{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a200c150-c137-4519-8069-261814c4fad8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib.pyplot import subplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d0944276-c72e-4c95-a85e-77cab3ee9322",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>family</th>\n",
       "      <th>father</th>\n",
       "      <th>mother</th>\n",
       "      <th>midparentHeight</th>\n",
       "      <th>children</th>\n",
       "      <th>childNum</th>\n",
       "      <th>sex</th>\n",
       "      <th>childHeight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>73.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>female</td>\n",
       "      <td>69.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>female</td>\n",
       "      <td>69.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  family  father  mother  midparentHeight  children  childNum     sex  \\\n",
       "0      1    78.5    67.0            75.43         4         1    male   \n",
       "1      1    78.5    67.0            75.43         4         2  female   \n",
       "2      1    78.5    67.0            75.43         4         3  female   \n",
       "\n",
       "   childHeight  \n",
       "0         73.2  \n",
       "1         69.2  \n",
       "2         69.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('family_heights.csv')\n",
    "data.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "aa65c161-d953-4395-80eb-3a1c912e393e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.6373609 , 22.63624055])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefficients = np.polyfit(data['midparentHeight'], data['childHeight'], 1)\n",
    "coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "661ab22b-70b0-47b2-ba95-fac314b23d95",
   "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>family</th>\n",
       "      <th>father</th>\n",
       "      <th>mother</th>\n",
       "      <th>midparentHeight</th>\n",
       "      <th>children</th>\n",
       "      <th>childNum</th>\n",
       "      <th>sex</th>\n",
       "      <th>childHeight</th>\n",
       "      <th>regressionEstimate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>73.2</td>\n",
       "      <td>70.712373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>female</td>\n",
       "      <td>69.2</td>\n",
       "      <td>70.712373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>female</td>\n",
       "      <td>69.0</td>\n",
       "      <td>70.712373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>female</td>\n",
       "      <td>69.0</td>\n",
       "      <td>70.712373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>75.5</td>\n",
       "      <td>66.5</td>\n",
       "      <td>73.66</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>73.5</td>\n",
       "      <td>69.584244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>75.5</td>\n",
       "      <td>66.5</td>\n",
       "      <td>73.66</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>male</td>\n",
       "      <td>72.5</td>\n",
       "      <td>69.584244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2</td>\n",
       "      <td>75.5</td>\n",
       "      <td>66.5</td>\n",
       "      <td>73.66</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>female</td>\n",
       "      <td>65.5</td>\n",
       "      <td>69.584244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>75.5</td>\n",
       "      <td>66.5</td>\n",
       "      <td>73.66</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>female</td>\n",
       "      <td>65.5</td>\n",
       "      <td>69.584244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3</td>\n",
       "      <td>75.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>72.06</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>71.0</td>\n",
       "      <td>68.564467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3</td>\n",
       "      <td>75.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>72.06</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>female</td>\n",
       "      <td>68.0</td>\n",
       "      <td>68.564467</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  family  father  mother  midparentHeight  children  childNum     sex  \\\n",
       "0      1    78.5    67.0            75.43         4         1    male   \n",
       "1      1    78.5    67.0            75.43         4         2  female   \n",
       "2      1    78.5    67.0            75.43         4         3  female   \n",
       "3      1    78.5    67.0            75.43         4         4  female   \n",
       "4      2    75.5    66.5            73.66         4         1    male   \n",
       "5      2    75.5    66.5            73.66         4         2    male   \n",
       "6      2    75.5    66.5            73.66         4         3  female   \n",
       "7      2    75.5    66.5            73.66         4         4  female   \n",
       "8      3    75.0    64.0            72.06         2         1    male   \n",
       "9      3    75.0    64.0            72.06         2         2  female   \n",
       "\n",
       "   childHeight  regressionEstimate  \n",
       "0         73.2           70.712373  \n",
       "1         69.2           70.712373  \n",
       "2         69.0           70.712373  \n",
       "3         69.0           70.712373  \n",
       "4         73.5           69.584244  \n",
       "5         72.5           69.584244  \n",
       "6         65.5           69.584244  \n",
       "7         65.5           69.584244  \n",
       "8         71.0           68.564467  \n",
       "9         68.0           68.564467  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1 = data.assign(regressionEstimate = coefficients[0]*data['midparentHeight'] + coefficients[1])\n",
    "data1.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e93481ab-1f55-4107-89ea-537a922629d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>family</th>\n",
       "      <th>father</th>\n",
       "      <th>mother</th>\n",
       "      <th>midparentHeight</th>\n",
       "      <th>children</th>\n",
       "      <th>childNum</th>\n",
       "      <th>sex</th>\n",
       "      <th>childHeight</th>\n",
       "      <th>regressionEstimate</th>\n",
       "      <th>residuals</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>73.2</td>\n",
       "      <td>70.712373</td>\n",
       "      <td>2.487627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>female</td>\n",
       "      <td>69.2</td>\n",
       "      <td>70.712373</td>\n",
       "      <td>-1.512373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>female</td>\n",
       "      <td>69.0</td>\n",
       "      <td>70.712373</td>\n",
       "      <td>-1.712373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>78.5</td>\n",
       "      <td>67.0</td>\n",
       "      <td>75.43</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>female</td>\n",
       "      <td>69.0</td>\n",
       "      <td>70.712373</td>\n",
       "      <td>-1.712373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>75.5</td>\n",
       "      <td>66.5</td>\n",
       "      <td>73.66</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>73.5</td>\n",
       "      <td>69.584244</td>\n",
       "      <td>3.915756</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  family  father  mother  midparentHeight  children  childNum     sex  \\\n",
       "0      1    78.5    67.0            75.43         4         1    male   \n",
       "1      1    78.5    67.0            75.43         4         2  female   \n",
       "2      1    78.5    67.0            75.43         4         3  female   \n",
       "3      1    78.5    67.0            75.43         4         4  female   \n",
       "4      2    75.5    66.5            73.66         4         1    male   \n",
       "\n",
       "   childHeight  regressionEstimate  residuals  \n",
       "0         73.2           70.712373   2.487627  \n",
       "1         69.2           70.712373  -1.512373  \n",
       "2         69.0           70.712373  -1.712373  \n",
       "3         69.0           70.712373  -1.712373  \n",
       "4         73.5           69.584244   3.915756  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = data1.assign(residuals = data1['childHeight'] - data1['regressionEstimate'])\n",
    "data2.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "74f95794-e9b8-476d-9c6c-123545de1e84",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = subplots(figsize = (5, 5))\n",
    "ax.scatter(data2['midparentHeight'], data2['residuals'])\n",
    "ax.axhline(y=0, color='red', linewidth = 3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a81c96b8-4537-4a5f-8cf9-fe8ef84b8bc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of the residuals =  -7.323002542212767e-14\n"
     ]
    }
   ],
   "source": [
    "# We showed in class that the mean of the residuals equals 0. \n",
    "# Let us check this for the heights data\n",
    "print('Mean of the residuals = ', data2['residuals'].mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80c6bff5-a36f-4f84-a4f4-433dee8d20c6",
   "metadata": {},
   "source": [
    "Due to precision errors, the value does not come out to be exactly 0, but it is really close!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "63f67ea4-1f4f-4009-9cf8-4b0df0f03354",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation of midparentHeights and residuals =  -1.3549018592547941e-15\n"
     ]
    }
   ],
   "source": [
    "# We showed in class that the correlation between the predictor and the residuals is 0\n",
    "# Let us check for the heights data\n",
    "print('Correlation of midparentHeights and residuals = ', data2['midparentHeight'].corr(data2['residuals']))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c56c4931-7d0c-4405-bdf5-dc8815e3a4d1",
   "metadata": {},
   "source": [
    "Again, due to precision errors, the value does not come out to be exactly 0, but it is really close!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b8cfec3-4aba-4e7f-ad79-e34e6f12be7a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}