halos_linear_regression_testing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"dark_matter.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_copy = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.drop(df.index[8474])\n",
    "df = df.drop(df.index[6815])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_copy = df_copy.drop(df.index[8474])\n",
    "df_copy = df_copy.drop(df.index[6815])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df.loc[:, ~df.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y = df.loc[:, df.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_log = x.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_log = x.transform(lambda a: np.log(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import RobustScaler\n",
    "scaler = RobustScaler()\n",
    "x_log[x.columns] = scaler.fit_transform(x_log[x.columns])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mass</th>\n",
       "      <th>kinetic_energy</th>\n",
       "      <th>mean_radius</th>\n",
       "      <th>Group_M_Crit200</th>\n",
       "      <th>Group_M_Crit500</th>\n",
       "      <th>Group_M_Mean200</th>\n",
       "      <th>Group_M_TopHat200</th>\n",
       "      <th>Group_R_Crit200</th>\n",
       "      <th>Group_R_Crit500</th>\n",
       "      <th>Group_R_Mean200</th>\n",
       "      <th>Group_R_TopHat200</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>21.174025</td>\n",
       "      <td>8.344036</td>\n",
       "      <td>0.194935</td>\n",
       "      <td>5.705371</td>\n",
       "      <td>5.598144</td>\n",
       "      <td>5.825421</td>\n",
       "      <td>5.826019</td>\n",
       "      <td>5.705295</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.686603</td>\n",
       "      <td>2.983820</td>\n",
       "      <td>0.085244</td>\n",
       "      <td>5.660482</td>\n",
       "      <td>5.068873</td>\n",
       "      <td>5.824574</td>\n",
       "      <td>5.868417</td>\n",
       "      <td>5.660391</td>\n",
       "      <td>5.068701</td>\n",
       "      <td>5.824390</td>\n",
       "      <td>5.868884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.289086</td>\n",
       "      <td>3.366994</td>\n",
       "      <td>0.209044</td>\n",
       "      <td>5.657459</td>\n",
       "      <td>5.627020</td>\n",
       "      <td>5.674491</td>\n",
       "      <td>5.715509</td>\n",
       "      <td>5.657300</td>\n",
       "      <td>5.626899</td>\n",
       "      <td>5.674334</td>\n",
       "      <td>5.715843</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.465517</td>\n",
       "      <td>3.218538</td>\n",
       "      <td>0.746296</td>\n",
       "      <td>5.009451</td>\n",
       "      <td>4.930719</td>\n",
       "      <td>5.105941</td>\n",
       "      <td>5.072324</td>\n",
       "      <td>5.009309</td>\n",
       "      <td>4.930506</td>\n",
       "      <td>5.105816</td>\n",
       "      <td>5.072615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.725421</td>\n",
       "      <td>2.244814</td>\n",
       "      <td>0.083188</td>\n",
       "      <td>5.417539</td>\n",
       "      <td>5.149648</td>\n",
       "      <td>5.404342</td>\n",
       "      <td>5.468534</td>\n",
       "      <td>5.417470</td>\n",
       "      <td>5.149408</td>\n",
       "      <td>5.404188</td>\n",
       "      <td>5.468921</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        mass  kinetic_energy  mean_radius  Group_M_Crit200  Group_M_Crit500  \\\n",
       "0  21.174025        8.344036     0.194935         5.705371         5.598144   \n",
       "1   9.686603        2.983820     0.085244         5.660482         5.068873   \n",
       "2   8.289086        3.366994     0.209044         5.657459         5.627020   \n",
       "3   7.465517        3.218538     0.746296         5.009451         4.930719   \n",
       "4   6.725421        2.244814     0.083188         5.417539         5.149648   \n",
       "\n",
       "   Group_M_Mean200  Group_M_TopHat200  Group_R_Crit200  Group_R_Crit500  \\\n",
       "0         5.825421           5.826019         5.705295         5.597937   \n",
       "1         5.824574           5.868417         5.660391         5.068701   \n",
       "2         5.674491           5.715509         5.657300         5.626899   \n",
       "3         5.105941           5.072324         5.009309         4.930506   \n",
       "4         5.404342           5.468534         5.417470         5.149408   \n",
       "\n",
       "   Group_R_Mean200  Group_R_TopHat200  \n",
       "0         5.825257           5.826462  \n",
       "1         5.824390           5.868884  \n",
       "2         5.674334           5.715843  \n",
       "3         5.105816           5.072615  \n",
       "4         5.404188           5.468921  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_log.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import sklearn.linear_model as lm\n",
    "from sklearn import datasets, linear_model, model_selection\n",
    "import sklearn\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression, Lasso, Ridge\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import RepeatedKFold\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9997.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>74.139024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>58.848546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>55.170160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>61.293182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>70.379020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "        dispersion\n",
       "count  9997.000000\n",
       "mean     74.139024\n",
       "std      58.848546\n",
       "min       0.000000\n",
       "25%      55.170160\n",
       "50%      61.293182\n",
       "75%      70.379020\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First Linear Regression Iteration with all the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_lr = x_log.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_lr_train, X_lr_test, y_lr_train, y_lr_test = sklearn.model_selection.train_test_split(X_lr, y, test_size = 0.20, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((7997, 11), (2000, 11), (7997, 1), (2000, 1))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_lr_train.shape, X_lr_test.shape, y_lr_train.shape, y_lr_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             dispersion   R-squared:                       0.272\n",
      "Model:                            OLS   Adj. R-squared:                  0.271\n",
      "Method:                 Least Squares   F-statistic:                     271.8\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):               0.00\n",
      "Time:                        15:20:20   Log-Likelihood:                -42699.\n",
      "No. Observations:                7997   AIC:                         8.542e+04\n",
      "Df Residuals:                    7985   BIC:                         8.551e+04\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const                73.6143      0.884     83.277      0.000      71.881      75.347\n",
      "mass                 24.2407      1.422     17.046      0.000      21.453      27.028\n",
      "kinetic_energy       22.3197      0.810     27.565      0.000      20.732      23.907\n",
      "mean_radius          20.3597      0.660     30.867      0.000      19.067      21.653\n",
      "Group_M_Crit200    6039.7149   9179.845      0.658      0.511    -1.2e+04     2.4e+04\n",
      "Group_M_Crit500   -1.433e+04   1.05e+04     -1.365      0.172   -3.49e+04    6246.240\n",
      "Group_M_Mean200   -1.015e+04   1.34e+04     -0.758      0.448   -3.64e+04    1.61e+04\n",
      "Group_M_TopHat200  7297.6681   1.05e+04      0.697      0.486   -1.32e+04    2.78e+04\n",
      "Group_R_Crit200   -6033.2065   9179.977     -0.657      0.511    -2.4e+04     1.2e+04\n",
      "Group_R_Crit500    1.432e+04   1.05e+04      1.365      0.172   -6253.087    3.49e+04\n",
      "Group_R_Mean200    1.011e+04   1.34e+04      0.755      0.450   -1.61e+04    3.63e+04\n",
      "Group_R_TopHat200 -7271.9822   1.05e+04     -0.694      0.488   -2.78e+04    1.33e+04\n",
      "==============================================================================\n",
      "Omnibus:                     8917.900   Durbin-Watson:                   1.967\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1032892.475\n",
      "Skew:                           5.659   Prob(JB):                         0.00\n",
      "Kurtosis:                      57.514   Cond. No.                     8.95e+04\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 8.95e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#Model statistics\n",
    "#Must add constant for y-intercept\n",
    "model = sm.OLS(y_lr_train, sm.add_constant(X_lr_train)).fit()\n",
    "Y_pred = model.predict(sm.add_constant(X_lr_test))\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/parth/opt/anaconda3/envs/env/lib/python3.6/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "sns.distplot(model.resid, fit=stats.norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb4a9609b70>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,8))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.set_xlabel(\"Y_Test\")\n",
    "ax.set_ylabel(\"Predicted value\")\n",
    "ax.set_title(\"Actual Values vs Predicted Values\")\n",
    "plt.scatter(y_lr_test, Y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_90 = y.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9997.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>74.139024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>58.848546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>55.170160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>61.293182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>70.379020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  9997.000000\n",
       "mean     74.139024\n",
       "std      58.848546\n",
       "min       0.000000\n",
       "25%      55.170160\n",
       "50%      61.293182\n",
       "75%      70.379020\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We will now perform regression for values of 'dispersion' below 90 and above 90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_90 = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_90 = y_90[y_90['dispersion'].between(0.00, 90.00)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9043.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>61.382718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.309829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>54.607731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>60.022600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>66.973970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>89.970380</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  9043.000000\n",
       "mean     61.382718\n",
       "std       9.309829\n",
       "min       0.000000\n",
       "25%      54.607731\n",
       "50%      60.022600\n",
       "75%      66.973970\n",
       "max      89.970380"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_90.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_90 = df_90[df_90['dispersion'].between(0.00, 90.00)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mass</th>\n",
       "      <th>dispersion</th>\n",
       "      <th>kinetic_energy</th>\n",
       "      <th>mean_radius</th>\n",
       "      <th>Group_M_Crit200</th>\n",
       "      <th>Group_M_Crit500</th>\n",
       "      <th>Group_M_Mean200</th>\n",
       "      <th>Group_M_TopHat200</th>\n",
       "      <th>Group_R_Crit200</th>\n",
       "      <th>Group_R_Crit500</th>\n",
       "      <th>Group_R_Mean200</th>\n",
       "      <th>Group_R_TopHat200</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9.043000e+03</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "      <td>9043.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>146.462789</td>\n",
       "      <td>61.382718</td>\n",
       "      <td>7.210497e+06</td>\n",
       "      <td>48.243651</td>\n",
       "      <td>46.411238</td>\n",
       "      <td>35.690916</td>\n",
       "      <td>64.525753</td>\n",
       "      <td>55.989113</td>\n",
       "      <td>108.756913</td>\n",
       "      <td>74.115512</td>\n",
       "      <td>185.055104</td>\n",
       "      <td>146.165356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>49.981224</td>\n",
       "      <td>9.309829</td>\n",
       "      <td>7.948301e+06</td>\n",
       "      <td>9.514413</td>\n",
       "      <td>88.351517</td>\n",
       "      <td>64.314345</td>\n",
       "      <td>131.350012</td>\n",
       "      <td>110.424604</td>\n",
       "      <td>41.180151</td>\n",
       "      <td>27.154981</td>\n",
       "      <td>72.708482</td>\n",
       "      <td>56.609906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.475066e+05</td>\n",
       "      <td>23.160006</td>\n",
       "      <td>1.576799</td>\n",
       "      <td>0.931173</td>\n",
       "      <td>3.018168</td>\n",
       "      <td>2.109668</td>\n",
       "      <td>40.782790</td>\n",
       "      <td>25.210709</td>\n",
       "      <td>78.098114</td>\n",
       "      <td>57.126507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>112.000000</td>\n",
       "      <td>54.607731</td>\n",
       "      <td>2.423016e+06</td>\n",
       "      <td>42.750617</td>\n",
       "      <td>12.829749</td>\n",
       "      <td>10.377800</td>\n",
       "      <td>16.728206</td>\n",
       "      <td>14.907875</td>\n",
       "      <td>82.026480</td>\n",
       "      <td>56.312062</td>\n",
       "      <td>138.207560</td>\n",
       "      <td>109.618630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>133.000000</td>\n",
       "      <td>60.022600</td>\n",
       "      <td>4.789329e+06</td>\n",
       "      <td>46.747287</td>\n",
       "      <td>20.224848</td>\n",
       "      <td>16.378328</td>\n",
       "      <td>26.418990</td>\n",
       "      <td>23.430400</td>\n",
       "      <td>95.465800</td>\n",
       "      <td>65.563780</td>\n",
       "      <td>160.944370</td>\n",
       "      <td>127.449295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>166.000000</td>\n",
       "      <td>66.973970</td>\n",
       "      <td>9.109586e+06</td>\n",
       "      <td>51.849725</td>\n",
       "      <td>41.125671</td>\n",
       "      <td>32.741615</td>\n",
       "      <td>54.594565</td>\n",
       "      <td>48.050594</td>\n",
       "      <td>120.944577</td>\n",
       "      <td>82.593955</td>\n",
       "      <td>205.003515</td>\n",
       "      <td>161.922240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>479.000000</td>\n",
       "      <td>89.970380</td>\n",
       "      <td>1.510843e+08</td>\n",
       "      <td>467.233497</td>\n",
       "      <td>1727.055700</td>\n",
       "      <td>1283.849500</td>\n",
       "      <td>2242.356700</td>\n",
       "      <td>2024.290600</td>\n",
       "      <td>420.391480</td>\n",
       "      <td>280.601930</td>\n",
       "      <td>707.306640</td>\n",
       "      <td>563.435670</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              mass   dispersion  kinetic_energy  mean_radius  Group_M_Crit200  \\\n",
       "count  9043.000000  9043.000000    9.043000e+03  9043.000000      9043.000000   \n",
       "mean    146.462789    61.382718    7.210497e+06    48.243651        46.411238   \n",
       "std      49.981224     9.309829    7.948301e+06     9.514413        88.351517   \n",
       "min       1.000000     0.000000    1.475066e+05    23.160006         1.576799   \n",
       "25%     112.000000    54.607731    2.423016e+06    42.750617        12.829749   \n",
       "50%     133.000000    60.022600    4.789329e+06    46.747287        20.224848   \n",
       "75%     166.000000    66.973970    9.109586e+06    51.849725        41.125671   \n",
       "max     479.000000    89.970380    1.510843e+08   467.233497      1727.055700   \n",
       "\n",
       "       Group_M_Crit500  Group_M_Mean200  Group_M_TopHat200  Group_R_Crit200  \\\n",
       "count      9043.000000      9043.000000        9043.000000      9043.000000   \n",
       "mean         35.690916        64.525753          55.989113       108.756913   \n",
       "std          64.314345       131.350012         110.424604        41.180151   \n",
       "min           0.931173         3.018168           2.109668        40.782790   \n",
       "25%          10.377800        16.728206          14.907875        82.026480   \n",
       "50%          16.378328        26.418990          23.430400        95.465800   \n",
       "75%          32.741615        54.594565          48.050594       120.944577   \n",
       "max        1283.849500      2242.356700        2024.290600       420.391480   \n",
       "\n",
       "       Group_R_Crit500  Group_R_Mean200  Group_R_TopHat200  \n",
       "count      9043.000000      9043.000000        9043.000000  \n",
       "mean         74.115512       185.055104         146.165356  \n",
       "std          27.154981        72.708482          56.609906  \n",
       "min          25.210709        78.098114          57.126507  \n",
       "25%          56.312062       138.207560         109.618630  \n",
       "50%          65.563780       160.944370         127.449295  \n",
       "75%          82.593955       205.003515         161.922240  \n",
       "max         280.601930       707.306640         563.435670  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_90.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "x90 = df_90.loc[:, ~df_90.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y90 = df_90.loc[:, df_90.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9043, 11)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x90.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "x90_log = x90.transform(lambda a: np.log(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "X90=x90_log\n",
    "y90=y90\n",
    "\n",
    "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(X90, y90, test_size = 0.20, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             dispersion   R-squared:                       0.604\n",
      "Model:                            OLS   Adj. R-squared:                  0.604\n",
      "Method:                 Least Squares   F-statistic:                     1002.\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):               0.00\n",
      "Time:                        15:54:26   Log-Likelihood:                -23110.\n",
      "No. Observations:                7234   AIC:                         4.624e+04\n",
      "Df Residuals:                    7222   BIC:                         4.633e+04\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const             -2.735e+04    2.5e+04     -1.096      0.273   -7.63e+04    2.16e+04\n",
      "mass                 10.3217      0.487     21.193      0.000       9.367      11.276\n",
      "kinetic_energy        1.0389      0.075     13.836      0.000       0.892       1.186\n",
      "mean_radius         -17.9172      0.421    -42.604      0.000     -18.742     -17.093\n",
      "Group_M_Crit200   -1990.9910    945.436     -2.106      0.035   -3844.322    -137.660\n",
      "Group_M_Crit500   -1674.9439   1097.009     -1.527      0.127   -3825.403     475.516\n",
      "Group_M_Mean200    -178.5854   1357.422     -0.132      0.895   -2839.530    2482.359\n",
      "Group_M_TopHat200  1084.5021   1070.174      1.013      0.311   -1013.353    3182.357\n",
      "Group_R_Crit200    5985.2552   2836.351      2.110      0.035     425.177    1.15e+04\n",
      "Group_R_Crit500    5017.2686   3291.073      1.525      0.127   -1434.198    1.15e+04\n",
      "Group_R_Mean200     553.3418   4072.234      0.136      0.892   -7429.429    8536.112\n",
      "Group_R_TopHat200 -3266.7346   3210.608     -1.017      0.309   -9560.466    3026.997\n",
      "==============================================================================\n",
      "Omnibus:                     3472.947   Durbin-Watson:                   2.000\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            23162.915\n",
      "Skew:                           2.221   Prob(JB):                         0.00\n",
      "Kurtosis:                      10.558   Cond. No.                     7.37e+06\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 7.37e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#Model statistics\n",
    "#Must add constant for y-intercept\n",
    "model = sm.OLS(y_train, sm.add_constant(X_train)).fit()\n",
    "y90_pred = model.predict(sm.add_constant(X_test))\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/parth/opt/anaconda3/envs/env/lib/python3.6/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "sns.distplot(model.resid, fit=stats.norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb4a97ced68>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,5))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.set_xlabel(\"Y_Test\")\n",
    "ax.set_ylabel(\"Predicted value\")\n",
    "ax.set_title(\"Actual Values vs Predicted Values\")\n",
    "plt.scatter(y_test, y90_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1\n",
    "y_1=y.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>954.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>195.056500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>139.004064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>90.051380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>105.302765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>139.641120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>228.227293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count   954.000000\n",
       "mean    195.056500\n",
       "std     139.004064\n",
       "min      90.051380\n",
       "25%     105.302765\n",
       "50%     139.641120\n",
       "75%     228.227293\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Now plotting the model with the rest of the data (i.e. dispersion over 90)\n",
    "y_1 = y_1[y_1['dispersion'].between(90.00, 1500.00)]\n",
    "y_1.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 2\n",
    "df_1 = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 3\n",
    "df_1 = df_1[df_1['dispersion'].between(90.00, 1500.00)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(954, 12)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 4\n",
    "df_1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 5\n",
    "x_1 = df_1.loc[:, ~df_1.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y_1 = df_1.loc[:, df_1.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 6\n",
    "x1_log = x_1.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 7\n",
    "x1_log = x1_log.transform(lambda a: np.log(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(954, 11)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 8\n",
    "x1_log.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 9\n",
    "X1=x1_log\n",
    "y_1=y_1\n",
    "\n",
    "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(X1, y_1, test_size = 0.20, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(763, 11)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 10\n",
    "X_train.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             dispersion   R-squared:                       0.540\n",
      "Model:                            OLS   Adj. R-squared:                  0.533\n",
      "Method:                 Least Squares   F-statistic:                     80.16\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):          1.08e-118\n",
      "Time:                        16:14:57   Log-Likelihood:                -4576.3\n",
      "No. Observations:                 763   AIC:                             9177.\n",
      "Df Residuals:                     751   BIC:                             9232.\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const             -9.593e+05   1.34e+06     -0.714      0.476    -3.6e+06    1.68e+06\n",
      "mass                -39.1204     10.879     -3.596      0.000     -60.477     -17.764\n",
      "kinetic_energy       58.3644      3.921     14.884      0.000      50.666      66.063\n",
      "mean_radius         311.5325     14.897     20.912      0.000     282.288     340.777\n",
      "Group_M_Crit200    3.928e+04   5.03e+04      0.781      0.435   -5.95e+04    1.38e+05\n",
      "Group_M_Crit500   -1.563e+04   5.73e+04     -0.273      0.785   -1.28e+05    9.68e+04\n",
      "Group_M_Mean200   -7.609e+04   7.13e+04     -1.067      0.286   -2.16e+05    6.39e+04\n",
      "Group_M_TopHat200 -2.752e+04   5.67e+04     -0.485      0.628   -1.39e+05    8.38e+04\n",
      "Group_R_Crit200   -1.182e+05   1.51e+05     -0.783      0.434   -4.15e+05    1.78e+05\n",
      "Group_R_Crit500    4.697e+04   1.72e+05      0.273      0.785    -2.9e+05    3.84e+05\n",
      "Group_R_Mean200    2.278e+05   2.14e+05      1.065      0.287   -1.92e+05    6.48e+05\n",
      "Group_R_TopHat200  8.331e+04    1.7e+05      0.490      0.625   -2.51e+05    4.17e+05\n",
      "==============================================================================\n",
      "Omnibus:                      213.745   Durbin-Watson:                   2.012\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              790.830\n",
      "Skew:                           1.285   Prob(JB):                    1.88e-172\n",
      "Kurtosis:                       7.274   Cond. No.                     8.45e+06\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 8.45e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#Step 11\n",
    "#Model statistics\n",
    "#Must add constant for y-intercept\n",
    "model = sm.OLS(y_train, sm.add_constant(X_train)).fit()\n",
    "y1_pred = model.predict(sm.add_constant(X_test))\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/parth/opt/anaconda3/envs/env/lib/python3.6/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 12\n",
    "from scipy import stats\n",
    "sns.distplot(model.resid, fit=stats.norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb498889550>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 13\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.set_xlabel(\"Y_Test\")\n",
    "ax.set_ylabel(\"Predicted value\")\n",
    "ax.set_title(\"Actual Values vs Predicted Values\")\n",
    "plt.scatter(y_test, y1_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now I will examine the data a few standard deviations away from the mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1/2 Standard Deviation from the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9997.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>74.139024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>58.848546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>55.170160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>61.293182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>70.379020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  9997.000000\n",
       "mean     74.139024\n",
       "std      58.848546\n",
       "min       0.000000\n",
       "25%      55.170160\n",
       "50%      61.293182\n",
       "75%      70.379020\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dispersion    29.424273\n",
       "dtype: float64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(y.std())/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dispersion    103.563297\n",
      "dtype: float64\n",
      "dispersion    44.714751\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(y.mean() + ((y.std())/2))\n",
    "print(y.mean() - ((y.std())/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1\n",
    "y_1sd = y.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9178.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>62.419584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>10.494455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>44.721070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>54.921754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>60.400692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>67.783170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>103.525185</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  9178.000000\n",
       "mean     62.419584\n",
       "std      10.494455\n",
       "min      44.721070\n",
       "25%      54.921754\n",
       "50%      60.400692\n",
       "75%      67.783170\n",
       "max     103.525185"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_1sd = y_1sd[y_1sd['dispersion'].between(44.714751, 103.563297)]\n",
    "y_1sd.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 2\n",
    "df_1sd = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 3\n",
    "df_1sd = df_1sd[df_1sd['dispersion'].between(44.714751, 103.563297)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9178, 12)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 4\n",
    "df_1sd.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 5\n",
    "x_1sd = df_1sd.loc[:, ~df_1sd.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y_1sd = df_1sd.loc[:, df_1sd.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 6\n",
    "x1sd_log = x_1sd.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 7\n",
    "x1sd_log = x1sd_log.transform(lambda a: np.log(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9178, 11)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 8\n",
    "x1sd_log.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 9\n",
    "X=x1sd_log\n",
    "y=y_1sd\n",
    "\n",
    "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(X, y, test_size = 0.20, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((7342, 11), (1836, 1))"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 10\n",
    "X_train.shape, y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Model for values lying within 1/2 Stand Dev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             dispersion   R-squared:                       0.535\n",
      "Model:                            OLS   Adj. R-squared:                  0.534\n",
      "Method:                 Least Squares   F-statistic:                     765.2\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):               0.00\n",
      "Time:                        16:33:13   Log-Likelihood:                -24841.\n",
      "No. Observations:                7342   AIC:                         4.971e+04\n",
      "Df Residuals:                    7330   BIC:                         4.979e+04\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const              1.875e+04   2.99e+04      0.626      0.531   -3.99e+04    7.74e+04\n",
      "mass                 16.0922      0.622     25.871      0.000      14.873      17.312\n",
      "kinetic_energy        1.3462      0.091     14.862      0.000       1.169       1.524\n",
      "mean_radius         -15.8749      0.533    -29.795      0.000     -16.919     -14.830\n",
      "Group_M_Crit200    -866.7976   1135.801     -0.763      0.445   -3093.294    1359.699\n",
      "Group_M_Crit500    -246.4716   1317.888     -0.187      0.852   -2829.912    2336.968\n",
      "Group_M_Mean200     588.1742   1629.875      0.361      0.718   -2606.850    3783.199\n",
      "Group_M_TopHat200  2051.3427   1283.298      1.598      0.110    -464.291    4566.976\n",
      "Group_R_Crit200    2616.2617   3407.416      0.768      0.443   -4063.253    9295.777\n",
      "Group_R_Crit500     727.1985   3953.688      0.184      0.854   -7023.167    8477.564\n",
      "Group_R_Mean200   -1754.1159   4889.631     -0.359      0.720   -1.13e+04    7830.968\n",
      "Group_R_TopHat200 -6163.7464   3849.943     -1.601      0.109   -1.37e+04    1383.250\n",
      "==============================================================================\n",
      "Omnibus:                     3925.239   Durbin-Watson:                   1.991\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            30609.442\n",
      "Skew:                           2.479   Prob(JB):                         0.00\n",
      "Kurtosis:                      11.688   Cond. No.                     7.40e+06\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 7.4e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#Step 11\n",
    "#Model statistics\n",
    "#Must add constant for y-intercept\n",
    "model = sm.OLS(y_train, sm.add_constant(X_train)).fit()\n",
    "y_pred = model.predict(sm.add_constant(X_test))\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/parth/opt/anaconda3/envs/env/lib/python3.6/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 12\n",
    "from scipy import stats\n",
    "sns.distplot(model.resid, fit=stats.norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb4bc463b70>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 13\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.set_xlabel(\"Y_Test\")\n",
    "ax.set_ylabel(\"Predicted value\")\n",
    "ax.set_title(\"Actual Values vs Predicted Values\")\n",
    "plt.scatter(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now, I will repeat the same steps for attributes not within 1/2 standard deviation from mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 0\n",
    "x = df.loc[:, ~df.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y = df.loc[:, df.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9997.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>74.139024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>58.848546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>55.170160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>61.293182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>70.379020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  9997.000000\n",
       "mean     74.139024\n",
       "std      58.848546\n",
       "min       0.000000\n",
       "25%      55.170160\n",
       "50%      61.293182\n",
       "75%      70.379020\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dispersion    103.563297\n",
      "dtype: float64\n",
      "dispersion    44.714751\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(y.mean() + ((y.std())/2))\n",
    "print(y.mean() - ((y.std())/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1\n",
    "y_2sd = y.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>819.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>205.471167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>149.245006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>115.210110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>155.551200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>250.017130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count   819.000000\n",
       "mean    205.471167\n",
       "std     149.245006\n",
       "min       0.000000\n",
       "25%     115.210110\n",
       "50%     155.551200\n",
       "75%     250.017130\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_2sd = y_2sd[~y_2sd['dispersion'].between(44.714751, 103.563297)]\n",
    "y_2sd.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 2\n",
    "df_2sd = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 3\n",
    "df_2sd = df_2sd[~df_2sd['dispersion'].between(44.714751, 103.563297)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(819, 12)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 4\n",
    "df_2sd.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 5\n",
    "x_2sd = df_2sd.loc[:, ~df_2sd.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y_2sd = df_2sd.loc[:, df_2sd.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 6\n",
    "x2sd_log = x_2sd.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 7\n",
    "x2sd_log = x2sd_log.transform(lambda a: np.log(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(819, 11)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 8\n",
    "x2sd_log.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 9\n",
    "X=x2sd_log\n",
    "y=y_2sd\n",
    "\n",
    "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(X, y, test_size = 0.20, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((655, 11), (164, 1))"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 10\n",
    "X_train.shape, y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Model for values lying beyond 1/2 Stand Dev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             dispersion   R-squared:                       0.502\n",
      "Model:                            OLS   Adj. R-squared:                  0.493\n",
      "Method:                 Least Squares   F-statistic:                     58.92\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):           8.10e-90\n",
      "Time:                        16:47:27   Log-Likelihood:                -3979.0\n",
      "No. Observations:                 655   AIC:                             7982.\n",
      "Df Residuals:                     643   BIC:                             8036.\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const               4.67e+04   1.52e+06      0.031      0.976   -2.95e+06    3.04e+06\n",
      "mass                -36.3974     12.576     -2.894      0.004     -61.093     -11.702\n",
      "kinetic_energy       77.3654      4.179     18.514      0.000      69.160      85.571\n",
      "mean_radius         272.5541     17.212     15.835      0.000     238.755     306.353\n",
      "Group_M_Crit200    8.138e+04   5.82e+04      1.398      0.163    -3.3e+04    1.96e+05\n",
      "Group_M_Crit500    2.245e+04   6.77e+04      0.332      0.740    -1.1e+05    1.55e+05\n",
      "Group_M_Mean200   -8.236e+04   8.09e+04     -1.018      0.309   -2.41e+05    7.65e+04\n",
      "Group_M_TopHat200 -4630.9352   6.43e+04     -0.072      0.943   -1.31e+05    1.22e+05\n",
      "Group_R_Crit200   -2.442e+05   1.75e+05     -1.398      0.162   -5.87e+05    9.87e+04\n",
      "Group_R_Crit500   -6.733e+04   2.03e+05     -0.332      0.740   -4.66e+05    3.31e+05\n",
      "Group_R_Mean200    2.468e+05   2.43e+05      1.017      0.310    -2.3e+05    7.24e+05\n",
      "Group_R_TopHat200  1.427e+04   1.93e+05      0.074      0.941   -3.64e+05    3.93e+05\n",
      "==============================================================================\n",
      "Omnibus:                       99.316   Durbin-Watson:                   2.000\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              199.860\n",
      "Skew:                           0.867   Prob(JB):                     3.99e-44\n",
      "Kurtosis:                       5.077   Cond. No.                     8.04e+06\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 8.04e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#Step 11\n",
    "#Model statistics\n",
    "#Must add constant for y-intercept\n",
    "model = sm.OLS(y_train, sm.add_constant(X_train)).fit()\n",
    "y_pred = model.predict(sm.add_constant(X_test))\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/parth/opt/anaconda3/envs/env/lib/python3.6/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 12\n",
    "from scipy import stats\n",
    "sns.distplot(model.resid, fit=stats.norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb460088160>"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 13\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.set_xlabel(\"Y_Test\")\n",
    "ax.set_ylabel(\"Predicted value\")\n",
    "ax.set_title(\"Actual Values vs Predicted Values\")\n",
    "plt.scatter(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I will repeat the process 1/4 Standard Deviation from the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 0\n",
    "x = df.loc[:, ~df.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y = df.loc[:, df.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9997.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>74.139024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>58.848546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>55.170160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>61.293182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>70.379020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  9997.000000\n",
       "mean     74.139024\n",
       "std      58.848546\n",
       "min       0.000000\n",
       "25%      55.170160\n",
       "50%      61.293182\n",
       "75%      70.379020\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dispersion    88.851161\n",
      "dtype: float64\n",
      "dispersion    59.426887\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(y.mean() + ((y.std())/4))\n",
    "print(y.mean() - ((y.std())/4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1\n",
    "y_3sd = y.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4730.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>68.141830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>6.953320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>59.427097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>62.490395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>66.330933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>72.108397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>88.835266</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  4730.000000\n",
       "mean     68.141830\n",
       "std       6.953320\n",
       "min      59.427097\n",
       "25%      62.490395\n",
       "50%      66.330933\n",
       "75%      72.108397\n",
       "max      88.835266"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_3sd = y_3sd[y_3sd['dispersion'].between(59.426887, 88.851161)]\n",
    "y_3sd.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 2\n",
    "df_3sd = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 3\n",
    "df_3sd = df_3sd[df_3sd['dispersion'].between(59.426887, 88.851161)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4730, 12)"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 4\n",
    "df_3sd.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 5\n",
    "x_3sd = df_3sd.loc[:, ~df_3sd.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y_3sd = df_3sd.loc[:, df_3sd.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 6\n",
    "x3sd_log = x_3sd.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 7\n",
    "x3sd_log = x3sd_log.transform(lambda a: np.log(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4730, 11)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 8\n",
    "x3sd_log.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 9\n",
    "X=x3sd_log\n",
    "y=y_3sd\n",
    "\n",
    "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(X, y, test_size = 0.20, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3784, 11), (946, 1))"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 10\n",
    "X_train.shape, y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Model for values lying within 1/4 Stand Dev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             dispersion   R-squared:                       0.300\n",
      "Model:                            OLS   Adj. R-squared:                  0.298\n",
      "Method:                 Least Squares   F-statistic:                     146.9\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):          4.71e-282\n",
      "Time:                        17:01:39   Log-Likelihood:                -12054.\n",
      "No. Observations:                3784   AIC:                         2.413e+04\n",
      "Df Residuals:                    3772   BIC:                         2.421e+04\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const             -2.341e+04   3.42e+04     -0.684      0.494   -9.06e+04    4.37e+04\n",
      "mass                 10.0359      0.698     14.385      0.000       8.668      11.404\n",
      "kinetic_energy        1.0627      0.104     10.213      0.000       0.859       1.267\n",
      "mean_radius          -3.5153      0.663     -5.300      0.000      -4.816      -2.215\n",
      "Group_M_Crit200   -2945.6701   1305.223     -2.257      0.024   -5504.681    -386.659\n",
      "Group_M_Crit500   -1465.6434   1498.314     -0.978      0.328   -4403.227    1471.940\n",
      "Group_M_Mean200    -101.8416   1853.439     -0.055      0.956   -3735.680    3531.997\n",
      "Group_M_TopHat200  2065.7820   1477.080      1.399      0.162    -830.171    4961.735\n",
      "Group_R_Crit200    8849.1451   3915.761      2.260      0.024    1171.932    1.65e+04\n",
      "Group_R_Crit500    4384.2804   4494.997      0.975      0.329   -4428.579    1.32e+04\n",
      "Group_R_Mean200     313.9152   5560.318      0.056      0.955   -1.06e+04    1.12e+04\n",
      "Group_R_TopHat200 -6203.8286   4431.127     -1.400      0.162   -1.49e+04    2483.809\n",
      "==============================================================================\n",
      "Omnibus:                      833.017   Durbin-Watson:                   2.065\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1745.278\n",
      "Skew:                           1.282   Prob(JB):                         0.00\n",
      "Kurtosis:                       5.121   Cond. No.                     7.63e+06\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 7.63e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#Step 11\n",
    "#Model statistics\n",
    "#Must add constant for y-intercept\n",
    "model = sm.OLS(y_train, sm.add_constant(X_train)).fit()\n",
    "y_pred = model.predict(sm.add_constant(X_test))\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/parth/opt/anaconda3/envs/env/lib/python3.6/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 12\n",
    "from scipy import stats\n",
    "sns.distplot(model.resid, fit=stats.norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb4bc8f2a58>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 13\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.set_xlabel(\"Y_Test\")\n",
    "ax.set_ylabel(\"Predicted value\")\n",
    "ax.set_title(\"Actual Values vs Predicted Values\")\n",
    "plt.scatter(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now taking elements not present between 1/4 standard deviation of the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 0\n",
    "x = df.loc[:, ~df.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y = df.loc[:, df.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1\n",
    "y_4sd = y.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5267.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>79.524770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>80.430531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>52.068373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>55.477978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>58.612896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1039.325700</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        dispersion\n",
       "count  5267.000000\n",
       "mean     79.524770\n",
       "std      80.430531\n",
       "min       0.000000\n",
       "25%      52.068373\n",
       "50%      55.477978\n",
       "75%      58.612896\n",
       "max    1039.325700"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_4sd = y_4sd[~y_4sd['dispersion'].between(59.426887, 88.851161)]\n",
    "y_4sd.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 2\n",
    "df_4sd = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 4\n",
    "df_4sd = df_4sd[~df_4sd['dispersion'].between(59.426887, 88.851161)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5267, 12)"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 4\n",
    "df_4sd.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 5\n",
    "x_4sd = df_4sd.loc[:, ~df_4sd.columns.isin(['dispersion'])] #Creating dependent variables dataframe\n",
    "y_4sd = df_4sd.loc[:, df_4sd.columns.isin(['dispersion'])]  #Creating predictor variable dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 6\n",
    "x4sd_log = x_4sd.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 7\n",
    "x4sd_log = x4sd_log.transform(lambda a: np.log(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5267, 11)"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 8\n",
    "x4sd_log.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 9\n",
    "X=x4sd_log\n",
    "y=y_4sd\n",
    "\n",
    "X_train, X_test, y_train, y_test = sklearn.model_selection.train_test_split(X, y, test_size = 0.20, random_state = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4213, 11), (1054, 1))"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Step 10\n",
    "X_train.shape, y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Model for values lying beyond 1/4 Stand Dev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             dispersion   R-squared:                       0.347\n",
      "Model:                            OLS   Adj. R-squared:                  0.345\n",
      "Method:                 Least Squares   F-statistic:                     202.7\n",
      "Date:                Thu, 30 Jun 2022   Prob (F-statistic):               0.00\n",
      "Time:                        17:07:11   Log-Likelihood:                -23448.\n",
      "No. Observations:                4213   AIC:                         4.692e+04\n",
      "Df Residuals:                    4201   BIC:                         4.700e+04\n",
      "Df Model:                          11                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "const             -4.533e+05   3.53e+05     -1.284      0.199   -1.15e+06    2.39e+05\n",
      "mass                 43.9889      5.391      8.160      0.000      33.420      54.558\n",
      "kinetic_energy       25.3844      0.978     25.957      0.000      23.467      27.302\n",
      "mean_radius         141.3337      5.237     26.987      0.000     131.066     151.601\n",
      "Group_M_Crit200   -6191.4109   1.33e+04     -0.467      0.641   -3.22e+04    1.98e+04\n",
      "Group_M_Crit500   -3000.5590   1.56e+04     -0.192      0.848   -3.36e+04    2.76e+04\n",
      "Group_M_Mean200   -2.489e+04   1.91e+04     -1.300      0.194   -6.24e+04    1.27e+04\n",
      "Group_M_TopHat200 -5199.4808   1.51e+04     -0.344      0.731   -3.48e+04    2.44e+04\n",
      "Group_R_Crit200    1.858e+04   3.98e+04      0.467      0.641   -5.95e+04    9.66e+04\n",
      "Group_R_Crit500    8982.3079   4.69e+04      0.192      0.848   -8.29e+04    1.01e+05\n",
      "Group_R_Mean200    7.454e+04   5.74e+04      1.298      0.194   -3.81e+04    1.87e+05\n",
      "Group_R_TopHat200   1.57e+04   4.53e+04      0.347      0.729   -7.31e+04    1.04e+05\n",
      "==============================================================================\n",
      "Omnibus:                     3520.154   Durbin-Watson:                   1.994\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           139087.515\n",
      "Skew:                           3.767   Prob(JB):                         0.00\n",
      "Kurtosis:                      30.122   Cond. No.                     7.32e+06\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 7.32e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "#Step 11\n",
    "#Model statistics\n",
    "#Must add constant for y-intercept\n",
    "model = sm.OLS(y_train, sm.add_constant(X_train)).fit()\n",
    "y_pred = model.predict(sm.add_constant(X_test))\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/parth/opt/anaconda3/envs/env/lib/python3.6/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 12\n",
    "from scipy import stats\n",
    "sns.distplot(model.resid, fit=stats.norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fb4bcc0cf60>"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Step 13\n",
    "fig = plt.figure(figsize=(15,5))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.set_xlabel(\"Y_Test\")\n",
    "ax.set_ylabel(\"Predicted value\")\n",
    "ax.set_title(\"Actual Values vs Predicted Values\")\n",
    "plt.scatter(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6.13",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.13"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "d5acf0f622c40394d21d2c0770201564bbbf7e98418870ee73c827488765a9be"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}