex__',\n",
       " '__contains__',\n",
       " '__copy__',\n",
       " '__deepcopy__',\n",
       " '__delattr__',\n",
       " '__delitem__',\n",
       " '__dir__',\n",
       " '__divmod__',\n",
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       " '__rshift__',\n",
       " '__rsub__',\n",
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       " '__rxor__',\n",
       " '__setattr__',\n",
       " '__setitem__',\n",
       " '__setstate__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__sub__',\n",
       " '__subclasshook__',\n",
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       " 'any',\n",
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       " 'argmin',\n",
       " 'argpartition',\n",
       " 'argsort',\n",
       " 'astype',\n",
       " 'base',\n",
       " 'byteswap',\n",
       " 'choose',\n",
       " 'clip',\n",
       " 'compress',\n",
       " 'conj',\n",
       " 'conjugate',\n",
       " 'copy',\n",
       " 'ctypes',\n",
       " 'cumprod',\n",
       " 'cumsum',\n",
       " 'data',\n",
       " 'diagonal',\n",
       " 'dot',\n",
       " 'dtype',\n",
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       " 'dumps',\n",
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       " 'itemsize',\n",
       " 'max',\n",
       " 'mean',\n",
       " 'min',\n",
       " 'nbytes',\n",
       " 'ndim',\n",
       " 'newbyteorder',\n",
       " 'nonzero',\n",
       " 'partition',\n",
       " 'prod',\n",
       " 'ptp',\n",
       " 'put',\n",
       " 'ravel',\n",
       " 'real',\n",
       " 'repeat',\n",
       " 'reshape',\n",
       " 'resize',\n",
       " 'round',\n",
       " 'searchsorted',\n",
       " 'setfield',\n",
       " 'setflags',\n",
       " 'shape',\n",
       " 'size',\n",
       " 'sort',\n",
       " 'squeeze',\n",
       " 'std',\n",
       " 'strides',\n",
       " 'sum',\n",
       " 'swapaxes',\n",
       " 'take',\n",
       " 'tobytes',\n",
       " 'tofile',\n",
       " 'tolist',\n",
       " 'tostring',\n",
       " 'trace',\n",
       " 'transpose',\n",
       " 'var',\n",
       " 'view']"
      ]
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   "source": [
    "A = np.array([3,5,11])\n",
    "dir(A)\n"
   ]
  },
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    " This indicates that the object `A.sum` exists. In this case it is a method\n",
    "that can be used to compute the sum of the array `A` as can be seen by typing `A.sum?`."
   ]
  },
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       "19"
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    "A.sum()\n"
   ]
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    "    "
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    "## Simple Linear Regression\n",
    "In this section we will  construct model \n",
    "matrices (also called design matrices) using the `ModelSpec()`  transform from `ISLP.models`.\n",
    "\n",
    "We  will use the `Boston` housing data set, which is contained in the `ISLP` package.  The `Boston` dataset records  `medv`  (median house value) for $506$ neighborhoods\n",
    "around Boston.  We will build a regression model to predict  `medv`  using $13$\n",
    "predictors such as  `rm`  (average number of rooms per house),\n",
    " `age`  (proportion of owner-occupied units built prior to 1940), and  `lstat`  (percent of\n",
    "households with low socioeconomic status).  We will use `statsmodels` for this\n",
    "task, a `Python` package that implements several commonly used\n",
    "regression methods.\n",
    "\n",
    "We have included a simple loading function `load_data()` in the\n",
    "`ISLP` package:"
   ]
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       "Index(['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'rad', 'tax',\n",
       "       'ptratio', 'lstat', 'medv'],\n",
       "      dtype='object')"
      ]
     },
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   ],
   "source": [
    "Boston = load_data(\"Boston\")\n",
    "Boston.columns\n"
   ]
  },
  {
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   "id": "27b9c8f5",
   "metadata": {},
   "source": [
    "Type `Boston?` to find out more about these data.\n",
    "\n",
    "We start by using the `sm.OLS()`  function to fit a\n",
    "simple linear regression model.  Our response will be\n",
    " `medv`  and  `lstat`  will be the single predictor.\n",
    "For this model, we can create the model matrix by hand.\n"
   ]
  },
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       "      <th>intercept</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.98</td>\n",
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       "   intercept  lstat\n",
       "0        1.0   4.98\n",
       "1        1.0   9.14\n",
       "2        1.0   4.03\n",
       "3        1.0   2.94"
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   "source": [
    "X = pd.DataFrame({'intercept': np.ones(Boston.shape[0]),\n",
    "                  'lstat': Boston['lstat']})\n",
    "X[:4]\n"
   ]
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    "We extract the response, and fit the model."
   ]
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   "source": [
    "y = Boston['medv']\n",
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a1d62f2",
   "metadata": {},
   "source": [
    "Note that `sm.OLS()` does\n",
    "not fit the model; it specifies the model, and then `model.fit()` does the actual fitting.  \n",
    "\n",
    "Our `ISLP` function `summarize()` produces a simple table of the parameter estimates,\n",
    "their standard errors, t-statistics and p-values.\n",
    "The function takes a single argument, such as the object `results` \n",
    "returned here by the `fit`\n",
    "method, and returns such a summary."
   ]
  },
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       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>34.5538</td>\n",
       "      <td>0.563</td>\n",
       "      <td>61.415</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>-0.9500</td>\n",
       "      <td>0.039</td>\n",
       "      <td>-24.528</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              coef  std err       t  P>|t|\n",
       "intercept  34.5538    0.563  61.415    0.0\n",
       "lstat      -0.9500    0.039 -24.528    0.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summarize(results)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31d6b202",
   "metadata": {},
   "source": [
    "Before we describe other methods for working with fitted models, we outline a more useful and general framework for constructing a model matrix~`X`.\n",
    "### Using Transformations: Fit and Transform\n",
    "Our model above has a single predictor, and constructing `X` was straightforward. \n",
    "In practice  we often fit models with more than one predictor, typically selected from an array or data frame.\n",
    "We may wish to introduce transformations to the variables before fitting the model, specify interactions between variables, and expand some particular variables into sets of variables (e.g. polynomials).\n",
    "The `sklearn`  package has a particular notion\n",
    "for this type of task: a *transform*. A transform is an object\n",
    "that is created with some parameters as arguments. The\n",
    "object has two main methods: `fit()` and `transform()`.\n",
    "\n",
    "We provide a general approach for specifying models and constructing\n",
    "the model matrix through the transform `ModelSpec()` in the `ISLP` library.\n",
    "`ModelSpec()`\n",
    "(renamed `MS()` in the preamble) creates a\n",
    "transform object, and then a pair of methods\n",
    "`transform()` and `fit()` are used to construct a\n",
    "corresponding model matrix.\n",
    "\n",
    "We first describe this process for our simple regression model  using a single predictor `lstat` in\n",
    "the `Boston` data frame, but will use it repeatedly in more\n",
    "complex tasks in this and other labs in this book.\n",
    "In our case the transform is created by the expression\n",
    "`design = MS(['lstat'])`.\n",
    "\n",
    "The `fit()`  method takes the original array and may do some\n",
    "initial computations on it, as specified in the transform object.\n",
    "For example, it may compute means and standard deviations for centering and scaling.\n",
    "The `transform()` \n",
    "method applies the fitted transformation to the array of data, and produces the model matrix.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "11b07af0",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2025-04-03T19:32:50.759257Z"
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   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>intercept</th>\n",
       "      <th>lstat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   intercept  lstat\n",
       "0        1.0   4.98\n",
       "1        1.0   9.14\n",
       "2        1.0   4.03\n",
       "3        1.0   2.94"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "design = MS(['lstat'])\n",
    "design = design.fit(Boston)\n",
    "X = design.transform(Boston)\n",
    "X[:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f35e5292",
   "metadata": {},
   "source": [
    "In this simple case, the `fit()`  method does very little; it simply checks that the variable `'lstat'` specified in `design` exists in `Boston`. Then `transform()` constructs the model matrix with two columns: an `intercept` and the variable `lstat`.\n",
    "\n",
    "These two operations can be  combined with the\n",
    "`fit_transform()`  method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d5c7b370",
   "metadata": {
    "execution": {
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    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>intercept</th>\n",
       "      <th>lstat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   intercept  lstat\n",
       "0        1.0   4.98\n",
       "1        1.0   9.14\n",
       "2        1.0   4.03\n",
       "3        1.0   2.94"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "design = MS(['lstat'])\n",
    "X = design.fit_transform(Boston)\n",
    "X[:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f09689d",
   "metadata": {},
   "source": [
    "Note that, as in the previous code chunk when the two steps were done separately, the `design` object is changed as a result of the `fit()` operation. The power of this pipeline will become clearer when we fit more complex models that involve interactions and transformations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94a7c0aa",
   "metadata": {},
   "source": [
    "Let's return to our fitted regression model.\n",
    "The object\n",
    "`results` has several methods that can be used for inference.\n",
    "We already presented a function `summarize()` for showing the essentials of the fit.\n",
    "For a full and somewhat exhaustive summary of the fit, we can use the `summary()` \n",
    "method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5b205c0b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.766508Z",
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>medv</td>       <th>  R-squared:         </th> <td>   0.544</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.543</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   601.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 03 Apr 2025</td> <th>  Prob (F-statistic):</th> <td>5.08e-88</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:32:50</td>     <th>  Log-Likelihood:    </th> <td> -1641.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3287.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3295.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th> <td>   34.5538</td> <td>    0.563</td> <td>   61.415</td> <td> 0.000</td> <td>   33.448</td> <td>   35.659</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>lstat</th>     <td>   -0.9500</td> <td>    0.039</td> <td>  -24.528</td> <td> 0.000</td> <td>   -1.026</td> <td>   -0.874</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>137.043</td> <th>  Durbin-Watson:     </th> <td>   0.892</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 291.373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.453</td>  <th>  Prob(JB):          </th> <td>5.36e-64</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.319</td>  <th>  Cond. No.          </th> <td>    29.7</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &       medv       & \\textbf{  R-squared:         } &     0.544   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared:    } &     0.543   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       } &     601.6   \\\\\n",
       "\\textbf{Date:}             & Thu, 03 Apr 2025 & \\textbf{  Prob (F-statistic):} &  5.08e-88   \\\\\n",
       "\\textbf{Time:}             &     15:32:50     & \\textbf{  Log-Likelihood:    } &   -1641.5   \\\\\n",
       "\\textbf{No. Observations:} &         506      & \\textbf{  AIC:               } &     3287.   \\\\\n",
       "\\textbf{Df Residuals:}     &         504      & \\textbf{  BIC:               } &     3295.   \\\\\n",
       "\\textbf{Df Model:}         &           1      & \\textbf{                     } &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     } &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                   & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{intercept} &      34.5538  &        0.563     &    61.415  &         0.000        &       33.448    &       35.659     \\\\\n",
       "\\textbf{lstat}     &      -0.9500  &        0.039     &   -24.528  &         0.000        &       -1.026    &       -0.874     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 137.043 & \\textbf{  Durbin-Watson:     } &    0.892  \\\\\n",
       "\\textbf{Prob(Omnibus):} &   0.000 & \\textbf{  Jarque-Bera (JB):  } &  291.373  \\\\\n",
       "\\textbf{Skew:}          &   1.453 & \\textbf{  Prob(JB):          } & 5.36e-64  \\\\\n",
       "\\textbf{Kurtosis:}      &   5.319 & \\textbf{  Cond. No.          } &     29.7  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   medv   R-squared:                       0.544\n",
       "Model:                            OLS   Adj. R-squared:                  0.543\n",
       "Method:                 Least Squares   F-statistic:                     601.6\n",
       "Date:                Thu, 03 Apr 2025   Prob (F-statistic):           5.08e-88\n",
       "Time:                        15:32:50   Log-Likelihood:                -1641.5\n",
       "No. Observations:                 506   AIC:                             3287.\n",
       "Df Residuals:                     504   BIC:                             3295.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept     34.5538      0.563     61.415      0.000      33.448      35.659\n",
       "lstat         -0.9500      0.039    -24.528      0.000      -1.026      -0.874\n",
       "==============================================================================\n",
       "Omnibus:                      137.043   Durbin-Watson:                   0.892\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              291.373\n",
       "Skew:                           1.453   Prob(JB):                     5.36e-64\n",
       "Kurtosis:                       5.319   Cond. No.                         29.7\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.summary()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c30baa4",
   "metadata": {},
   "source": [
    "The fitted coefficients can also be retrieved as the\n",
    "`params` attribute of `results`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4b024467",
   "metadata": {
    "execution": {
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "intercept    34.553841\n",
       "lstat        -0.950049\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.params\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb7bbd4c",
   "metadata": {},
   "source": [
    "The `get_prediction()`  method can be used to obtain predictions, and produce confidence intervals and\n",
    "prediction intervals for the prediction of  `medv`  for  given values of  `lstat`.\n",
    "\n",
    "We first create a new data frame, in this case containing only the variable `lstat`, with the values for this variable at which we wish to make predictions.\n",
    "We then use the `transform()` method of `design` to create the corresponding model matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "195e0ace",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.778190Z",
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    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>intercept</th>\n",
       "      <th>lstat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>10</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   intercept  lstat\n",
       "0        1.0      5\n",
       "1        1.0     10\n",
       "2        1.0     15"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_df = pd.DataFrame({'lstat':[5, 10, 15]})\n",
    "newX = design.transform(new_df)\n",
    "newX\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43565f15",
   "metadata": {},
   "source": [
    "Next we compute the predictions at `newX`, and view them by extracting the `predicted_mean` attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "768374f6",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2025-04-03T19:32:50.784190Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([29.80359411, 25.05334734, 20.30310057])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_predictions = results.get_prediction(newX);\n",
    "new_predictions.predicted_mean\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "313c1720",
   "metadata": {},
   "source": [
    "We can produce confidence intervals for the predicted values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1a86b943",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.785520Z",
     "iopub.status.busy": "2025-04-03T19:32:50.785454Z",
     "iopub.status.idle": "2025-04-03T19:32:50.787492Z",
     "shell.execute_reply": "2025-04-03T19:32:50.787305Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[29.00741194, 30.59977628],\n",
       "       [24.47413202, 25.63256267],\n",
       "       [19.73158815, 20.87461299]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_predictions.conf_int(alpha=0.05)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3595344e",
   "metadata": {},
   "source": [
    "Prediction intervals are computed by setting `obs=True`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ea9727ca",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.788600Z",
     "iopub.status.busy": "2025-04-03T19:32:50.788538Z",
     "iopub.status.idle": "2025-04-03T19:32:50.790459Z",
     "shell.execute_reply": "2025-04-03T19:32:50.790248Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[17.56567478, 42.04151344],\n",
       "       [12.82762635, 37.27906833],\n",
       "       [ 8.0777421 , 32.52845905]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_predictions.conf_int(obs=True, alpha=0.05)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b157334d",
   "metadata": {},
   "source": [
    " For instance, the 95% confidence interval associated with an\n",
    " `lstat`  value of 10 is (24.47, 25.63), and the 95% prediction\n",
    "interval is (12.82, 37.28).  As expected, the confidence and\n",
    "prediction intervals are centered around the same point (a predicted\n",
    "value of 25.05 for  `medv`  when  `lstat`  equals\n",
    "10), but the latter are substantially wider.\n",
    "\n",
    "Next we will plot  `medv`  and  `lstat` \n",
    "using `DataFrame.plot.scatter()`, \\definelongblankMR{plot.scatter()}{plot.slashslashscatter()}\n",
    "and wish to\n",
    "add the regression line to the resulting plot."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05f5b29a",
   "metadata": {},
   "source": [
    "### Defining Functions\n",
    "While there is a function\n",
    "within the `ISLP` package that adds a line to an existing plot, we take this opportunity\n",
    "to define our first function to do so."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "796c20f6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.791606Z",
     "iopub.status.busy": "2025-04-03T19:32:50.791541Z",
     "iopub.status.idle": "2025-04-03T19:32:50.793223Z",
     "shell.execute_reply": "2025-04-03T19:32:50.793036Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "def abline(ax, b, m):\n",
    "    \"Add a line with slope m and intercept b to ax\"\n",
    "    xlim = ax.get_xlim()\n",
    "    ylim = [m * xlim[0] + b, m * xlim[1] + b]\n",
    "    ax.plot(xlim, ylim)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eb99e73",
   "metadata": {},
   "source": [
    " A few things are illustrated above. First we see the syntax for defining a function:\n",
    "`def funcname(...)`. The function has arguments `ax, b, m`\n",
    "where `ax` is an axis object for an existing plot, `b` is the intercept and\n",
    "`m` is the slope of the desired line. Other plotting  options can be passed on to\n",
    "`ax.plot` by including additional optional arguments as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a258b8c0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.794312Z",
     "iopub.status.busy": "2025-04-03T19:32:50.794246Z",
     "iopub.status.idle": "2025-04-03T19:32:50.795895Z",
     "shell.execute_reply": "2025-04-03T19:32:50.795688Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "def abline(ax, b, m, *args, **kwargs):\n",
    "    \"Add a line with slope m and intercept b to ax\"\n",
    "    xlim = ax.get_xlim()\n",
    "    ylim = [m * xlim[0] + b, m * xlim[1] + b]\n",
    "    ax.plot(xlim, ylim, *args, **kwargs)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be8f4615",
   "metadata": {},
   "source": [
    "The addition of `*args` allows any number of\n",
    "non-named arguments to `abline`, while `**kwargs` allows any\n",
    "number of named arguments (such as `linewidth=3`) to `abline`.\n",
    "In our function, we pass\n",
    "these arguments verbatim to `ax.plot` above. Readers\n",
    "interested in learning more about\n",
    "functions are referred to the section on\n",
    "defining functions in [docs.python.org/tutorial](https://docs.python.org/3/tutorial/controlflow.html#defining-functions).\n",
    "\n",
    "Let’s use our new function to add this regression line to a plot of\n",
    "`medv` vs. `lstat`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "56b75491",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.796931Z",
     "iopub.status.busy": "2025-04-03T19:32:50.796870Z",
     "iopub.status.idle": "2025-04-03T19:32:50.884204Z",
     "shell.execute_reply": "2025-04-03T19:32:50.882265Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/16/8y65_zv174qgdp4ktlmpv12h0000gq/T/ipykernel_70382/1591428221.py:3: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  results.params[0],\n",
      "/var/folders/16/8y65_zv174qgdp4ktlmpv12h0000gq/T/ipykernel_70382/1591428221.py:4: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  results.params[1],\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = Boston.plot.scatter('lstat', 'medv')\n",
    "abline(ax,\n",
    "       results.params[0],\n",
    "       results.params[1],\n",
    "       'r--',\n",
    "       linewidth=3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04a1e56f",
   "metadata": {},
   "source": [
    "Thus, the final call to `ax.plot()` is `ax.plot(xlim, ylim, 'r--', linewidth=3)`.\n",
    "We have used the argument `'r--'` to produce a red dashed line, and added\n",
    "an argument to make it of width 3.\n",
    "There is some evidence for non-linearity in the relationship between  `lstat`  and  `medv`. We will explore this issue later in this lab.\n",
    "\n",
    "As mentioned above, there is an existing function to add a line to a plot --- `ax.axline()` --- but knowing how to write such functions empowers us to create more expressive displays.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a083307",
   "metadata": {},
   "source": [
    "Next we examine some diagnostic plots, several of which were discussed\n",
    "in Section 3.3.3.\n",
    "We can find the fitted values and residuals\n",
    "of the fit as attributes of the `results` object.\n",
    "Various influence measures describing the regression model\n",
    "are computed with the `get_influence()` method.\n",
    "As we will not use the `fig` component returned\n",
    "as the first value from `subplots()`, we simply\n",
    "capture the second returned value in `ax` below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "74be2100",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.888362Z",
     "iopub.status.busy": "2025-04-03T19:32:50.887998Z",
     "iopub.status.idle": "2025-04-03T19:32:50.983668Z",
     "shell.execute_reply": "2025-04-03T19:32:50.983019Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = subplots(figsize=(8,8))[1]\n",
    "ax.scatter(results.fittedvalues, results.resid)\n",
    "ax.set_xlabel('Fitted value')\n",
    "ax.set_ylabel('Residual')\n",
    "ax.axhline(0, c='k', ls='--');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c00db5a1",
   "metadata": {},
   "source": [
    " We add a horizontal line at 0 for reference using the\n",
    " `ax.axhline()`   method, indicating\n",
    "it should be black (`c='k'`) and have a dashed linestyle (`ls='--'`).\n",
    "\n",
    "On the basis of the residual plot, there is some evidence of non-linearity.\n",
    "Leverage statistics can be computed for any number of predictors using the\n",
    "`hat_matrix_diag` attribute of the value returned by the\n",
    "`get_influence()`  method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "db8bc925",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:50.987634Z",
     "iopub.status.busy": "2025-04-03T19:32:50.987335Z",
     "iopub.status.idle": "2025-04-03T19:32:51.093124Z",
     "shell.execute_reply": "2025-04-03T19:32:51.092860Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "374"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "infl = results.get_influence()\n",
    "ax = subplots(figsize=(8,8))[1]\n",
    "ax.scatter(np.arange(X.shape[0]), infl.hat_matrix_diag)\n",
    "ax.set_xlabel('Index')\n",
    "ax.set_ylabel('Leverage')\n",
    "np.argmax(infl.hat_matrix_diag)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e7aa0bb",
   "metadata": {},
   "source": [
    " The `np.argmax()`  function identifies the index of the largest element of an array, optionally computed over an axis of the array.\n",
    "In this case, we maximized over the entire array\n",
    "to determine which observation has the largest leverage statistic."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e98db373",
   "metadata": {},
   "source": [
    "## Multiple Linear Regression\n",
    "In order to fit a multiple linear regression model using least squares, we again use\n",
    "the `ModelSpec()`  transform to construct the required\n",
    "model matrix and response. The arguments\n",
    "to `ModelSpec()` can be quite general, but in this case\n",
    "a list of column names suffice. We consider a fit here with\n",
    "the two variables `lstat` and `age`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e479373c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.094541Z",
     "iopub.status.busy": "2025-04-03T19:32:51.094455Z",
     "iopub.status.idle": "2025-04-03T19:32:51.105229Z",
     "shell.execute_reply": "2025-04-03T19:32:51.104994Z"
    },
    "lines_to_next_cell": 0
   },
   "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>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>33.2228</td>\n",
       "      <td>0.731</td>\n",
       "      <td>45.458</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>-1.0321</td>\n",
       "      <td>0.048</td>\n",
       "      <td>-21.416</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>0.0345</td>\n",
       "      <td>0.012</td>\n",
       "      <td>2.826</td>\n",
       "      <td>0.005</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              coef  std err       t  P>|t|\n",
       "intercept  33.2228    0.731  45.458  0.000\n",
       "lstat      -1.0321    0.048 -21.416  0.000\n",
       "age         0.0345    0.012   2.826  0.005"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = MS(['lstat', 'age']).fit_transform(Boston)\n",
    "model1 = sm.OLS(y, X)\n",
    "results1 = model1.fit()\n",
    "summarize(results1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c79b00d",
   "metadata": {},
   "source": [
    "Notice how we have compacted the first line into a succinct expression describing the construction of `X`.\n",
    "\n",
    "The  `Boston`   data set contains 12 variables, and so it would be cumbersome\n",
    "to have to type all of these in order to perform a regression using all of the predictors.\n",
    "Instead, we can use the following short-hand:\\definelongblankMR{columns.drop()}{columns.slashslashdrop()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b903170c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.106458Z",
     "iopub.status.busy": "2025-04-03T19:32:51.106379Z",
     "iopub.status.idle": "2025-04-03T19:32:51.108676Z",
     "shell.execute_reply": "2025-04-03T19:32:51.108453Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'rad', 'tax',\n",
       "       'ptratio', 'lstat'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "terms = Boston.columns.drop('medv')\n",
    "terms\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "179b7846",
   "metadata": {},
   "source": [
    "We can now fit the model with all the variables in `terms` using\n",
    "the same model matrix builder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bbe47670",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.109894Z",
     "iopub.status.busy": "2025-04-03T19:32:51.109814Z",
     "iopub.status.idle": "2025-04-03T19:32:51.124106Z",
     "shell.execute_reply": "2025-04-03T19:32:51.123871Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>41.6173</td>\n",
       "      <td>4.936</td>\n",
       "      <td>8.431</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>crim</th>\n",
       "      <td>-0.1214</td>\n",
       "      <td>0.033</td>\n",
       "      <td>-3.678</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zn</th>\n",
       "      <td>0.0470</td>\n",
       "      <td>0.014</td>\n",
       "      <td>3.384</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>indus</th>\n",
       "      <td>0.0135</td>\n",
       "      <td>0.062</td>\n",
       "      <td>0.217</td>\n",
       "      <td>0.829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>chas</th>\n",
       "      <td>2.8400</td>\n",
       "      <td>0.870</td>\n",
       "      <td>3.264</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nox</th>\n",
       "      <td>-18.7580</td>\n",
       "      <td>3.851</td>\n",
       "      <td>-4.870</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rm</th>\n",
       "      <td>3.6581</td>\n",
       "      <td>0.420</td>\n",
       "      <td>8.705</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>0.0036</td>\n",
       "      <td>0.013</td>\n",
       "      <td>0.271</td>\n",
       "      <td>0.787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dis</th>\n",
       "      <td>-1.4908</td>\n",
       "      <td>0.202</td>\n",
       "      <td>-7.394</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rad</th>\n",
       "      <td>0.2894</td>\n",
       "      <td>0.067</td>\n",
       "      <td>4.325</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tax</th>\n",
       "      <td>-0.0127</td>\n",
       "      <td>0.004</td>\n",
       "      <td>-3.337</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ptratio</th>\n",
       "      <td>-0.9375</td>\n",
       "      <td>0.132</td>\n",
       "      <td>-7.091</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>-0.5520</td>\n",
       "      <td>0.051</td>\n",
       "      <td>-10.897</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              coef  std err       t  P>|t|\n",
       "intercept  41.6173    4.936   8.431  0.000\n",
       "crim       -0.1214    0.033  -3.678  0.000\n",
       "zn          0.0470    0.014   3.384  0.001\n",
       "indus       0.0135    0.062   0.217  0.829\n",
       "chas        2.8400    0.870   3.264  0.001\n",
       "nox       -18.7580    3.851  -4.870  0.000\n",
       "rm          3.6581    0.420   8.705  0.000\n",
       "age         0.0036    0.013   0.271  0.787\n",
       "dis        -1.4908    0.202  -7.394  0.000\n",
       "rad         0.2894    0.067   4.325  0.000\n",
       "tax        -0.0127    0.004  -3.337  0.001\n",
       "ptratio    -0.9375    0.132  -7.091  0.000\n",
       "lstat      -0.5520    0.051 -10.897  0.000"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = MS(terms).fit_transform(Boston)\n",
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n",
    "summarize(results)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "183c3c40",
   "metadata": {},
   "source": [
    "What if we would like to perform a regression using all of the variables but one?  For\n",
    "example, in the above regression output,   `age`  has a high $p$-value.\n",
    "So we may wish to run a regression excluding this predictor.\n",
    "The following syntax results in a regression using all predictors except  `age`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a1484d00",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.125356Z",
     "iopub.status.busy": "2025-04-03T19:32:51.125276Z",
     "iopub.status.idle": "2025-04-03T19:32:51.138960Z",
     "shell.execute_reply": "2025-04-03T19:32:51.138745Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>41.5251</td>\n",
       "      <td>4.920</td>\n",
       "      <td>8.441</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>crim</th>\n",
       "      <td>-0.1214</td>\n",
       "      <td>0.033</td>\n",
       "      <td>-3.683</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zn</th>\n",
       "      <td>0.0465</td>\n",
       "      <td>0.014</td>\n",
       "      <td>3.379</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>indus</th>\n",
       "      <td>0.0135</td>\n",
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       "      <td>0.217</td>\n",
       "      <td>0.829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>chas</th>\n",
       "      <td>2.8528</td>\n",
       "      <td>0.868</td>\n",
       "      <td>3.287</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nox</th>\n",
       "      <td>-18.4851</td>\n",
       "      <td>3.714</td>\n",
       "      <td>-4.978</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rm</th>\n",
       "      <td>3.6811</td>\n",
       "      <td>0.411</td>\n",
       "      <td>8.951</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dis</th>\n",
       "      <td>-1.5068</td>\n",
       "      <td>0.193</td>\n",
       "      <td>-7.825</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rad</th>\n",
       "      <td>0.2879</td>\n",
       "      <td>0.067</td>\n",
       "      <td>4.322</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tax</th>\n",
       "      <td>-0.0127</td>\n",
       "      <td>0.004</td>\n",
       "      <td>-3.333</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ptratio</th>\n",
       "      <td>-0.9346</td>\n",
       "      <td>0.132</td>\n",
       "      <td>-7.099</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>-0.5474</td>\n",
       "      <td>0.048</td>\n",
       "      <td>-11.483</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              coef  std err       t  P>|t|\n",
       "intercept  41.5251    4.920   8.441  0.000\n",
       "crim       -0.1214    0.033  -3.683  0.000\n",
       "zn          0.0465    0.014   3.379  0.001\n",
       "indus       0.0135    0.062   0.217  0.829\n",
       "chas        2.8528    0.868   3.287  0.001\n",
       "nox       -18.4851    3.714  -4.978  0.000\n",
       "rm          3.6811    0.411   8.951  0.000\n",
       "dis        -1.5068    0.193  -7.825  0.000\n",
       "rad         0.2879    0.067   4.322  0.000\n",
       "tax        -0.0127    0.004  -3.333  0.001\n",
       "ptratio    -0.9346    0.132  -7.099  0.000\n",
       "lstat      -0.5474    0.048 -11.483  0.000"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minus_age = Boston.columns.drop(['medv', 'age']) \n",
    "Xma = MS(minus_age).fit_transform(Boston)\n",
    "model1 = sm.OLS(y, Xma)\n",
    "summarize(model1.fit())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74ec4654",
   "metadata": {},
   "source": [
    "## Multivariate Goodness of Fit\n",
    "We can access the individual components of `results` by name\n",
    "(`dir(results)` shows us what is available). Hence\n",
    "`results.rsquared` gives us the $R^2$,\n",
    "and\n",
    "`np.sqrt(results.scale)` gives us the RSE.\n",
    "\n",
    "Variance inflation factors (section 3.3.3) are sometimes useful\n",
    "to assess the effect of collinearity in the model matrix of a regression model.\n",
    "We will compute the VIFs in our multiple regression fit, and use the opportunity to introduce the idea of *list comprehension*.\n",
    "\n",
    "### List Comprehension\n",
    "Often we encounter a sequence of objects which we would like to transform\n",
    "for some other task. Below, we compute the VIF for each\n",
    "feature in our `X` matrix and produce a data frame\n",
    "whose index agrees with the columns of `X`.\n",
    "The notion of list comprehension can often make such\n",
    "a task easier.\n",
    "\n",
    "List comprehensions are simple and powerful ways to form\n",
    "lists of `Python` objects. The language also supports\n",
    "dictionary and *generator* comprehension, though these are\n",
    "beyond our scope here. Let's look at an example. We compute the VIF for each of the variables\n",
    "in the model matrix `X`, using the function `variance_inflation_factor()`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "46ac946c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.140138Z",
     "iopub.status.busy": "2025-04-03T19:32:51.140067Z",
     "iopub.status.idle": "2025-04-03T19:32:51.146004Z",
     "shell.execute_reply": "2025-04-03T19:32:51.145771Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vif</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>crim</th>\n",
       "      <td>1.767486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zn</th>\n",
       "      <td>2.298459</td>\n",
       "    </tr>\n",
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       "      <th>indus</th>\n",
       "      <td>3.987181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>chas</th>\n",
       "      <td>1.071168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nox</th>\n",
       "      <td>4.369093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rm</th>\n",
       "      <td>1.912532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>3.088232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dis</th>\n",
       "      <td>3.954037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rad</th>\n",
       "      <td>7.445301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tax</th>\n",
       "      <td>9.002158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ptratio</th>\n",
       "      <td>1.797060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>2.870777</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              vif\n",
       "crim     1.767486\n",
       "zn       2.298459\n",
       "indus    3.987181\n",
       "chas     1.071168\n",
       "nox      4.369093\n",
       "rm       1.912532\n",
       "age      3.088232\n",
       "dis      3.954037\n",
       "rad      7.445301\n",
       "tax      9.002158\n",
       "ptratio  1.797060\n",
       "lstat    2.870777"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vals = [VIF(X, i)\n",
    "        for i in range(1, X.shape[1])]\n",
    "vif = pd.DataFrame({'vif':vals},\n",
    "                   index=X.columns[1:])\n",
    "vif\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45a29903",
   "metadata": {},
   "source": [
    "The function `VIF()` takes two arguments: a dataframe or array,\n",
    "and a variable column index. In the code above we call `VIF()` on the fly for all columns in `X`.  \n",
    "We have excluded column 0 above (the intercept), which is not of interest. In this case the VIFs are not that exciting.\n",
    "\n",
    "The object `vals` above could have been constructed with the following for loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "b626ecb9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.147247Z",
     "iopub.status.busy": "2025-04-03T19:32:51.147171Z",
     "iopub.status.idle": "2025-04-03T19:32:51.151571Z",
     "shell.execute_reply": "2025-04-03T19:32:51.151341Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "vals = []\n",
    "for i in range(1, X.values.shape[1]):\n",
    "    vals.append(VIF(X.values, i))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e504ae2",
   "metadata": {},
   "source": [
    "List comprehension allows us to perform such repetitive operations in a more straightforward way.\n",
    "## Interaction Terms\n",
    "It is easy to include interaction terms in a linear model using `ModelSpec()`.\n",
    "Including a tuple `(\"lstat\",\"age\")` tells the model\n",
    "matrix builder to include an interaction term between\n",
    " `lstat`  and  `age`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8bf77477",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.152822Z",
     "iopub.status.busy": "2025-04-03T19:32:51.152716Z",
     "iopub.status.idle": "2025-04-03T19:32:51.163070Z",
     "shell.execute_reply": "2025-04-03T19:32:51.162825Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>36.0885</td>\n",
       "      <td>1.470</td>\n",
       "      <td>24.553</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat</th>\n",
       "      <td>-1.3921</td>\n",
       "      <td>0.167</td>\n",
       "      <td>-8.313</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>-0.0007</td>\n",
       "      <td>0.020</td>\n",
       "      <td>-0.036</td>\n",
       "      <td>0.971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lstat:age</th>\n",
       "      <td>0.0042</td>\n",
       "      <td>0.002</td>\n",
       "      <td>2.244</td>\n",
       "      <td>0.025</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              coef  std err       t  P>|t|\n",
       "intercept  36.0885    1.470  24.553  0.000\n",
       "lstat      -1.3921    0.167  -8.313  0.000\n",
       "age        -0.0007    0.020  -0.036  0.971\n",
       "lstat:age   0.0042    0.002   2.244  0.025"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = MS(['lstat',\n",
    "        'age',\n",
    "        ('lstat', 'age')]).fit_transform(Boston)\n",
    "model2 = sm.OLS(y, X)\n",
    "summarize(model2.fit())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2323ab9",
   "metadata": {},
   "source": [
    "## Non-linear Transformations of the Predictors\n",
    "The model matrix builder can include terms beyond\n",
    "just column names and interactions. For instance,\n",
    "the `poly()` function supplied in `ISLP` specifies that\n",
    "columns representing polynomial functions\n",
    "of its first argument are added to the model matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "6289c3cb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.164397Z",
     "iopub.status.busy": "2025-04-03T19:32:51.164312Z",
     "iopub.status.idle": "2025-04-03T19:32:51.175546Z",
     "shell.execute_reply": "2025-04-03T19:32:51.175305Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        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>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>17.7151</td>\n",
       "      <td>0.781</td>\n",
       "      <td>22.681</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>poly(lstat, degree=2)[0]</th>\n",
       "      <td>-179.2279</td>\n",
       "      <td>6.733</td>\n",
       "      <td>-26.620</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>poly(lstat, degree=2)[1]</th>\n",
       "      <td>72.9908</td>\n",
       "      <td>5.482</td>\n",
       "      <td>13.315</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>0.0703</td>\n",
       "      <td>0.011</td>\n",
       "      <td>6.471</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              coef  std err       t  P>|t|\n",
       "intercept                  17.7151    0.781  22.681    0.0\n",
       "poly(lstat, degree=2)[0] -179.2279    6.733 -26.620    0.0\n",
       "poly(lstat, degree=2)[1]   72.9908    5.482  13.315    0.0\n",
       "age                         0.0703    0.011   6.471    0.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = MS([poly('lstat', degree=2), 'age']).fit_transform(Boston)\n",
    "model3 = sm.OLS(y, X)\n",
    "results3 = model3.fit()\n",
    "summarize(results3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bd67b14",
   "metadata": {},
   "source": [
    "The effectively zero *p*-value associated with the quadratic term\n",
    "(i.e. the third row above) suggests that it leads to an improved model.\n",
    "\n",
    "By default, `poly()` creates a basis matrix for inclusion in the\n",
    "model matrix whose\n",
    "columns are *orthogonal polynomials*, which are designed for stable\n",
    "least squares computations. {Actually, `poly()` is a  wrapper for the workhorse and standalone  function `Poly()` that does the  work in building the model matrix.}\n",
    "Alternatively, had we included an argument\n",
    "`raw=True` in the above call to `poly()`, the basis matrix would consist simply of\n",
    "`lstat` and `lstat**2`. Since either of these bases\n",
    "represent quadratic polynomials, the fitted values  would not\n",
    "change in this case, just the polynomial coefficients.  Also by default, the columns\n",
    "created by `poly()` do not include an intercept column as\n",
    "that is automatically added by `MS()`.\n",
    "\n",
    "We use the `anova_lm()` function to further quantify the extent to which the quadratic fit is\n",
    "superior to the linear fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b6542ac6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.176770Z",
     "iopub.status.busy": "2025-04-03T19:32:51.176688Z",
     "iopub.status.idle": "2025-04-03T19:32:51.180893Z",
     "shell.execute_reply": "2025-04-03T19:32:51.180653Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>df_resid</th>\n",
       "      <th>ssr</th>\n",
       "      <th>df_diff</th>\n",
       "      <th>ss_diff</th>\n",
       "      <th>F</th>\n",
       "      <th>Pr(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>503.0</td>\n",
       "      <td>19168.128609</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>502.0</td>\n",
       "      <td>14165.613251</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5002.515357</td>\n",
       "      <td>177.278785</td>\n",
       "      <td>7.468491e-35</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   df_resid           ssr  df_diff      ss_diff           F        Pr(>F)\n",
       "0     503.0  19168.128609      0.0          NaN         NaN           NaN\n",
       "1     502.0  14165.613251      1.0  5002.515357  177.278785  7.468491e-35"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anova_lm(results1, results3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3685159a",
   "metadata": {},
   "source": [
    "Here `results1` represents the linear submodel containing\n",
    "predictors `lstat` and `age`,\n",
    "while `results3` corresponds to the larger model above  with a quadratic\n",
    "term in `lstat`.\n",
    "The `anova_lm()` function performs a hypothesis test\n",
    "comparing the two models. The null hypothesis is that the quadratic\n",
    "term in the bigger model is not needed, and the alternative hypothesis is that the\n",
    "bigger model is superior. Here the *F*-statistic is 177.28 and\n",
    "the associated *p*-value is zero.\n",
    "In this case the *F*-statistic is the square of the\n",
    "*t*-statistic for the quadratic term in the linear model summary\n",
    "for `results3` --- a consequence of the fact that these nested\n",
    "models differ by one degree of freedom.\n",
    "This provides very clear evidence that the quadratic polynomial in\n",
    "`lstat` improves the linear model.\n",
    "This is not surprising, since earlier we saw evidence for non-linearity in the relationship between `medv`\n",
    "and  `lstat`.\n",
    "\n",
    "The function `anova_lm()` can take more than two nested models\n",
    "as input, in which case it compares every successive pair of models.\n",
    "That also explains why there are `NaN`s in the first row above, since\n",
    "there is no previous model with which to compare the first.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8e4c6004",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.182118Z",
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     "shell.execute_reply": "2025-04-03T19:32:51.233183Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = subplots(figsize=(8,8))[1]\n",
    "ax.scatter(results3.fittedvalues, results3.resid)\n",
    "ax.set_xlabel('Fitted value')\n",
    "ax.set_ylabel('Residual')\n",
    "ax.axhline(0, c='k', ls='--');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c7e0661",
   "metadata": {},
   "source": [
    "We see that when the quadratic term is included in the model,\n",
    "there is little discernible pattern in the residuals.\n",
    "In order to create a cubic or higher-degree polynomial fit, we can simply change the degree argument\n",
    "to `poly()`.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a4967d",
   "metadata": {},
   "source": [
    "## Qualitative Predictors\n",
    "Here we use the  `Carseats`  data, which is included in the\n",
    "`ISLP` package. We will  attempt to predict `Sales`\n",
    "(child car seat sales) in 400 locations based on a number of\n",
    "predictors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "a83f4bd2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.234718Z",
     "iopub.status.busy": "2025-04-03T19:32:51.234617Z",
     "iopub.status.idle": "2025-04-03T19:32:51.239575Z",
     "shell.execute_reply": "2025-04-03T19:32:51.239354Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Sales', 'CompPrice', 'Income', 'Advertising', 'Population', 'Price',\n",
       "       'ShelveLoc', 'Age', 'Education', 'Urban', 'US'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Carseats = load_data('Carseats')\n",
    "Carseats.columns\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69025ecd",
   "metadata": {},
   "source": [
    "The `Carseats`  \n",
    " data includes qualitative predictors such as\n",
    " `ShelveLoc`, an indicator of the quality of the shelving\n",
    " location --- that is,\n",
    "the  space within a store in which the car seat is displayed. The predictor\n",
    " `ShelveLoc`  takes on three possible values, `Bad`, `Medium`, and `Good`.\n",
    "Given a qualitative variable such as  `ShelveLoc`, `ModelSpec()` generates dummy\n",
    "variables automatically.\n",
    "These variables are often referred to as a *one-hot encoding* of the categorical\n",
    "feature. Their columns sum to one, so to avoid collinearity with an intercept, the first column is dropped. Below we see\n",
    "the column `ShelveLoc[Bad]` has been dropped, since `Bad` is the first level of `ShelveLoc`.\n",
    "Below we fit a multiple regression model that includes some interaction terms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "24efc6f1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-04-03T19:32:51.240897Z",
     "iopub.status.busy": "2025-04-03T19:32:51.240800Z",
     "iopub.status.idle": "2025-04-03T19:32:51.261250Z",
     "shell.execute_reply": "2025-04-03T19:32:51.261014Z"
    },
    "lines_to_next_cell": 0
   },
   "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>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>intercept</th>\n",
       "      <td>6.5756</td>\n",
       "      <td>1.009</td>\n",
       "      <td>6.519</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CompPrice</th>\n",
       "      <td>0.0929</td>\n",
       "      <td>0.004</td>\n",
       "      <td>22.567</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Income</th>\n",
       "      <td>0.0109</td>\n",
       "      <td>0.003</td>\n",
       "      <td>4.183</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Advertising</th>\n",
       "      <td>0.0702</td>\n",
       "      <td>0.023</td>\n",
       "      <td>3.107</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Population</th>\n",
       "      <td>0.0002</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.433</td>\n",
       "      <td>0.665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Price</th>\n",
       "      <td>-0.1008</td>\n",
       "      <td>0.007</td>\n",
       "      <td>-13.549</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ShelveLoc[Good]</th>\n",
       "      <td>4.8487</td>\n",
       "      <td>0.153</td>\n",
       "      <td>31.724</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ShelveLoc[Medium]</th>\n",
       "      <td>1.9533</td>\n",
       "      <td>0.126</td>\n",
       "      <td>15.531</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>-0.0579</td>\n",
       "      <td>0.016</td>\n",
       "      <td>-3.633</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Education</th>\n",
       "      <td>-0.0209</td>\n",
       "      <td>0.020</td>\n",
       "      <td>-1.063</td>\n",
       "      <td>0.288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Urban[Yes]</th>\n",
       "      <td>0.1402</td>\n",
       "      <td>0.112</td>\n",
       "      <td>1.247</td>\n",
       "      <td>0.213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>US[Yes]</th>\n",
       "      <td>-0.1576</td>\n",
       "      <td>0.149</td>\n",
       "      <td>-1.058</td>\n",
       "      <td>0.291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Income:Advertising</th>\n",
       "      <td>0.0008</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2.698</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Price:Age</th>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.801</td>\n",
       "      <td>0.424</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      coef  std err       t  P>|t|\n",
       "intercept           6.5756    1.009   6.519  0.000\n",
       "CompPrice           0.0929    0.004  22.567  0.000\n",
       "Income              0.0109    0.003   4.183  0.000\n",
       "Advertising         0.0702    0.023   3.107  0.002\n",
       "Population          0.0002    0.000   0.433  0.665\n",
       "Price              -0.1008    0.007 -13.549  0.000\n",
       "ShelveLoc[Good]     4.8487    0.153  31.724  0.000\n",
       "ShelveLoc[Medium]   1.9533    0.126  15.531  0.000\n",
       "Age                -0.0579    0.016  -3.633  0.000\n",
       "Education          -0.0209    0.020  -1.063  0.288\n",
       "Urban[Yes]          0.1402    0.112   1.247  0.213\n",
       "US[Yes]            -0.1576    0.149  -1.058  0.291\n",
       "Income:Advertising  0.0008    0.000   2.698  0.007\n",
       "Price:Age           0.0001    0.000   0.801  0.424"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allvars = list(Carseats.columns.drop('Sales'))\n",
    "y = Carseats['Sales']\n",
    "final = allvars + [('Income', 'Advertising'),\n",
    "                   ('Price', 'Age')]\n",
    "X = MS(final).fit_transform(Carseats)\n",
    "model = sm.OLS(y, X)\n",
    "summarize(model.fit())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8a76419",
   "metadata": {},
   "source": [
    "In the first line above, we made `allvars` a list, so that we\n",
    "could add the interaction terms two lines down. \n",
    "Our model-matrix builder has created a `ShelveLoc[Good]`\n",
    "dummy variable that takes on a value of 1 if the\n",
    "shelving location is good, and 0 otherwise. It has also created a `ShelveLoc[Medium]`\n",
    "dummy variable that equals 1 if the shelving location is medium, and 0 otherwise.\n",
    "A bad shelving location corresponds to a zero for each of the two dummy variables.\n",
    "The fact that the coefficient for `ShelveLoc[Good]` in the regression output is\n",
    "positive indicates that a good shelving location is associated with high sales (relative to a bad location).\n",
    "And `ShelveLoc[Medium]` has a smaller positive coefficient,\n",
    "indicating that a medium shelving location leads to higher sales than a bad\n",
    "shelving location, but lower sales than a good shelving location.\n",
    "\n"
   ]
  }
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