Ch03-linreg-lab.ipynb

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   "source": [
    "\n",
    "# Chapter 3"
   ]
  },
  {
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   "source": [
    "# Lab: Linear Regression\n",
    "\n",
    "## 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"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "735a61a6",
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   "source": [
    "### 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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   "id": "a10a1d7d",
   "metadata": {
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   "source": [
    "import statsmodels.api as sm\n"
   ]
  },
  {
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   "id": "4c10ec5f",
   "metadata": {},
   "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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   "execution_count": 3,
   "id": "756c0524",
   "metadata": {
    "execution": {}
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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": "686eb4ee",
   "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",
   "execution_count": 4,
   "id": "2c370a6e",
   "metadata": {
    "execution": {}
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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",
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   "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"
   ]
  },
  {
   "cell_type": "markdown",
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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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       " '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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   "source": [
    "    "
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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  `rmvar`  (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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    {
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      "text/plain": [
       "Index(['crim', 'zn', 'indus', 'chas', 'nox', 'rm', 'age', 'dis', 'rad', 'tax',\n",
       "       'ptratio', 'lstat', 'medv'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Boston = load_data(\"Boston\")\n",
    "Boston.columns\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4fefb35",
   "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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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>intercept</th>\n",
       "      <th>lstat</th>\n",
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       "      <td>1.0</td>\n",
       "      <td>4.98</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>9.14</td>\n",
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       "      <td>1.0</td>\n",
       "      <td>4.03</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.94</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"
   ]
  },
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   "id": "e87fbd51",
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   "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>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",
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       "              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"
      ]
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    "summarize(results)\n"
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    "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"
   ]
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       "      <th></th>\n",
       "      <th>intercept</th>\n",
       "      <th>lstat</th>\n",
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       "      <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": "1de3a91e",
   "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": "edf2efcb",
   "metadata": {
    "execution": {},
    "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>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": "4eab8574",
   "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": "7336a90b",
   "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": "49fc8992",
   "metadata": {
    "execution": {}
   },
   "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>Mon, 21 Aug 2023</td> <th>  Prob (F-statistic):</th> <td>5.08e-88</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:59:30</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:}             & Mon, 21 Aug 2023 & \\textbf{  Prob (F-statistic):} &  5.08e-88   \\\\\n",
       "\\textbf{Time:}             &     23:59:30     & \\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:                Mon, 21 Aug 2023   Prob (F-statistic):           5.08e-88\n",
       "Time:                        23:59:30   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": "cbadf6fb",
   "metadata": {},
   "source": [
    "The fitted coefficients can also be retrieved as the\n",
    "`params` attribute of `results`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6d0f4c3a",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "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": "f97d477a",
   "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": "132ffded",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>intercept</th>\n",
       "      <th>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",
       "    </tr>\n",
       "    <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": "e99b90dc",
   "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": "b654a050",
   "metadata": {
    "execution": {},
    "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": "cca6cef5",
   "metadata": {},
   "source": [
    "We can produce confidence intervals for the predicted values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "148ed59d",
   "metadata": {
    "execution": {},
    "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": "c217e5e2",
   "metadata": {},
   "source": [
    "Prediction intervals are computing by setting `obs=True`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d9d7b844",
   "metadata": {
    "execution": {},
    "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": "a26d3660",
   "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": "50db5bf6",
   "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": "79de2913",
   "metadata": {
    "execution": {},
    "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": "f66dd38d",
   "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 exisiting 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": "a9b843c7",
   "metadata": {
    "execution": {},
    "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": "25ba4401",
   "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": "7e116800",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qd+6GRe+kKq2sQdr8TBSbSey1Z1RESmCRV1COHflFmLlmv8nzZGakmb0ujuYQESmT1P6bgYwC5RWU69WHMWSpc5eq9Epib85x8ZEZscDJEimBhdgxpiydmISBic1MPi814CMiIvcitf9msq8COasCb0igL1Y/1BfL70sSfV7Kcm5DUvZyEjvGFHOJy9pigXUGsbot7SYiIvfEQEaBnF2Bt87CmJ3UwElKYGHqGEPeKhUGJESaHXnilgtERJ6Pyb4KpK0dY+uqJFPq560IgqD7f7kCJzkDCymJy9xygYjI8zGQUSh7ViUZspSTMiAhEqltwpGdX2Rz4JRXUI6zpZfNHqMNoMyZO7IrUtqES3pPRwV8RETkPhjIKFRIoC+WpyfbvCqpPks5KVuOXkBKm6bo1y7C6sBJSuKuYWBhLvi4K7m11MsCIG/AR0RE7oerltyUs+qeWFoBVV9mRhpOFVViz6li9GwdhmsTIi2+RmzVkCHDVUullTVGwYe9S6blCPiIiMh5pPbfHJFxM86oe1I/SLJm9+wpK3fjwL9lktulTdw1xdQ0kZyjTVrxEQxgiIg8EQMZNyNHFVtTxIKk3rFhkl//V70gRkq7LAVJUSGNzAYXDD6IiMgSLr92I46ueyIWJO02sw2BIcPJIUvt4qohIiJyNAYy9lCrgVGjgE8/Berq7D6dI+uemAqS1Daf8SpT7WoT2RhhJqadwgJ9OdpCRER2YyBjj6++AtasAcaPB665BvjuO8CO3GlHjmBYkwtjyNL+kKbalVdQbnKvpuLKGlbWJSIiuzGQsVVNDfDss1f/fOAAMHw40K8fsGmTTafU1j3xVulHDlKq2FpiKUgyF6z0b6epI2Ntu1hZl4iIHI2BjK2++w44csT48W3bgOuuA266Cdi71+rTvjO2B/q1i9B7TI66J+aCpNQ24ejfTn8pdVJsGBaO7YHMjDQsT0/G+//pZXW73DFHJq+gHJm55zkaRETkIVhHxlaCAPz0EzBzJrB/v+nj7roLeOkloF07q07viLonluqzSHlPa9vlLrtPO2NZOxERyUdq/81Axl5qNbByJfDcc0B+vvgxPj5Aejrw/PNATIz8bbCSM4vDOaK4nS3cJaAiIiJpGMhc4bTKvtXVwOLFwIsvAufOiR8TEABMnQo8/TQQJr1+iyW2VAF2VuVg7Xtl5xdBANBH4j5Jcr+/uerFmRlpXEFFRORmWNnX2fz8gEceASZMAN56C3jtNaBMv4AcLl3SPP7995rkYJWF5UAW2DJd4ugplryCcuzILwSgQqfmwViw/rDLR2OkJB0zkCEiUiaOyDhKUZEmaHn7beCywa7P778PPPig3W9hy3SJ1NdYO2JTUlmNRz7fja3HCs0eZ+t0jj0jSByRISJSHo7IuFrTpppAZupUzXTTkiWaonnt2gH33Wf36U3tY1S/2q5h52zpNauyT6KjjaMoU1futRjEWGqfGDlGkLQrtkwFcAxiiIiUi8uvHa1FC+CDD4CDB4ExY4CXXwZ8TXTAeXnAjz9KKqpnS40WS6+ZsWY/hi/cYhTsaPdU0jXTYAmzpc0hpbZPjLm9p6zhqGXtRETkWhyRcZb27YFVq8wf89xzwIoVQP/+wJw5mv+aYEuNFlujVu0oyp+nSoxGa5LiwtA7zvrEZSk1ZGwZdTLFETtqExGR63FExl38+admGTcAbN4MXHstcMstwL59oodLqQJsOHJi775Kz3y732h0JOd4Md7bmCf5HNZUKXZEZeD4iCAMTGzGIIaIyENwRMZdPPOM8ZTSjz9qiu7dfbcmz6ZNG72n3xnbw6hGS792EXh5RBeMX5JtlFfyxND2djXxwL9llg+ywJrpHHesDExERO6FgYw7EARg9GjNkuwTJ4yf+/xz4IsvgAce0Ew/RUcDMD1dol2ZVJ/2z2JJr5Z4q1To2LwJDpy2PpBJbROOmcM6oLCy2qrpnJLKasz+7qDJ9jBJl4iIAE4tuQeVSrODdm6uZrl2ZKTxMbW1wKJFQNu2mtGbkhLdU/VX0GvzSgwDFW1eScYN7Y2SXi3p1y4Cr9zeVfLxE/vGYc7IrsjMSMPKB/qgW6tQDExsBkEQJO9zJJbkW789TNIlIiKAIzLuxd8fmDIFuPde4H//A15/Hbh4Uf+Yykrg1VeB997DpekZmNK0P347efWYLi3M18oprKjWG8UJD/TDfJHl1hlD2xuNoiTFhWHXiWKoLQzmjO8bpzdaYu0SakuroF4Y3pn7IxEREQAWxHNvFy4Ac+cC774LVFWJHnK2cTim3fIEtsV2AwB4qWA20Fh+XxLqBBhN85hbzSMWiIgxLHanLWK36Pej2H2yRHLhvszc85i4NMfk+yydmISBic3MtoWIiJSNBfE8QUQEMH8+8NhjmmTfjz/WbFJZT9PKUpwKjdL9WRvEeEF/lZKXCgj088b4j68GCPVHReIjrgYwhlV0xaZ5vAA0buSDssu1use0Uz5SAh9zS6iZ5EtERFIxkFGCVq2Ajz4CnnhCk+z71Ve6pz7vMQz/hEQZvaRTTLBecq5aAMqr6vSO0RaW046KiAUgSXFhyDlebHR+NYCyy7X4ND0ZtWpBbyRHLNnYFLF9jliJl4iIpGKyr5J06ACsXg3k5KDyukGo8G2Ed1PHiB76zt09kXVfV3SJCYaprSnrj4oAmgTbzQajKDtPGAcx9dWqBb26LKaSjU0xNbrCSrxERCQFR2SUqHdvBG7cgGnz1qKk2Fev/oxu1KKRgNr+SXgsJB6vD7gHhyPjTJ7ueGEFSiurRaeCLMUjhoGIpSJ2Ru00MbqihEq89mxkSURE8mAgo2CzH70JhSIF8d4Z2wN4cx58Cs7j+oLzGHw0G990GYg3+48TnYY6W3oZr/54yKr3NhWIWMpvMWqnBfVzd9yFHBtZEhGRPLhqyQMYjVoUFmqqAJfpF7Cr9vLB5z2GYWHqaFwIsn5/pPrMddzaHBnD/JaesaF4ZGA7xY9gmLo+U6uwXIUjRkSkZFy11IAYjVocPAj4+Rkd56euxcRd32P0vl+xOGkEFiffjov+1ndwc0Z2xdjk1iafN7V1gieMWMi5kaWjcMSIiBoSjsh4qrIy4I03ICxYAFV5ueghRQHBWNTnDnza8xZU+RgHPqZkZqRJ6qydld/izJEHJdS4UcqIERGROVL7b65a8lTBwcDs2VDl5QGPPw5BZISm6aUyPJv5MTI/fACj/1wPb3WdyImusmbnasDxO02XVFZj/JJsDFqQhYlLczBw/kaMX5KN0soah7wf4P41bixtUSFlewgiIiVhIOPpIiOBN9+E6vBhzdYHXsa3PObiBcz75W2sXzIZw/7ebHKpklzLn/MKys3uuWTpeS2xQn3a2jiOoq1x463SX9RubZDnKJZWjR0vZCBDRJ7FpYHMe++9h27duiE4OBjBwcFITU3Fzz//rHv+8uXLmDx5MsLDw9G4cWOMGjUK586dc2GLFSw2Fli6FNi/H7j9dtFD2hb9gwezvzZ6fNr1CcjMSMPy9GS7cizERlDufH+rbgTFmhEWV448mKpx88TQ9pI3xXQUdx8xIiKSm0sDmZYtW2Lu3LnYtWsXdu7ciUGDBmH48OH466+/AADTpk3D999/j9WrVyMrKwunT5/GyJEjXdlk5evUCVizBuUbN+Ngh15GT88bMEGzG3c9t3VvIctIg2YERT9RNud4MdLmZ6K0ssaqERZXjjxoa9xkZqRh6cQkrJ3cDwAwfOEWp01xmeLuI0ZERHJzaSBz66234qabbkJCQgLat2+PV155BY0bN8b27dtRWlqKJUuW4I033sCgQYPQq1cvLF26FFu3bsX27dtNnrOqqgplZWV6Pw2VuSmaxtf1Q6OsTPxn9EvYF90OAPBH7DXYGneN3nFydX5XR1CMnyuurMG4xdutGmFxh5EHbQ7QgvWHZZvikjqtZg6rIhNRQ+I2y6/r6uqwevVqVFRUIDU1Fbt27UJNTQ2GDBmiO6ZDhw5o3bo1tm3bhj59+oieZ86cOXjhhRec1Wy3JHX57YniS9gc3wOb467BsNwtOBEWY3SujBvaa/4nMxP49FOcmPIk8gLDrV4hZGkEpf6+UGIM92Ryl/2Y5FqOLeeSaSVURSYikovLk33379+Pxo0bw9/fHw899BC++eYbdOrUCWfPnoWfnx9CQ0P1jo+KisLZs2dNnm/mzJkoLS3V/Zw6dcrBV+B+pE7R6EY1VCr83KE/Dka1MTpXYUU1IAiofeppYOlSRCd1Q95/HsCoF9daNX0iteKvKWIjLO4w8iDXFJcjEpcdvWqMiMgduHxEJjExEXv37kVpaSm++uorTJgwAVlZWTafz9/fH/7+/jK2UFmsGSFoE9nY5O7WWnHhQcC338Jnp6Z2in9dLdJ3rsWYfeuxOHkknrycjg8nD7TYLinv1bVFMA6evig6wiIIAjJzz+uNLrjDyIMcU1xKKLJHROSuXB7I+Pn5oV07TY5Gr169kJOTg7feegtjxoxBdXU1SkpK9EZlzp07h+joaBe11v1JGSHQdoolldXwEVmOXd+stX/h/XdehmF33bj6Eh7f/DkKd32PwuJnEJ4xFWjUyOy5Fo9PQtr8TBSbGMXZ/28ZwgJ99Z5Pjm+KWrUagxZcDW4Np1xcuR+THFNc1twzIiLS5/KpJUNqtRpVVVXo1asXfH19sWHDBt1zubm5OHnyJFJTU13YQvdmzQjB1JV7kZ1fZPb4LUcv4IE7n8fSXrei2ss47g2/VIbw555GbbsEzfLu2lqT5woJ9MXGjIFIijW9z1PZpVokxYVh6cQkZGakwdfbCzvy9Nto75SLHAm19dk7xeUOictERErl0hGZmTNnYtiwYWjdujUuXryIFStWYOPGjVi3bh1CQkKQnp6O6dOno2nTpggODsaUKVOQmppqMtGXpI8QmJrOMFQnCNh80QebhzyIJUkjMG3z57j9QCa8oL+6yOfff4D77kPdvHnwfuUV5PW/HieKLxlN94QE+mL1w32x6XABxn+cLfp+OceLERceBOHK1IrYMbZMuThqDyJ7p7jcJXGZiEiJXDoic/78eYwfPx6JiYkYPHgwcnJysG7dOlx//fUAgDfffBO33HILRo0ahQEDBiA6Ohpr1qxxZZMV4Ymh7dGxeRO9xwxHCCxNZ4j5JyQKT9w8HTfe9w7WJ4gHk95//w2MGoWya3rjw9mL9Wqq1B8JMVxmbeh4YYVNibTmRlscXQnYnuRad0hcJiJSIm4a6UHERhy6tAjGq7d3RbeWoXrH5hWU6+Wd2KLnv4fwdNYypJw6YPKY6TdPw9qugxEcoJ/70js2DDtPmE78zcxIgyAIZttYf/NKS6Mtlq5X6kaYjsYl00REGtw0sgESG3E4dPoi5q87bHSsqQqw1tjdoiPGjJ2DCXe+gANRbY2eLwgMxS/t+6JOgFGC756TJQgL9BWtQNs7NgzHCyugulKNVkqVWnOjLXkF5fh+32mz1+IuexBxyTQRkXUYyHgIW/YeEpvOCLM2V0SlQlabXrh1wpt49LankB/W/Or5+45BpV+A6MvqBAHFlTXoGRuq93hwgA92nijWlfqvVauRHN9U7xjDKRdL1z5oQRbe/PWI2ctwZEKt3MnFRER0lcuXX5M8bFnCa5ik2jTQDwvWH9abngkL9EVJZQ0M5x99vFQQBEG35YCg8sJPHQfgl/Z9cef+3zDywO9Yec2NJttz/ZHt2NmiIx4ZmIS48CAcL6zAosyj2H2iRO+4HXlF6NcuApkZaSanXGzJ99FyZEKto5KLiYjoKgYyHsKeJbzaOizjl2QbTc+UXaqBt5cKtWr9UEatFhBiUPOlf0IkatVqfOkzzGwQ07L0HN5dOxfV3r6oDXoCYc88DaFpoGixvLp6K5cGJjYTPZ89VYMdmVBrbrpreXqyQ96TiKihYSDjIexdwmu6uiwAkXxwNTR5L5+mJ6NWLehGSkorazBl5R6jUZ3Syhqor/z58c0r4F9XC/+6WmDuy6j+8D0U3zsFfqruqPYRH6kwVxTO1LWbM+36BNzWvQUEQcDuU8WyJ9eyWq/j5RWU40RRJROjiRo4BjIe5J2xPYyCCKkjDrZOz9SqBb2RErGaKk0D/XTtSig4gdv/ytQ7h19RIXq9MRu/BzfDG9eOw7ed0qD28tY7xlIOi9i1m9O7dRhmrf3LYdM+rNbrOJyyI6L6uPzaA9myhNfW5djWLFvOv1CBM/tz0W3RPAR+/SW8TPzq5Ua0xvwB4/FruxR4e3mhX7sIyVMx9a/dMFCpLyzQF2WXakVHr+SY9lHKcm93Jzbqop0CddS9IyL3ILX/5oiMB7Jl7yFzU1PBAT5Gnb4XgE4x1gWG8RFBiB/YE3ldFuORJv2RsWk5hhzLMTou8cJJfLTmZeyOScTP4x7Ho2Ovt+49rlz7E0MTTAYyYvs9yTntw2q99jE16vLE0PacsiMiPVx+TTqmqst+N7m/0eNqAAdOl+lV7pXqRFEl/m4Wj/vvmIU7xr2G7JadRI/reToXz7z+MEJG3grs3m319RRZ0ab65Kopw2q9tjOVKP3MN/vNvs5d6gERkfNwaomMmJqayr9QgSkrd+Pg6TLUX8Rk7bC+0bSLICAtbyeezlqGjgXHTb/wrruAzz4DvL1NH2PufSSSe9qH1XqtY0/VaU7ZEXkOVvYlm8VHBCG2aSCOF1boFXETBAEH/tUPYoCrw/qrsk+KFn0zLAhnVFVYpcLGtkm4aeLbmHprBk6ERos3zMtLchAj+j4WiFUMlgOr9VrHUqJ0lxbBkqo9E1HDwBEZ0mNuRcjuU5qKu5ZojxcgmDwXAJOrjHzrajBm36+YumUlmlVoassIPj5Q/f030NZ4KwRzy3DFloNbarcSVr548tJjSyMy3z3aD/PXHeaqJSIPJ7X/ZiBDesytCJl9WydJQ/7a4wEYncsLmsJ52mmo/AsVmLLiynSVwXkCqi9j4q7v8NCOr5GTeiMGZ36l97w26Nr69xn41tXikl8jkx3apsMFGP9xtsk2f5qejGsTIi1em6s1lKXHUlYmccqOyLNxaomsZmnPIlObOBrSHi92LjWATUcKsO+fEgCaaZfP7++D/iJBxCW/RliUOhrXPrgYT3QbZTRtpU0IHb3/V2z68H78Z/ePyM49gykr94i2yRzDysXuyly1YE8iJVGaU3ZEBDCQoXqkFHET62Bs8d96q0+0RfTmjOwqemxpQBOUBATrrUjRBl2+1Zfw2JaViKwowcu/vod1Hz2EsG+/RP75i3rnsGcLB3dhy8agSqX9ncjMSMPSiUnIzEjD8vRkjxp1IiJ5MJAhHSmdff0OxlTgIcWBf8uMOt4Ug12uxd5fSxt0Tdj9A6LKi3SPx5acxVs/LEDkgD7Ajz/qtlcwlfirpCRRKYGmp+GoCxFZwkCGdKzp7OMjgjA2ubXZ47tYKJhn2PFa8/7aoKvj+XzRczfOPQjccgtw7bXA5s0AlF/XxRNGlYiI5MZAhvRY29mbO/6V282P2Ih1vFLfXxv0PHHbUxgzdg52xXQQf5MtWzTBzC23IOTIQUVPV3jCqBIRkdxsWrX08ssvY9y4cYiPj3dEm2TFVUu2sWZFSF5BOXbkF0EFIKVNuN7x45dkY/PRAqsL6El5f72l1YKAIUezMWvHCrT695j4SVUqYOxY4MUXRZdxK4HYcnJPXLVEROTQ5dfdu3fHgQMHkJKSgv/85z8YPXo0IiLsTwB1BAYyjiNlKfDJwkoMX7hZb2+jsEBffDe5P1qFm58qkUov6AlrBKxYATz/PHD8uOjxgo8PVJMmAc89BzRvLksbnI1Lj4nI0zm8jsxff/2Fzz//HKtWrcI///yD66+/HuPGjcOIESMQGChPByUHBjLyMSzCZqrWR4/WoRjVqwUAFdbs/ge7T5SYrEtjrqibXUXfqqqAjz4CXnoJOH9e9JDdcxchLH08AwEiIjfk1IJ4W7ZswYoVK7B69WpcvnwZZWVl9p5SNg09kJGjAqzYyEtSXBhyjhfL1Uy9kRw5i76VnC/CZ3dNx/gtqxFcfXXVz4Gotrh1wpsQVF6cmiEickNOLYgXFBSEgIAA+Pn5oabGth2HSV4lldUYvyQbgxZkYeLSHJt2qda6f9lObDYo8b/rhHxBDHC1qFteQTn+s2QHNh8tEH3eWvd//TfmJ9+JAQ8txgfJI1HlrQlW5g0YD0HlpTv3/ctz9PaDIiIiZbB5RCY/Px8rVqzAihUrkJubi+uuuw5333037rjjDoSEhMjdTps11BEZKSXeLSmprMak5TtlHXmxlzW7G4vt2RNddgG3HcrCh8kjNcm/IhZnL0XfCSMQeM/dmo0q653PFfsbWfu+nrwPExE1HFL7bx9bTt6nTx/k5OSgW7dumDhxIsaOHYsWLVrY3FiSl7YCrKH6FWCldHBTV+6VfeTFXscLpbUdAHbkFxk9djY4Ah+mjDL5muRTBzAk82sg82vgfwuAOXNQcu1ATF31p8WpLrkDCGun2BrKPkxERPXZFMgMHjwYH3/8MTp16iR3e0gGUirASllSLWXHaGeTUvRNrEOXRBDwVNayq3/euxcYNgxn2/fApeS7gRYddU9pp7qWpyc7LIAwt6+S2KiatccTEXkCm3JkXnnlFQYxbkyOCrCWgiF3JtahS9Hn1H70/veQ0eMdDu/B6s+exEdfv4jEguMA9Ee3HLGRo7X7KjWkfZiIiOqTPCIzffp0ySd94403bGoMyUNbAdZUjoyUaY+mbjoVYTiaZDidY89I0vZWXfHA7c8gY9OnaF940uj5649mY/DRHHzTOQ1v9h+Hf0KjsT2v0OI0niAIVk85WTuqJscoHBGREkkOZPbs0f92uXv3btTW1iIxMREAcPjwYXh7e6NXr17ytpBs8s7YHkYVYK3ZV2jB+iOOappdtKNJpqZzRie1tOp8HaOb4PC5ck3Ap1JhfftUZCak4MmCnXhgwyfASf2AxgsCRv2ViVsP/YEV19yINQH3AfAzef4pK3bjwOmr5QikTjlZO6rGfZhISZiQTnKSHMhkZmbq/v+NN95AkyZNsGzZMoSFhQEAiouLMXHiRFx77bXyt5Kspt2l2toKsJrtBsRHGVwttd72B6amcy7V1Fp1zrAgP/RrF6F3vantozBm1rPIK5qKT++diUe3foHwS/q1kfzUtbh39w+4c/9v+Lj3cHyYMhIX/Y0/34On9V8nNWfF2lE1OUbhiByNCenkCDYtv27RogXWr1+Pzp076z1+4MABDB06FKdPn5atgfZqqMuvrWVzgqwT9W0bjhWT+oguq64vyM8bFdV1ks+bmZEGAEYBX2bueUxcmoOgqkqk71yLSdlr0KT6kug5/gluhrQHPkStt+a7gZcKevtLib2npeCitLIG9y/P0Vv+bu4ffe7DRO5OjrIQ1HA4dPl1WVkZCgqMO7yCggJcvHjRllOSi9maIGtoZI8YrNnjmEB267FC5F+oMBrlMGRNEANoAhixqRntYxX+gXi731h81uMmPLLtS9yz50f41+mP/Gzqe5MuiAGATjHBOPCv6XZaylnRBpb1g5ik2DCTQYl2qP6F4Z1151fisD2nHDyXXGUhiAzZFMjcfvvtmDhxIhYsWIDkZE0UvWPHDjz55JMYOXKkrA0kx5NzqXVSfLjDAhlA00F/svW4rOdclHlUL2DoHRuGm7o2R4CfN5LiwrDreDHUAIoCQ/Dy4En4OGk4Htu8Encc2ABvQY2igGD0XfQqMpsE6wIIQRDMjhpZylm5f9lO7Dao4bP7ZInRtJSpofonhibgeKFmpZIrOgdrAxJOOXg+JqSTo9gUyLz//vvIyMjA3XffrduSwMfHB+np6Xj99ddlbSA5nlxLrdtGBuHjzfmynMuU86WXsVOmIn3eKhWCA3yw+0SJ3uM7TxSbfY/Twc3w9E2P4cPkkcj441Nc6N4b98RrdtGu/w/xgIRI/LU/Dx3PHMXmuGsAlQpeKs1ojSnaaspi7y/2zVVsJG3TkQKXBQS2BiSsgeP5mJBOjmLXppEVFRU4duwYAKBt27YICnK/X0TmyFhmKedEpQLs31rUPl4qICTAF8U27BWlFdzIB2WXr04J9Y4NkyUouqZFCB4b2h7eKqBOgG4UorSyBltuvxc3rV+BLbHdMG/ABPwZk6h7nVgHP35JNjYfLTCbX7N0YhIGJjazeN+0nJmDYEsOhKXrsGZbCnJvzJEhazg0R0brzJkzOHPmDAYMGICAgAAIggCVif1ryH01DfJDWKBxkOAFoFvLUNSq1XpLiF2hsb+PpA0vE5o1xrGCcr1AwAtAr9gwrH64LzYdLsCeU8Xo2ToMtWoBE5fm2N22vf+WGp1nQEIk3h0QiZuyvgYA9DuxD2s/fQK/tE/F/GvvwdGI1th8pADjFm/HUzcmok7Q/IMuZYpP+81V6kias3IQpORAiNXU4ZRDw2FvWQgiMTYFMoWFhRg9ejQyMzOhUqlw5MgRtGnTBunp6QgLC8OCBQvkbic50NSVe1F2yThI8PJSYe8/Jbo/d2mhiYjNJbE6QvtmQTh8Xlpl2iPny40e658QiZdHdMH4Jdl6/4B2MTPFY68tRy9g97JXkVZVpff4jYe34fojO7Cm8yD8r//dOABg/MfSgikvaK5F26lbGqo3JDUgsDXh1lJAYqqmDqccGg5by0IQmWPTFgXTpk2Dr68vTp48icDAq/8IjRkzBr/88otsjSPHu1ra3vi5WoP5jYOny5wexADAkI5RVr/GC5pAJTMjDcvTk/Hstwew2WC0wJGjTHWCgO+btEFtjPFmqt6CGnce+A2/f/QAnv/tQ4RXlEg6Z68rq5a0tLVjvCWOgloKCEoqqzF+STYGLcjCxKU5GDh/I8YvyZY0EgZYDqxM1dQxdR3eKhUG1AvcyHPERwRhYGIz3luShU2BzPr16/Haa6+hZUv9KqoJCQk4ceKELA0j57Am0ddc3oYjdW0ZavVr1LgaqGiDNbW8zbLo666DseXnrSh84VUUBRiP/vjX1eK+Xd8h68NJeHzz52hcJX4vvFRAUpxmaswwYfadsT3Qr12E2XZIDQjs3TPKVEDideWPhp9//SknsevglAMRSWHT1FJFRYXeSIxWUVER/P397W4UOY+10xOusDL7FAYkRFpMghWjXYLsKq1jwhH+/Ew80DQFXVYtRnr2Nwiquax3TOPqS3h8y0qM3/0jFqaOxmc9bkKVz9VtD/q3izTq0OtP/yxPT8amw+ex51QJEqOaYMWOU1bnIMhV40MsB0JqTR1OORCRLWwKZK699losX74cL730EgBApVJBrVZj3rx5GDhwoKwNJMcyVdpeDonNGsPLS4VDZ+0rkrjpSAE6RjW2aUQoLjwIpZXVdr2/LbxVKvRoHaoLpF6/71pMCWiMZT1uxuRtX2Lc3p+Miuo1vVSG535fjPty1qLof+/gQr+BRh262PJmw0TtAQmR+G5yPxRWVksOCORKuBXLgbCmpk58BAMYIrKOTYHMvHnzMHjwYOzcuRPV1dV46qmn8Ndff6GoqAhbtmyRu43kYGLfosMCfVFaWWPXdEyuSOKtGEvl/AHg0Dlp59LyVqnQM1YTSCzKPGrVa+UQHOCDnSeKdauZtImtRcM7496lMfg4aTge37wCt/+VCW9B/1NucbEAZ4LDRIMQsekfw9Vm2uelLmfNKyjH2dLLZo+RknBrmCRsWFPHnfeBYkVhIuWyuY5MSUkJFi5ciD///BPl5eXo2bMnJk+ejObNm8vdRruwjox09b9FNw30MwpuHCUpLkyvsq4cDGvGWGxDbBhKL9XgsEjwFRLgi1KRVV2mdG0RjIOnL5qslfHnqWIMX7gVAJBQcAIZf3yKG45s1x37Q2J/PDpiBgD9WjNS68ZoLb8vGXWCYLJzlrK/lpQaH1KK4P15qgTPfLPfpp3AHYkVhYncl9T+2+ZA5vLly9i3bx/Onz8PtVr/G+Vtt91myykdgoGMfVZln8SMNfsdcm7tcmLtVMSUFbtx8HSZTaNA3iogyN+64MWwLebe99P0ZNSqBaPtDKylLe42fkk2NtdLQO7x7994atMyJJ36C0PTFyEv/GoifWqbcKx8oA8yc89j8gebUOkXYPX7miq+Z2lKUUqnbq7I2dtjrzEKFLq0CMart3dFNxuSuOXGAm1E7suhgcwvv/yCe+65B0VFRTB8uUqlQl2ddZv2ORIDGftYOwqgZSkwADSjIIsnJOk6SbHdm6WSYyrMnLkju+Ku5NYorazBvUuzsedUiU3nmXZ9Am7r3gJNA/2MdraGIKBd4SkcjWht9LrMjDQINTWo69oNR8JbYcGAe3AsvJXk9zXsnC3d17kjuyKlTbjFaRZL50mKC8PuEyVuGSiwojCRe5Paf9u0/HrKlCkYPXo0Tp8+DbVarffjTkEM2c9SjY/MjDQsHNsDSbFhes/3T4hE37bhJs8rtpxYmyiamZGGadcnSGpfY39vLL8vCcUODGIAYMnmfJRW1iAk0BcLRne3+Txv/noEA+dvxJSVezCsc7T+kyqVaBADANvzCtHm5zVIKDyFmw5vxfolkzH357fRvExa0Fd/9RFgObk3KqSRLEnCOceLjUZ8DNviKlISnInI/dkUyJw7dw7Tp09HVJT1hcpIeczV+IiPCMLN3WOw+uG+yMxIw9KJSboidO+N6yUazKS2Ccfi8Ukm3y8+Igi3doux2K7QAF/8PHUAyi7ZNp1kjWMF5bp6KpY6wI7RTSyeb9ORArz44yHJ7+9ddRmYPfvqnwU17tq3Hhs/fADP/L4YYZWlks6j7ZzlqqZrz/J9VwcKrChM5BlsWrV0xx13YOPGjWjbtq3c7SE3ZGpJ7e5TxXqJpIYrVUICfbFiUh/kX6jAjrxCCABahAagThBQVFltNu+iTWRji5s6fjO5H2rUaryx/rBs12qKWoBuFMFSB+iI3cbaFZxATdlFGH5i/nU1mJTzLe76cx0+Sh6JuJeewfRf8kyeR9s5m1p2b+1KInPn6dE61Oz9c3WgINdnQESuZVOOTGVlJe68805ERkaia9eu8PXV/+d16tSpsjXQXsyRkZetqzxsed2Pf57GZDNVZbu0MF9ozRG0O08bJutqWbtaSgofLxVq1QKCL5djUvY3SN/5LQJrqsQPjozEp4PvwastB+CS99XvKWJ5KWI5Sbas2DF3nikr97h1Mq1cnwERyc+hyb5LlizBQw89hEaNGiE8PFxvx2uVSoW8PNPfCJ2NgYy8bF3lYe3r8grKsSO/CDPNrJiSUn/GknHJLfF59j+Sj9cmgJZW1iBtfqbxjuEytMmSyPJiPLptFcbuXQc/tXjQVBDeHHNT7sI3ndOg9vI2WsZdv2aKdqTNW6Uyu1zbErGqvCcLKzB84Ra9zyks0BffTe6PVuHuU1WaFYWJ3I9DA5no6GhMnToVM2bMgJeXTWk2TsNARj62rvKw5nVSapvIxbAirhTattq6mktOrUrOYtrmzzHir43wgvhf4/KERFQ89wKi/jMaJZdqREfFXh7RBc9+e8AhoxJc3kxEtnLoqqXq6mqMGTPG7YMYkpetqzyseZ1Y5VpHsabInZa2rdZstukop0KjMf2WJzDsvnfwazvxoKDxkVxEPT8DqKkxuSnk8IWb7dos0pSrO6u756olR8krKEdm7nmPvT4id2NTJDJhwgR88cUXdr/5nDlzkJSUhCZNmqBZs2YYMWIEcnNz9Y65fPkyJk+ejPDwcDRu3BijRo3CuXPn7H5vsp6tqzykvs5Ux+cotu7dBABNrRypcGTInxsZh0mjnseocfOwo2Vno+ef6TkaW06UmgwqiitrTAYbmw4X2NwpN7TlzSWV1Ri/JBuDFmRh4tIcDJy/EeOXZKPUylE/IrKOTauW6urqMG/ePKxbtw7dunUzSvZ94403JJ0nKysLkydPRlJSEmpra/Hf//4XQ4cOxcGDBxEUpOkwpk2bhh9//BGrV69GSEgIHn30UYwcOZJ7OrmAras8pL7OHUY5TDFs64L1R6x6vakaN439vVFZVSdLDZxdLTthzN1zkZa3C09tWoZO5/NxKDIOK9v2w9rPdtl0zvEfZ+v+39rpJnde3uyIvZVMjXhNWbmH02hEDmRTjoy5Ha5VKhV+//13mxpTUFCAZs2aISsrCwMGDEBpaSkiIyOxYsUK3HHHHQCAv//+Gx07dsS2bdvQp08fo3NUVVWhqurqio6ysjK0atWKOTIysXWVh5TX2Zt30tjfG+VVlgsySqk6bMiePY9cQSWoceuhP1AQFIptseIF/NoXHMe9u37AW/3uwrkmEaLH1OelAnrFhmH1Q30lt0NqjoyzNm101N5KrBJMJD+pOTI2jchkZmba3DBzSks1Rb2aNm0KANi1axdqamowZMgQ3TEdOnRA69atTQYyc+bMwQsvvOCQ9pF4TRkp/0BLeZ2pkRsvaDrQAD8f0SXPWuVVdZKWP4dYmeT7aXoyrk2I1P3ZnUeOtASVF77rdJ3eY7FNA/BP8WXdZ5vxx2cYemQ7Rv71Oz7peQve63MnSgNMF/NTC5pKvXe+t1VvawlzxHZW1xZTBJy/aaOjRk2kTKMxkCFyDLfJ1lWr1Xj88cfRr18/dOnSBQBw9uxZ+Pn5ITQ0VO/YqKgonD17VvQ8M2fORGlpqe7n1KlTjm56gxQfEYSBic2s/sfZ0uvEqgirAeScKEatWo1EC1VzzQUxKlyp8yKxErC3StOp1g9iAPuq2brSzGEddZ9tz38PYeiVHbcb1Vbjoew1+OOD+zF56xcIqL5s9jy7ThRLTgSuv+1E/arP2iDFXGAhN0cmH9syjcakYCJ5uE0gM3nyZBw4cACrVq2y6zz+/v4IDg7W+yHl0HZ8SXFh8DIokbsjrwiNG9k0iAgAEKAJdKQmE6tUKrwyoovR46b2n3Jnjf29kdg8WPPZxoZh6hbjv2fBVRV48o9PsenD+zF+1/fwrRMftVIDVnf82gBWEARd5+3sVU2WRk125BXafG5Le5LVD9yZFEwkL7cIZB599FH88MMPyMzMRMuWLXWPR0dHo7q6GiUlJXrHnzt3DtHRBhvukcfIKyhHzvFio1VFdYKAnOPFSIoNE+0wehtsXGmvWrWA6av3ij4nNnLkDpJiwxAmMiVTXlWHgfM34s73tyLnRDGevOkxfNrjJtR4eRsdG1lRghd/+wAbPnoII/7KhJdaPO9Iu+ooK/c83tpwGH+Yqf0j1nlPXWV+1EXuVU2WRk1mrNlvV0Bhbk+y+pw5CkXUENiU7CsXQRAwZcoUfPPNN9i4cSMSEvR3PNYm+65cuRKjRo0CAOTm5qJDhw4mc2QMsSCe8mTmnsfEpTkmn184tge+2PmPyZL4m48WyFpd11yiZv6FCnz3579481frVjE5Qo+WIfjkvhQIEHDP4h3Yf9p4+wbDysOxxacx/Y/PMfyQ6UTVvyNi8fp147GhbTJQL4D8LD0JU1buFa3aW6NW6yXviiX9WqqC7IgEWbF21CdHsT5zeWBMCiaSzqGVfeXyyCOPYMWKFVi7di0SExN1j4eEhCAgIAAA8PDDD+Onn37CJ598guDgYEyZMgUAsHXrVknvwUBGeaT+Yy/WYYitjrLXtOsTcFv3FiY7GFevYlIB6B13dTWRqX2gzOl0Lg8Zm5ZjUN5Ok8fsbNER866bgF2tu6Jfuwj8+U+JaFFB7d5QWpY2/zRcRebIyr9Sfz8cFVBYCtK1e3kRkYMr+8rlvffeQ2lpKdLS0tC8eXPdT/1ie2+++SZuueUWjBo1CgMGDEB0dDTWrFnjwlaTozUN8hOdHvEC9PINxBKHtTk2PVqFytaeN389YjaPwdU5M9cmRGLx+CQAVxNaLQUxhn/xD0a1wX13zsadd89FTotOoq/p/e8hfLliBv6b9xvuSm5psjJyrcEwy24zQQwAtGoaoPdnsekYuWh/P+aM7Gr2OEcV63Pn2jpESmV75qQMpAwGNWrUCAsXLsTChQud0CJyB1NX7kWZSCcZEugrqYPLKyjHnlMlsrdr85ECk8t0Xx7RBcMXbra4rLtrTDAOnrloc/ViLxXQKSYYT9/YAf8UX4IKQEqbcN0qIKlLw3vFhiFHJMDIadUFd457DYOO5eDJTcvRseC43vOVvv54P7IHfH84JLnNloKqE0WXAGh2M3/19q7o1jJU8rltlRLf1OzzjgoobC0qSUSmuUWyL5HW1ZUsxs8VV9Zg378lFs/hqDovhqt16i+fffbbA2aXdWtXr3x2fx+7koT7t4vEort74aNN+Zi5Zj9mrNmvN1okZWl4WKAvVj/cF5kZaXjn7h5IijNIklap8Hu7ZNx871t47JYncDIkSvfU0l63oaBxU5wuNb9EW4zhKjRDh05fxPx1h60+ry2sWWUkN6lJwUQkjUtzZJyBOTLKYimHALBcMM2WnBUphfS03h3bA18aJBtbYk9l4PbNgjDz5k5mE2fr55VIyZGZM7Ir+rQJx6y1f5lNfgUA37oa3PXnOozf/SNG/ed1lDVqLHpcysn9ONQs3uTzSXFhyDlufpoJcF7Cq61VquVibVFJooZGEcm+zsBARlmkdPJSkkHFO3ugcSNfo9yOkABfXLxUIzk5Nik2DLtPlkieHpo7sivuSm6t+7OUYE0rLNAXGzMGSt7GITMjDU0D/TBu8XYcEFm1ZBdB0Fu1VF/w5XL88X46AOC9Pnfik1634LJvIwD690vKKi9nJ7wyoLCds7aWUAp+HvJy6BYFRI5iKoegvvoF08xVCDYuja/5tl1UWY3teYVQAYgJbYTxH0sLKgCga4tg0dwSc1LahOv9Wep8blJcGBaP198KQEopfEEQMK5Pa8xcc8CqdlpkJpn5wR1fI6RKM+U2I+sTTNz1Hd7uexe+6DYUTZoE6AoLxkcE4bqESLOBjLMTXuMj2OlYy9lbS7g7fh6uxREZcjtSl8hK+eZu6du2taMjL43ogkdXSCtcZjhyJPaPneHxPVuH4pFB7Uy219KITJKJJF5bfJqejFq1gEWZR7H7hOkRqMjyImz6YBICaquMnjse2hz/G/AfFN8yEssmaeo+jV+SbfIzCAv0xZ7nh8rSfnIcqZuBNhT8PBxDEcuvicRol8guv8/8PwBSvrlb2ttJ6r5JXVsGY2PGQHRqLj0YNkzgFKvoWl+P1qG4t2+c2WFpc0mqTfx9ZAlitAmv1yZEYmBiMywen4QerUNNH69W47d24vcqruQM/vfd63j62btxduUa5J2/aDZALa6s4d5DErlqryZnby3h7vh5uB6nlshtDWgf6fClqlKmsrxUQFiAP0ICfRES6Gu2TS8M7yw6AqT9x86Uri2CsfNEsa5wnLlhabFpsyB/b8nJypYYBmAhgb6YPKidyZGrs8ERmDL8aay7aTzu/OY9XJe/2+iYTufzgbtHoaR3H/RKHIldLcVr1QDO2ylaqfkMtkxjyHmt3OlbHz8P12MgQ25NPNdF3qWqYu9Rn1qAXk6OuTaFBPqK/qNl6R+7/f/qJ+Zq994RG5bWjlhpp80W/X7UbOVccywFYFpSRq7+bdMRE0a/iD4n9+GprGXoeTrX6JjQndvx9c7t+K1tEuYPGI+/m8UbHWNupE2ODlnp+Qzm9moy/H1xxLWyqJ8+fh6uxxwZUgRnrCxZlX0SM9bsN/m8YU6ONW3ae7IYIxZJ21ajPktLke3dHsGaTm38kmyL+1glxYVp8mnUalx/dAcyNi1H4oWToseqocLaTtdhxo1TUOXrr2uPWPAmZ4es5HwGa/dqctS1KvkzdAR+Ho7BHBnyKJZyXeSQbGW1V2va9IaNm0qaK5VfUlltcQdpcz5NT8by9GTJgcA7Y3ugU4z5LwMT+sZpir2pVPg1oQ+GTXwHH9w3C+rWsUbHekFAdHkhqnz8AADXtAzFmN4tRXMK5NoxWun5DFKmMbQcea0s6qePn4drcWqJFE+u+X9HlY+3lB9jjrlh6akr9+KgHbViWoZJS3TWCgn0xdt39TA7ItA5JgTL02MMRqtuA6pmAh9+CLz0ElBw9bMof/5FPJfYCb8cOIuc48WYfCUwqb/03NTnJ2UZviGl5zNYM43hyGs1nN609++eUvOVtOT+PMg6DGRIsRwx/++InBxbtkywFDzZExxpSe3I6ncyUoM9o9os/v7AlCnAvfcC//sf8PrrwODBuD59BMYvyTbaWDInvwg3zPkF62beKGuHrPR8BmuCbWdcq701eJSer2SINYlcg4EMKZY1SY9S2fLNytK3SalLvOuzFDzJsZ+UpY7MVCfzyogueObbA3qP94wNxeiklpZHR5o0AZ57Dnj4YeDSJZMB2ZCj2Xh5/UKsyrsf178+Q9J1SPlW7wmbNkoNtpVwrY74O0wNDwMZUiQ5pxvESPlmZenbZP2O1dIS7wEJkci4oT0KK6olBU+2BEf1dYkJtvgepjqZZ749oAv2/vq3FMu2HkfO8WLdPkpJsWFYPCHJ/DfqCE0+wYnc80ZPeanrkLFpOaLLi/Dginmo2b4GTw65F2+GdUctrtbP0XbIYYG+RkX2rF2+rqR8BmuCbXe+Vkf/HaaGg4EMKZI75DqY6ugf+mwXfL299P6R7ts2HMnxTbEtr9DoPEmxYVYPpUupf2POq7d3Nfu81E5m1tq/sMtwWuhEMdLmZ+rtEWWKWEA2/GAWOlw4ofuzb95RTP7wWdzcOhHPp9yNTfE9gStBjLajtuZbvafkM0gJtt35Wt3h7zB5Bq5aIkVyda6DuRUh2/IKsfmofhCwI68Ivt5eSIoNM/pLt/tkidWrbwDxlRKWeKk0oxXdWoWaPU5KJ6P9DMQ22yyurMH9yy1v/dAmsjGS4sL0Hks5Jb5HVNzJXCxfPQt7Ns7B1rRALE9PRmFFlc0rc5yxEs5dSL1WZ1YLdvXfYfIcDGRIkcyV6h+QEOnwzslSR29Ya0XbseacKDbq+G1dDhsS6IvZt5mukCum/5WNMy2x1Mn4eKksfgY5x4slXdPi8UkIqzdyM2PYVNw95mX82TxB9Piw7K2IGTYIGDECBTuMqwjXZ275ekNiKUApqazG+CXZGLQgCxOX5mDg/I0YvyQbpZU1osfLwdV/h8lzMJAhxXJl7QZ7c1TE2NLpypH0K6ZpkJ9ecGHoniXZWJR51OJ5pFxTSKAvNmYMRFLs1ZGZrXHX4OVnl6JixRdAhw7iL1y7Fsm3pWH+j2+iZek50UOkfqt31b5FjiY1QJGrTo+1WH+F5MDKvqR4rpr/F6vm6QWITrVIYamKrxhLlV5VKqD+33Cp1UbHL8nGZhPTRvXPZWmPJ2uuqaSyGpOW79QlDQNXknbv7IqQr1cBs2YBp06Jvrbaywef9xiGd1PHoDAoVPJ1etryX0NSKs5aWy3YEdwxh4dcj5V9qcFwVa6D2LfJ/gmR6Ns2HN4q4+PDAn2vPCffULqp4XntX2zDrylSprHM5b4YnsvSRpWniir1RjrMjXxMWr7TKHF4y9ELmLJ6PzBxInD4MPDGG7oVT/X5qWsxcdf3GH5Q0yFL/VbvqpEIZ5Ba2deaasGO0pDylUh+XLVEBNsqi5paEVJaWYO0+ZkoNhi+L62sgSBoOlkpy2GltklsiW2nmGAcMFP119yKEDmnq8Z/nK37/+BGPnqBj3bkQ4CA+5ftFN340mgp7rRpQHq6JqBZsAAoL9cdW9uiJa5781ncExOO+Igg5BWUY/epYpOfn6cv/5W6KohJt6R0DGSoQZNjasFwGWxhRZVREANoppy25RUiMyMNAEwOpVvbJrGAShAEs9MF5jqnsADHTKkYjt5oRz5q6tQWd+/WC7yCg4HZs4HJk4FXXwUWLQKqq+Hz0ou4rltrXV6Ipc/P05f/Sg1QlFA4j8gcTi1Rg+aIqQWpHaSpoXRb21T/nPasCLF1g0traUc+xGrrGBINvCIjgTff1Ew5zZgB3HMPAPHPr8eyd7AsY4HeXJunj0RY8zvgzKRbT02sJtfhiAw1WI6aWrC1g8wrKMeO/CLZ2mRLVVc59nCSkwrAtWYCr7yCcpy4HIC4J55FvI+PaPvbFp7C1M0r4P2HGlXbVsP/9deAIUMaxEiE1N8BZxTO8/TEanIdBjLUYDlqasHaDlLsH3g52mRL52TpM5k7siuiQhrBW6XSy39xlHbNGosGXqY6xdFJLY2Onf7HZ/AWNKnL/nt3A9dfDwweDMyZ49Yl/OVg7e+AIzc9lGNfJSXskq2ENnoaBjLUYDlyasGaDlLsH3g522Spc6r/D6+lzySlTbjuXAMSIrH5aIFR8T85fTi+t+i39fuX7TTaMXvL0Qu4VKOfh9PhfD5uzt1ifOING4DkZISMHInlL7+M/OGdPXr5r6t3ZbZ39FMJozlKaKOnYo4MNViOrCyq/SacmZGGpROTkJmRhuXpyUb/oJlaImvIEdVOxYqlzf7uIEJNJPuGBfoa5VX0ig0TPVYOfduGi45e3fn+Vuw0USE553gxkmLDdPf078g4PDx8BvKathB/kzVrgC5dEP/UFAwMuOySzr4h5IzYu8RbCcvkldBGT8VAhho0Ryc5WqqPIXWpsxxtMuwwxf7h3XykACWXxMvSF1fW4I963zZDAn2x+qG+ovtH2WtAQiTeG9fL6PGpK/ca1ZoxdG/fuKv3VKXCzx3648U5X6Jy4ftAC5GARq0Gli4FEhI0y7sL7M8RkhKcuGJbAFvZG2zZM/optR6OK1lq46rsk27RTsAzA2dOLVGD5urdgS39Az93ZFe96RxbiA15944NE13ybKkI3j1Lso2GyxdPSDKaRrPVtOsTcFv3FlbVfTHUqUUIlnePEbmnfYGJ4zXLtV99FSgq0n9hdTXwv/8BixcDGRnA9OlAkyZWtd+a6QU5ckYcTa7pEnsSq5WwTN5SG2es2Q/AtVNNnjz1xREZIriusqil6a27klvb3SaxDtMwv8Qa2s5W+82uqLJabxotKS7M6HqkMhXEAJY7Cy9o/mEWBAGZuecBwPieBgQgb/yD2LRuB4qnPwUEibxXebmmTk379kCFdd9apU4vKGGUAZB3usTW0U8lLJOXuveaK6eaPHnqiyMyRC7myJUzpkYxLI28eKmMd/DW0na29Qvuab/ZxUcEoWmgH575Zr/ZysJG7wfN9g7mgjZLnUW3VqGoVatF2xUS6Gv8jdR3AG55MQ0Ljv4I/8UfAjUGUzq33ioe6JhgTUKrO4wyWFpdI3d5AltHP5WwTN5UGw25qmq0p1exZiBD5GKOnN6yOIphELB4q1RIjm8KX28vq6aKthy9gIc/3wUfL/3XdWkRjFdv74rbF25BnZl85k4xwRYDN1OdhZcK6BUbhgBfH7NTNWLfSH86r0Zuuzsx5cu7MHDlIjRZvUpTNK9RI+D55yVfP2D5s845Xqi7r64cZZA6xeCoYMuWFVRKWCYv1kZTnD0d5g6BsyMxkCFyE45YImupw+wVG6a327S2cyisqMKP+09jwXppVX7rBAFbjxUazVUfOn0RL35/0GwQAwDv3N3T7Dy9dvQgY2h7ANDrLPq3i8QTQxMwfOFW0XZtOlKATYfPmxyZOnK+HFPPA4gfh9HP3YRXdn0B344dgJbGNWkAAJcvAzt2ANddp/ewpc/6xe8PIrJJI8SFB6FpkB/CAn2NtrKQMjJlL6m5OU0t5E04c0rH1blsUtRv4/a8Qsy8khcjxtnTYUqYnrMHAxkiD2ZpWN6wcwgL9LUrcVdsSbSlfZQAYNbav0STDk2NHnz3aD8UVlTrOjRtTowpe06VSGr/l1VhOHv7c1h+r/GKKZ1Fi4AnngCGDtUkDffSHNsmsjG6mNmss7yqDhOX5gDQLGUvFVkdFhLo69BRBmumGMwFsXKXApDK1fVwpNC28ef9Z91mOkwJ03P2YLIvkYezlGRZP9HZmuJ8cjJMOtQmEk9atlN09GD+usN6ibyWvnH2aBUquS2bjhQgv/iy+JNlZZrgBQDWrwd690b58JE4tW03MnPPo1uLEEnvUVxZI5qDVFxZg6LKaslttZbUei6WVohl3NBe1nZ5ImfuX6XE9siJIzJEHk7qsLylziu2aSDeubsH5q87bHVF36S4MOw+UWIyEVI7IvDnqRIsWH/YbDvERg8sfeMc0L6ZpGRMLZM5AwsWAIX6m1w2/u4bNPp+Lf7odj1+7zsWCI4wfp0VHJmvIHWKwVLAU1jhuGDLU7jbdJi7tUdOHJEhaiDsLc53oqgSEz7OxisjuqBTTLCk99QuI188Psno26CYZ77dL3lEyLAarKVvnGLPm2IyZ6BNGxSHGJ/DR1Dj7j/XIevDSZiZ+TFCL0lfsSX5vWUgtZq1p+dUOJOrSjuY4m7tkQMDGSICIK0WRnFlDaav3ou375I2HK0NJLTfBpffl2T2+AP/lkkaMQGMO1NL20LUf75LC9OBmLn8j7ybRiE1/X3MSbsXpf7Gx/jX1eDB7DXY9P79eHTrKgRWX5J0LcDVYEJbB8dRtWSkTDE4cvsOIrmpBEHivxoKVVZWhpCQEJSWliI4WNq3SKKGavySbGw+UmCxzkxmRhpmrf1LdCqnZ+tQPDKoncmh6/FLskVf17F5E8m1Z8ICfbHn+aGiz0nZfbi0sgYPf74LW4/pTxOltgnH+//pZXIFVWbueV3CbvDlcjy442tM3PUdAmuqRI+vDA3Hp4P/g//FD8Ql76sz+V7QBFb1Vy31bRsOQQC25V1tkyMrr1qaYiitrDFK/PaUSrCkDFL7bwYy5PakdEwkj9LKGqQvy7G40mjpxCT0bBVmU0dnqoN8Ymh7DF8oslO1CZkZaXq/D7aUYM+/UIEdeYUQAPSRsBVEXkG5XsE9AIgsL8KUrV9g7J+/wFddJ/q6gojmeCrtAWS2TdJrV1FltS6YMBUY9mgdislmAkNH88ScClIGBjJXMJBRLk/eG8Td3frOH9j/r+nRkfpBhK0dndjrxEZrTFk6MQkDE5vp/mxqpEe7zFwuptrYuvgMpm3+HMMPZsELxu3PX7oSx1MH6a63foAuCIJRgCRGyb///EJC1mIgcwUDGeVyVsfUUFjTkZRW1iBtfqZRwTZvFdCvXaTe5y9nByU2WmNK/WBKbKTE1LH2stTG5LJTeHD9xxh8LEf32M6WnfD2rI+x/P4U0QC9S4tgHDATOGop8fefX0jIVlL7by6/Jrfk6XuDOJMtHUlIoC82ZgzE/ctzDCr/RuqSQh3RQRkuEV30+1HsPllisYiXlPoogiDIEnCJLWPVvoe3Chj/MZB9xyz0/ucvPJW1DMn/HMTc6yZg59ELyL9QoZtC0vKtq8FBiblBSvz9V8Iu36RsDGTILXn63iDOZGtHEhLoi9UP9TU5deTIDkpbHVUsD0esiJelFVeLfj+KnHp5P3KMCBhWmTWsMLyzZWeMvvs1XHPmMPbGJAIAfvjztH6ALghY/uXzKAgKw4Jr/4NTYTEWE60B5fz+8wsJOQMDGXJLrGMhDzk6ErGy8M7qoKQW8TJXEC84wAe7T5boHe+oEQGj31uVShfEAMCCXw/rPX1d/m6kntTsyTMsdwt+63MzZl0zCuebhJt9H6X8/vMLCTkD68iQW2IdC3lILUnvLuc1RUoRL7H6KD1jQ1FcWWOUmFs/4NLSbotgT/0WU7+3YlSCGk9lLdP92Vddh2Fbv8P2pQ8hq+gXpEV6K/73n19IyBk4IkNu652xPSRNK9BVhom3jupI3LGDEhu9OV5Yoav7ImZHXiHCAn1lzfUR+70V06boX7QqPWf0uNelS4j96F0sDfkUqwffjVmxg3HJrxEA5f3+e/pmheQeuGqJ3B7rWFhmLvF2yso9Dln9pYRVZZZWMwGa4npll2pQV+9fQjmuY2X2Scxcs9/sMSGXLuLhHV/hvt0/wM9EUb3aZlE49tA0+D34AOJjwmxuj6uwsB7Zisuvr2AgQw2BuaBCbIRAjo5EKR2UNbVpDGVmpNm82slSEKUC0DkmGO/c3RPxVSXASy8BixcDdeJF9dCmjeaYu+4CvFyfFWDtsnt+ISFrMZC5goEMeTqpNVQc1ZHkX6jA9rwLAFSSquM6mzW1aQwZ1nexNlCTsuWDXo2bI0eA558HVq0y/YJu3YBXXwVuugmQkItjyN66P6wLQ87CQOYKBjLk6erv/yPGsAKuIXs6NiV1alKmegx5qQC1HVNOpZU1GLd4u9k9pETvz549wH//C/zyi/iLwsKA48cBK/5Nk+teuWJKkVWBGyap/bfrxyeJyC62Jt6WVFZj/JJsDFqQhYlLczBw/kaMX5KNUoNqvuaYqyXjblLim1r9GrXB1zyx1U7mhAT64m0Lybmi96dHD+Dnn4GNG4HUVOPnZ860KogB5LlX2mX3UlaByUGO31HyfC4NZDZt2oRbb70VMTExUKlU+Pbbb/WeFwQBzz//PJo3b46AgAAMGTIER44ccU1jidyUrUvV7e3YnN2p2cvU5+QFTcKvNaxZXm5XKYHrrgO2bAHWrgW6dNE8FhMDPPqoVe2V6145e9m9kgJlch2XBjIVFRXo3r07Fi5cKPr8vHnz8Pbbb+P999/Hjh07EBQUhBtuuAGXL192ckuJ3JtYDRVzS3Xl6Nic3anJQexz6p8QiY0ZA7H8viTJ57F2ebm190ePSgXcdhuwdy+wfDnw5ptAQIDeIdoaOCcPHAWmTgXOnNF7Xq575cxl90oLlMl1XFpHZtiwYRg2bJjoc4Ig4H//+x+effZZDB8+HACwfPlyREVF4dtvv8Vdd90l+rqqqipUVV1dxlhWJm0PEyIlk1oBV0uOiqu2dGquznUw9znVScgWtLX+ibX3R/zNvYF77tF7yDDv5eV1C/GfvT9DWLIEqsceA556CggNlS0AcWZdGFYFJqncNkcmPz8fZ8+exZAhQ3SPhYSEICUlBdu2bTP5ujlz5iAkJET306pVK2c0l8gtSKmAC8jzzdqaKRN3y3UQ+5wsfSaA/QXpDN/X3mrC9adeYotPY8y+9QAAVWUlMGeOZsn2vHloE+QlW6Vsu0aXrOCORRfJPbltIHP27FkAQFRUlN7jUVFRuufEzJw5E6WlpbqfU6dOObSdREok1xYQUjs1JeQ6mMuh6RITjMyMNCxPT5ZlNZYcgZ3h1MvULSvhqzaoQVNcDDz9NNCuHT6o3IkBcaF6T9sSgGhHlzIz0rB0YpKsn0t93KaEpPK4LQr8/f3h7+/v6mYQuT05toCQMmWipB2QxT6T/g5YTi7HzuGGUy+vD5iAKh8/jN73K3wEg8o1Z84gYOpkLG3XDuefegZ/9b8RcZFN7PrcxTYTlRu3KSEp3DaQiY6OBgCcO3cOzZs31z1+7tw5XHPNNS5qFZHnkCVv4wpznZqSch3k/ExMkSuwM5x6ORscgf/eOAWLk27H9D8+wy25m41fdPQomj0wEc2uuUYz9XTDDTYV1XMWZ9wPUj63nVqKj49HdHQ0NmzYoHusrKwMO3bsQKpYXQUisonUvBpbuTrXwZY8FEd+JnKtIDI19XIiohW+fHIBsHMnMHSo+Iv37gWGDQPS0oCtWyW9nyt5eN1WspNLR2TKy8tx9OhR3Z/z8/Oxd+9eNG3aFK1bt8bjjz+Ol19+GQkJCYiPj8dzzz2HmJgYjBgxwnWNJiKruGoHZHetOixnYGd26iXQF1i3Dvj9d00Bvexs4xNs2gT06wfMnavJpXEz7noPyb24dIuCjRs3YuDAgUaPT5gwAZ988gkEQcCsWbPw4YcfoqSkBP3798eiRYvQvn17ye/BLQqIXM+RG0yaWtLtrFL6tiwpl7tt5qZeSiqrMXXFHgT89B0yNn2KhEKDBRBeXsD+/UCnTjZfj6O4+w7r7vRZeSLutXQFAxki9yFnrsOfp4rxzDcH9PYx0gZHhRVVkjbStIc9owVigV1SXBgm9I1D55gQWTvF+sGAl7oOI//KxLTNn6NF2ZX3vvdeYOlStxv9kLoZqiu422flqRjIXMFAhsiziHUiWtpv6xP7x9m1kaYUcowW5F+owF//lmLZ1uPIOVGse1zO0SqxYMCvtgbj9v6EZw79BJ+tW4DYWNHr6XouDzE9O+ODKYPsaoeptpkbzbB3M1RHcveRIk/BTSOJyCNNXbkXm48aBzHA1ZU/hgmwhuxNMJarfH58RBC+3PkPdp8s0Xtcrho7phKLq318sbT3cGxenw3Exopej19tDRZ98wrmPH07Cl+cA1y6ZHd7AOk1dFydJG4Kt05wPwxkiEgxtJ2I4a7UhuoEwaHF1ORaeeToTtFSMBAbFQJA/HrG/vkLWpWeQ9NLZQif9V+gfXtg8WKgttauNkktjuiuBfGUuMeYp2MgQ0SKYakT0YoLD3JoKX25Rgsc3SlKDQYMryew+hKmbF2lf7J//gEmTdLswv3VV4ANWQnWBm7O2g7BGu46UtSQuW1BPCIiQ5Y6ES9oKvFqO2hHFVOTa0m5nJ2iqZwTKdVxDa8nqPoSclp2xrDDIjVmcnOBO+8EevXSFNUbMkRyUT1riyO6Y0E8V5UTINOY7EtEiiKWaKnlzJUjci0ptzdxVOoKGkvBgNj13Ot9Hs9u+RQ+WZmmGzBokCagSbbcVlesRHLEEmlHlhOgq7hq6QoGMkSeRawT6dIiGK/e3hXdWoY6vbaHvaMF9naKTqlJ89tvwIwZwK5dpl94++3Ayy/r6tEA4kGEPe215t46Y4m0O40UeSIGMlcwkCHyTIadiNJqexh2yrZ0ik4d4RAEYM0a4JlnNNNLYry8gPHjUTLndUz9MU/0XgCwOnCz5d42pCXSnlqYj4HMFQxkiBoGpXRccgZcLqm1UlsLLFsGzJ6tSQA21KkTJjy+GJvzis3eC2sCN2vvrTsX05OT0oJ3a7GODBE1GEqq7SF1+bEULllB4+MDpKcDhw8D8+cDTZvqPX32qWeRdazI4r2QujGnLfe2oSyRlvN3SckYyBCR4iml45I74HJprZWAAOCJJ4C8POC554CgICAlBYdSTFcB9lbXWX0vbLm3DWGJtJKCd0djIENEiqeUjssRAZfLa62EhAAvvggcOwYsXYpYE591tzOHkfXB/eiybo1VRfVsubfuWkxPTkoJ3p2BgQwRKZ5SOi5HBFzaWiuZGWlYOjEJmRlpWJ6e7PwciagooGNHk/fi6axlaFlWgMjHHga6ddMkDl8ZTcgrKEdm7nnRUQRb763LAzwHU0rw7gxM9iUij6CU2h5KSUq2h+G96Hd8Lz7/4lmj42p7J+H16+7FBz6xusfE7pk999aTl0h7+u8SVy1dwUCGqGFx945LKQGXHLT3oufrzyNkyQcmj9sU1wOvDxiP/c0TzHbE7n5vnc3Tf5cYyFzBQIaI3FGD6pQFAVi/Hpg5E9hjekXNj4n9sODae5AX3tJjlkg7g6f+LjGQuYKBDBGRPpcVUFOrgdWrNaucjhwRPaRW5YXVXYcg9u3X0Pe6a5zXNnI7DGSuYCBDRKThNgXUampQ8PZ7qJv9AqLLi0QPUfv7w+vRRzWjOOHhzmsbuQ0WxCMiIj1uU0DN1xeRT0zFM/O+wdyB96GkUWOjQ7yqqoAFCzQ/RGYwkCEiagDcsYDaGxNScXDcgxjw4GK8mzoalb7++geEhAAZGU5vFykLAxkiIhmYq4XiDtyxgJq2Bs7aZ29B56Xv4MKeg8DkyZptEADgqaeQV+fn1p8ruZ6PqxtARKRkbpN3YoE7F1CLj9AmHTcD3n0XmD4dVXNfw+TQfvit3uaPep/rBx8A0dHAbbcBBsXyqGHhiAwRkR3cJu/EAqVUPwYAtGmDSSnpyDylPwqj+1zPndPs8zRiBNC3L5Bleqdr8nwMZIiIbOSOeSfmKKVsv6XPtfTZ2UDFlc92+3YgLQ248UZg926nt5Vcj1NLREQ2kpJ34k4jHdqcFHcvoGbuc40pO48my5YYP7FuneZnzBjgpZeAhAQHtpDcCUdkiIhs5M55J+bERwRhYGIztwxiAPOf65kmEbjw7gdA27biB3zxBdCxI/Dgg8C//zqoheROGMgQEdlIUXknCmLuc722fRSaPTAROHQIeO89TcKvobo64MMPgXbtgKeeAorEi+6RZ2AgQ0RkB6XknSiNxc/V1xd46CHg2DFgzhwgNNT4JJcvA6+/DrRpA7zyytW8GvIo3KKAiEgG7p53olSSP9fiYmDePOCtt4BLl8SPiYoCDhwAIiLEnye3wr2WrmAgQ0TUgJw+rUn2XbwYqK3Vf+6WW4Dvv3dNu8hq3GuJiIganpgYTe7MoUPA2LFXH1epNNNL5HEYyBARkedp1w5YsQLYswcYNgy4+26gWzfxY9VqIDvbue0j2TCQISIiz3XNNcBPPwEff2z6mC++AFJSNFNPf/7ptKaRPBjIEBGR5/PzE3+8pgZ47jnN///4I9CjBzBunGY1FCkCAxkiImq4lizRD1oEQTMl1aED8MgjwJkzrmsbScJAhoiIGq6gIM2ybEO1tZqk4bZtgf/+FygpcXrTSBoGMkRE1HDdcw9w9Cjw8suA2BLfS5c0Bffi44HXXgMqze+vRc7HQIaIiBq2xo2BZ54B8vKAJ58EGjUyPqakBJgxQ7Ma6v33Nbk15BYYyBAREQFAeLimOvCRI8CkSYC3t/ExZ84ADz+s2ZiSxfXcAgMZIiKi+lq21Gw6efAgMHq0+DHHjgFnzzq3XSSKgQwREZGY9u01NWZ27gSGDjV+buJE17SL9DCQISIiMqdXL2DdOuD33zWF8wDNfk4+PuLH19U5r23EQIaIiEiSgQOBbds0Qc0dd5g+7p57ND95ec5rWwPGQIaIiEgqlUozzeRlovvcswdYuRL47DNNUb0pU4Bz55zbxgaGgQwREZFc/vvfq/9fUwO8+y7Qpg3w7LNAaanr2uXBGMgQERHJ4d9/gS1bjB+vrAReeUUT0MyfrymyR7JhIENERCSHFi00eTHTpwP+/sbPFxVpCu4lJAAffaTZBoHsxkCGiIhILhERwIIFwOHDwH33iefS/Psv8MADQOfOwOrVgFrt/HZ6EAYyREREcmvdWrOz9oEDwKhR4sccPqwpuJeUBKxfr9l5m6zGQIaIiMhROnYEvvoKyM4GhgwRP2b3buDWW7m6yUYMZIiIiBwtKQn49VfNT+/exs9PngxERzu/XR6AgQwREZGzDBmiGZ35+mtNnRlAs/v2zJmubZeCKSKQWbhwIeLi4tCoUSOkpKQgOzvb1U0iIiKyjUoFjBwJ7N+vyaOZMweIjBQ/9uJFYMYM4Px557ZRQdw+kPniiy8wffp0zJo1C7t370b37t1xww034DxvKhERKZmPj2Zl06OPmj7mzTeB114D2rYFZs0Cysqc1z6FUAmCe6dJp6SkICkpCe+++y4AQK1Wo1WrVpgyZQpmzJhhdHxVVRWqqqp0fy4rK0OrVq1QWlqK4OBgp7WbiIjILhcuaIroXbx49bHwcE314EceARo1cl3bnKCsrAwhISEW+2+3HpGprq7Grl27MKRepreXlxeGDBmCbdu2ib5mzpw5CAkJ0f20atXKWc0lIiKSz2uv6QcxAFBYCDzxBNC+PfDxxyyqBzcPZC5cuIC6ujpERUXpPR4VFYWzZ8+KvmbmzJkoLS3V/Zw6dcoZTSUiIpLX5MnAhAniRfVOnQLS04GuXTWJw+49ueJQbh3I2MLf3x/BwcF6P0RERIoTFwd88gmwbx8wYoT4MX//DdxxB5CSAmzY4MTGuQ+3DmQiIiLg7e2NcwZFgs6dO4dorrcnIqKGoHNn4JtvgG3bgLQ08WNycjRLu4cM0fx/A+LWgYyfnx969eqFDfWiTLVajQ0bNiA1NdWFLSMiInKyPn2A338H1q0DevYUP2bDBiA5WbPCqYFw60AGAKZPn46PPvoIy5Ytw6FDh/Dwww+joqICEydOdHXTiIiInEulAoYO1Yy6fPGFZidtMQMHOrddLuTj6gZYMmbMGBQUFOD555/H2bNncc011+CXX34xSgAmIiJqMLy8NBtO3n67Jo9m9mzg9GnNczfcYHoKygO5fR0Ze0ldh05ERKRYly4BCxcCc+dqdtI2NfV05IhmT6cmTZzbPht4RB0ZIiIikiAgAMjI0CzLNhXECAIwdqymSvDbbwP1iscqGQMZIiIiTxEQYPq5r78Gdu0CCgqAxx4DEhOBZcuAujrntc8BGMgQERF5utpa4Nln9R87cQK4916gWzfg228VW1SPgQwREZGnKynRjMCIOXhQkzScmgps3OjMVsmCgQwREZGni4gA1q4FtmwBrr1W/JgdOzTLtm+4QTMFpRAMZIiIiBqKvn2BrCzgp5+Aa64RP2b9eqB3b2DMGODwYac2zxYMZIiIiBoSlQoYNkwz6rJypWYVk5gvvwQ6dQIeeAAoKnJuG63AQIaIiKgh8vIC7roLOHQIeO89oHlz42Pq6oDvvwf8/Z3fPokYyBARETVkvr7AQw8BR49qCuqFhuo//9xzQFCQS5omBQMZIiIiAgIDgaefBvLygJkzNTVp2rQB7r/f9GvcYMk2AxkiIiK6KiwMePVV4NgxYMUKwM9P/Lj8fKBjR+Czz1xaVI+BDBERERlr3hxISTH9/KxZQG4uMHGiZmsEF2EgQ0RERNbZv18zEgMADz4IxMW5rCkMZIiIiMg6K1Zo8mMCA423PnAyH5e+OxERESnPq68C/ftrppSio13aFAYyREREZB2VCrj5Zle3AgCnloiIiEjBGMgQERGRYjGQISIiIsViIENERESKxUCGiIiIFIuBDBERESkWAxkiIiJSLAYyREREpFgMZIiIiEixGMgQERGRYjGQISIiIsViIENERESKxUCGiIiIFMvjd78WBAEAUFZW5uKWEBERkVTaflvbj5vi8YHMxYsXAQCtWrVycUuIiIjIWhcvXkRISIjJ51WCpVBH4dRqNU6fPo0mTZpApVLJeu6ysjK0atUKp06dQnBwsKzndheefo2efn0Ar9ETePr1AZ5/jZ5+fYD81ygIAi5evIiYmBh4eZnOhPH4ERkvLy+0bNnSoe8RHBzssb+YWp5+jZ5+fQCv0RN4+vUBnn+Nnn59gLzXaG4kRovJvkRERKRYDGSIiIhIsRjI2MHf3x+zZs2Cv7+/q5viMJ5+jZ5+fQCv0RN4+vUBnn+Nnn59gOuu0eOTfYmIiMhzcUSGiIiIFIuBDBERESkWAxkiIiJSLAYyREREpFgMZOywcOFCxMXFoVGjRkhJSUF2drarmySb2bNnQ6VS6f106NDB1c2y2aZNm3DrrbciJiYGKpUK3377rd7zgiDg+eefR/PmzREQEIAhQ4bgyJEjrmmsjSxd47333mt0T2+88UbXNNYGc+bMQVJSEpo0aYJmzZphxIgRyM3N1Tvm8uXLmDx5MsLDw9G4cWOMGjUK586dc1GLrSPl+tLS0ozu4UMPPeSiFlvvvffeQ7du3XQF01JTU/Hzzz/rnlfy/dOydI1Kv4eG5s6dC5VKhccff1z3mLPvIwMZG33xxReYPn06Zs2ahd27d6N79+644YYbcP78eVc3TTadO3fGmTNndD+bN292dZNsVlFRge7du2PhwoWiz8+bNw9vv/023n//fezYsQNBQUG44YYbcPnyZSe31HaWrhEAbrzxRr17unLlSie20D5ZWVmYPHkytm/fjl9//RU1NTUYOnQoKioqdMdMmzYN33//PVavXo2srCycPn0aI0eOdGGrpZNyfQAwadIkvXs4b948F7XYei1btsTcuXOxa9cu7Ny5E4MGDcLw4cPx119/AVD2/dOydI2Asu9hfTk5Ofjggw/QrVs3vcedfh8FsklycrIwefJk3Z/r6uqEmJgYYc6cOS5slXxmzZoldO/e3dXNcAgAwjfffKP7s1qtFqKjo4XXX39d91hJSYng7+8vrFy50gUttJ/hNQqCIEyYMEEYPny4S9rjCOfPnxcACFlZWYIgaO6Zr6+vsHr1at0xhw4dEgAI27Ztc1UzbWZ4fYIgCNddd53w2GOPua5RDhAWFiYsXrzY4+5ffdprFATPuYcXL14UEhIShF9//VXvmlxxHzkiY4Pq6mrs2rULQ4YM0T3m5eWFIUOGYNu2bS5smbyOHDmCmJgYtGnTBuPGjcPJkydd3SSHyM/Px9mzZ/XuZ0hICFJSUjzqfgLAxo0b0axZMyQmJuLhhx9GYWGhq5tks9LSUgBA06ZNAQC7du1CTU2N3n3s0KEDWrdurcj7aHh9Wp9//jkiIiLQpUsXzJw5E5WVla5ont3q6uqwatUqVFRUIDU11ePuH2B8jVqecA8nT56Mm2++We9+Aa75e+jxm0Y6woULF1BXV4eoqCi9x6OiovD333+7qFXySklJwSeffILExEScOXMGL7zwAq699locOHAATZo0cXXzZHX27FkAEL2f2uc8wY033oiRI0ciPj4ex44dw3//+18MGzYM27Ztg7e3t6ubZxW1Wo3HH38c/fr1Q5cuXQBo7qOfnx9CQ0P1jlXifRS7PgC4++67ERsbi5iYGOzbtw9PP/00cnNzsWbNGhe21jr79+9HamoqLl++jMaNG+Obb75Bp06dsHfvXo+5f6auEfCMe7hq1Srs3r0bOTk5Rs+54u8hAxkSNWzYMN3/d+vWDSkpKYiNjcWXX36J9PR0F7aMbHXXXXfp/r9r167o1q0b2rZti40bN2Lw4MEubJn1Jk+ejAMHDig6b8scU9f3wAMP6P6/a9euaN68OQYPHoxjx46hbdu2zm6mTRITE7F3716Ulpbiq6++woQJE5CVleXqZsnK1DV26tRJ8ffw1KlTeOyxx/Drr7+iUaNGrm4OACb72iQiIgLe3t5GWdjnzp1DdHS0i1rlWKGhoWjfvj2OHj3q6qbITnvPGtL9BIA2bdogIiJCcff00UcfxQ8//IDMzEy0bNlS93h0dDSqq6tRUlKid7zS7qOp6xOTkpICAIq6h35+fmjXrh169eqFOXPmoHv37njrrbc85v4Bpq9RjNLu4a5du3D+/Hn07NkTPj4+8PHxQVZWFt5++234+PggKirK6feRgYwN/Pz80KtXL2zYsEH3mFqtxoYNG/TmQT1JeXk5jh07hubNm7u6KbKLj49HdHS03v0sKyvDjh07PPZ+AsA///yDwsJCxdxTQRDw6KOP4ptvvsHvv/+O+Ph4ved79eoFX19fvfuYm5uLkydPKuI+Wro+MXv37gUAxdxDMWq1GlVVVYq/f+Zor1GM0u7h4MGDsX//fuzdu1f307t3b4wbN073/06/jw5JIW4AVq1aJfj7+wuffPKJcPDgQeGBBx4QQkNDhbNnz7q6abJ44oknhI0bNwr5+fnCli1bhCFDhggRERHC+fPnXd00m1y8eFHYs2ePsGfPHgGA8MYbbwh79uwRTpw4IQiCIMydO1cIDQ0V1q5dK+zbt08YPny4EB8fL1y6dMnFLZfO3DVevHhRyMjIELZt2ybk5+cLv/32m9CzZ08hISFBuHz5squbLsnDDz8shISECBs3bhTOnDmj+6msrNQd89BDDwmtW7cWfv/9d2Hnzp1CamqqkJqa6sJWS2fp+o4ePSq8+OKLws6dO4X8/Hxh7dq1Qps2bYQBAwa4uOXSzZgxQ8jKyhLy8/OFffv2CTNmzBBUKpWwfv16QRCUff+0zF2jJ9xDMYYrsZx9HxnI2OGdd94RWrduLfj5+QnJycnC9u3bXd0k2YwZM0Zo3ry54OfnJ7Ro0UIYM2aMcPToUVc3y2aZmZkCAKOfCRMmCIKgWYL93HPPCVFRUYK/v78wePBgITc317WNtpK5a6ysrBSGDh0qREZGCr6+vkJsbKwwadIkRQXeYtcGQFi6dKnumEuXLgmPPPKIEBYWJgQGBgq33367cObMGdc12gqWru/kyZPCgAEDhKZNmwr+/v5Cu3bthCeffFIoLS11bcOtcN999wmxsbGCn5+fEBkZKQwePFgXxAiCsu+flrlr9IR7KMYwkHH2fVQJgiA4ZqyHiIiIyLGYI0NERESKxUCGiIiIFIuBDBERESkWAxkiIiJSLAYyREREpFgMZIiIiEixGMgQERGRYjGQISIiIsViIENEbiEtLQ2PP/64q5tBRArDQIaIFMXWgOfee+/FiBEjZG8PEbkWAxkiIiJSLAYyROR2Fi1ahISEBDRq1AhRUVG44447AGhGVbKysvDWW29BpVJBpVLh+PHjqKurQ3p6OuLj4xEQEIDExES89dZbuvPNnj0by5Ytw9q1a3Wv27hxo4uujojk5OPqBhAR1bdz505MnToVn376Kfr27YuioiL88ccfAIC33noLhw8fRpcuXfDiiy8CACIjI6FWq9GyZUusXr0a4eHh2Lp1Kx544AE0b94co0ePRkZGBg4dOoSysjIsXboUANC0aVOXXSMRyYeBDBG5lZMnTyIoKAi33HILmjRpgtjYWPTo0QMAEBISAj8/PwQGBiI6Olr3Gm9vb7zwwgu6P8fHx2Pbtm348ssvMXr0aDRu3BgBAQGoqqrSex0RKR+nlojIrVx//fWIjY1FmzZtcM899+Dzzz9HZWWlxdctXLgQvXr1QmRkJBo3bowPP/wQJ0+edEKLiciVGMgQkVtp0qQJdu/ejZUrV6J58+Z4/vnn0b17d5SUlJh8zapVq5CRkYH09HSsX78ee/fuxcSJE1FdXe28hhORSzCQISK34+PjgyFDhmDevHnYt28fjh8/jt9//x0A4Ofnh7q6Or3jt2zZgr59++KRRx5Bjx490K5dOxw7dkzvGLHXEZHyMUeGiNzKDz/8gLy8PAwYMABhYWH46aefoFarkZiYCACIi4vDjh07cPz4cTRu3BhNmzZFQkICli9fjnXr1iE+Ph6ffvopcnJyEB8frztvXFwc1q1bh9zcXISHhyMkJAS+vr6uukwikglHZIjIrYSGhmLNmjUYNGgQOnbsiPfffx8rV65E586dAQAZGRnw9vZGp06dEBkZiZMnT+LBBx/EyJEjMWbMGKSkpKCwsBCPPPKI3nknTZqExMRE9O7dG5GRkdiyZYsrLo+IZKYSBEFwdSOIiIiIbMERGSIiIlIsBjJERESkWAxkiIiISLEYyBAREZFiMZAhIiIixWIgQ0RERIrFQIaIiIgUi4EMERERKRYDGSIiIlIsBjJERESkWAxkiIiISLH+D9tMdOSpUYNXAAAAAElFTkSuQmCC",
      "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": "9a3e8b26",
   "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": "1d78b981",
   "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": "b524399e",
   "metadata": {
    "execution": {},
    "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": "590a8be9",
   "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": "8c95b6b0",
   "metadata": {
    "execution": {},
    "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": "7712b1e1",
   "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": "c17dacc1",
   "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": "04ed8362",
   "metadata": {
    "execution": {},
    "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": "3af076fd",
   "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": "6483e190",
   "metadata": {
    "execution": {}
   },
   "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": "b79a6810",
   "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": "99a6f9d0",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "        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>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": "719d42ae",
   "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": "78cf55d0",
   "metadata": {
    "execution": {}
   },
   "outputs": [
    {
     "data": {
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       "\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>41.5251</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",
       "      <td>0.062</td>\n",
       "      <td>0.217</td>\n",
       "      <td>0.829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>chas</th>\n",
       "      <td>2.8528</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": "526a80bc",
   "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": "902f6474",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "\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>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",
       "    <tr>\n",
       "      <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": "2a1567ea",
   "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": "ea1c88e9",
   "metadata": {
    "execution": {},
    "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": "18fb24e5",
   "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": "e9ff159c",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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": "92604d18",
   "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": "c98f54b2",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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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>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": "ccc11d8c",
   "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": "53065cac",
   "metadata": {
    "execution": {},
    "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>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": "c0696dc2",
   "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 their 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": "8c654809",
   "metadata": {
    "execution": {},
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x2906aa3e0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": "f79b542d",
   "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": "6123a191",
   "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": "2182f0ec",
   "metadata": {
    "execution": {},
    "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": "66672403",
   "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": "d614fdcb",
   "metadata": {
    "execution": {},
    "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": "2402763b",
   "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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