HW/HW2/HW2-Linear_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f98ff6dc",
   "metadata": {},
   "source": [
    "In this homework, we will use the California Housing Prices from [Kaggle](https://www.kaggle.com/datasets/camnugent/california-housing-prices).\n",
    "\n",
    "The goal of this homework is to create a regression model for predicting housing prices (column `'median_house_value'`).\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9b03c37d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import wget\n",
    "\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8b70248b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100% [..........................................................................] 1423529 / 1423529"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'housing (2).csv'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wget.download(\"https://raw.githubusercontent.com/alexeygrigorev/datasets/master/housing.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a7d3fa8",
   "metadata": {},
   "source": [
    "### EDA\n",
    "\n",
    "* Load the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a6871308",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "      <th>housing_median_age</th>\n",
       "      <th>total_rooms</th>\n",
       "      <th>total_bedrooms</th>\n",
       "      <th>population</th>\n",
       "      <th>households</th>\n",
       "      <th>median_income</th>\n",
       "      <th>median_house_value</th>\n",
       "      <th>ocean_proximity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-122.23</td>\n",
       "      <td>37.88</td>\n",
       "      <td>41.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>129.0</td>\n",
       "      <td>322.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>8.3252</td>\n",
       "      <td>452600.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-122.22</td>\n",
       "      <td>37.86</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7099.0</td>\n",
       "      <td>1106.0</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>1138.0</td>\n",
       "      <td>8.3014</td>\n",
       "      <td>358500.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-122.24</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1467.0</td>\n",
       "      <td>190.0</td>\n",
       "      <td>496.0</td>\n",
       "      <td>177.0</td>\n",
       "      <td>7.2574</td>\n",
       "      <td>352100.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-122.25</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1274.0</td>\n",
       "      <td>235.0</td>\n",
       "      <td>558.0</td>\n",
       "      <td>219.0</td>\n",
       "      <td>5.6431</td>\n",
       "      <td>341300.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-122.25</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1627.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>565.0</td>\n",
       "      <td>259.0</td>\n",
       "      <td>3.8462</td>\n",
       "      <td>342200.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
       "0    -122.23     37.88                41.0        880.0           129.0   \n",
       "1    -122.22     37.86                21.0       7099.0          1106.0   \n",
       "2    -122.24     37.85                52.0       1467.0           190.0   \n",
       "3    -122.25     37.85                52.0       1274.0           235.0   \n",
       "4    -122.25     37.85                52.0       1627.0           280.0   \n",
       "\n",
       "   population  households  median_income  median_house_value ocean_proximity  \n",
       "0       322.0       126.0         8.3252            452600.0        NEAR BAY  \n",
       "1      2401.0      1138.0         8.3014            358500.0        NEAR BAY  \n",
       "2       496.0       177.0         7.2574            352100.0        NEAR BAY  \n",
       "3       558.0       219.0         5.6431            341300.0        NEAR BAY  \n",
       "4       565.0       259.0         3.8462            342200.0        NEAR BAY  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df= pd.read_csv(\"housing.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "489596cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "      <th>housing_median_age</th>\n",
       "      <th>total_rooms</th>\n",
       "      <th>total_bedrooms</th>\n",
       "      <th>population</th>\n",
       "      <th>households</th>\n",
       "      <th>median_income</th>\n",
       "      <th>median_house_value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20433.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-119.569704</td>\n",
       "      <td>35.631861</td>\n",
       "      <td>28.639486</td>\n",
       "      <td>2635.763081</td>\n",
       "      <td>537.870553</td>\n",
       "      <td>1425.476744</td>\n",
       "      <td>499.539680</td>\n",
       "      <td>3.870671</td>\n",
       "      <td>206855.816909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.003532</td>\n",
       "      <td>2.135952</td>\n",
       "      <td>12.585558</td>\n",
       "      <td>2181.615252</td>\n",
       "      <td>421.385070</td>\n",
       "      <td>1132.462122</td>\n",
       "      <td>382.329753</td>\n",
       "      <td>1.899822</td>\n",
       "      <td>115395.615874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-124.350000</td>\n",
       "      <td>32.540000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.499900</td>\n",
       "      <td>14999.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-121.800000</td>\n",
       "      <td>33.930000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>1447.750000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>787.000000</td>\n",
       "      <td>280.000000</td>\n",
       "      <td>2.563400</td>\n",
       "      <td>119600.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-118.490000</td>\n",
       "      <td>34.260000</td>\n",
       "      <td>29.000000</td>\n",
       "      <td>2127.000000</td>\n",
       "      <td>435.000000</td>\n",
       "      <td>1166.000000</td>\n",
       "      <td>409.000000</td>\n",
       "      <td>3.534800</td>\n",
       "      <td>179700.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-118.010000</td>\n",
       "      <td>37.710000</td>\n",
       "      <td>37.000000</td>\n",
       "      <td>3148.000000</td>\n",
       "      <td>647.000000</td>\n",
       "      <td>1725.000000</td>\n",
       "      <td>605.000000</td>\n",
       "      <td>4.743250</td>\n",
       "      <td>264725.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>-114.310000</td>\n",
       "      <td>41.950000</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>39320.000000</td>\n",
       "      <td>6445.000000</td>\n",
       "      <td>35682.000000</td>\n",
       "      <td>6082.000000</td>\n",
       "      <td>15.000100</td>\n",
       "      <td>500001.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          longitude      latitude  housing_median_age   total_rooms  \\\n",
       "count  20640.000000  20640.000000        20640.000000  20640.000000   \n",
       "mean    -119.569704     35.631861           28.639486   2635.763081   \n",
       "std        2.003532      2.135952           12.585558   2181.615252   \n",
       "min     -124.350000     32.540000            1.000000      2.000000   \n",
       "25%     -121.800000     33.930000           18.000000   1447.750000   \n",
       "50%     -118.490000     34.260000           29.000000   2127.000000   \n",
       "75%     -118.010000     37.710000           37.000000   3148.000000   \n",
       "max     -114.310000     41.950000           52.000000  39320.000000   \n",
       "\n",
       "       total_bedrooms    population    households  median_income  \\\n",
       "count    20433.000000  20640.000000  20640.000000   20640.000000   \n",
       "mean       537.870553   1425.476744    499.539680       3.870671   \n",
       "std        421.385070   1132.462122    382.329753       1.899822   \n",
       "min          1.000000      3.000000      1.000000       0.499900   \n",
       "25%        296.000000    787.000000    280.000000       2.563400   \n",
       "50%        435.000000   1166.000000    409.000000       3.534800   \n",
       "75%        647.000000   1725.000000    605.000000       4.743250   \n",
       "max       6445.000000  35682.000000   6082.000000      15.000100   \n",
       "\n",
       "       median_house_value  \n",
       "count        20640.000000  \n",
       "mean        206855.816909  \n",
       "std         115395.615874  \n",
       "min          14999.000000  \n",
       "25%         119600.000000  \n",
       "50%         179700.000000  \n",
       "75%         264725.000000  \n",
       "max         500001.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1742156b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 20640 entries, 0 to 20639\n",
      "Data columns (total 10 columns):\n",
      " #   Column              Non-Null Count  Dtype  \n",
      "---  ------              --------------  -----  \n",
      " 0   longitude           20640 non-null  float64\n",
      " 1   latitude            20640 non-null  float64\n",
      " 2   housing_median_age  20640 non-null  float64\n",
      " 3   total_rooms         20640 non-null  float64\n",
      " 4   total_bedrooms      20433 non-null  float64\n",
      " 5   population          20640 non-null  float64\n",
      " 6   households          20640 non-null  float64\n",
      " 7   median_income       20640 non-null  float64\n",
      " 8   median_house_value  20640 non-null  float64\n",
      " 9   ocean_proximity     20640 non-null  object \n",
      "dtypes: float64(9), object(1)\n",
      "memory usage: 1.6+ MB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86e56ed6",
   "metadata": {},
   "source": [
    "* Look at the `median_house_value` variable. Does it have a long tail? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ac7d87d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HMDY21ju3hISEAr+XIUOGYNmyZfjoo49w4MABnDp1ClFRUbCysirUz2tepkyZgtmzZ+P999/HL7/8gj/++ANRUVFo3rz5Gx23IuHVQAQA+OGHH7B37168++67WLZsGT744AO0bdtW2h4aGgojIyPs2bNH9o/mzp07y6C1JcPS0hKnTp3SK09ISCiD1ry+GjVqwNTUVG/R8cvbgRfnmZmZiaSkJNk/KIU5z9jYWPz5558ICQnB8OHDpfIrV668YeuLztLSEvHx8Xrld+/eBfB/553zc/vqourc/gGrU6cO1qxZAwD4+++/sXXrVvj5+SE9PR0rV66Ujvnzzz9Lo0pFkVufJyQkoH79+rKywt53yMrKCsePH0d2dnaegaVGjRpQqVQ4duyYFBxf9nKZs7MzQkNDIYTAuXPnEBISgvnz58PU1BQzZswoVJvys3HjRjg4OOCnn36SneOr3xEAeHh4wMbGBmvXroWHhwfWrl2Ltm3byq6IqlGjBiwtLaX1I6/K77YBKSkp2LNnD+bOnSs7t5x1NW9i48aN+PDDD+Hv7y8rf/DgAapVq/ZGx64oOLJCOH/+PCZOnIgPP/wQx44dQ7NmzfDBBx8gOTlZqqNSqWBoaCibGkpNTcWGDRvKosklwtXVFY8fP8a+fftk5aGhoWXUotfj6emJq1evwtLSUm80rU2bNrC3twcAdO7cGQCwadMm2f6bN28u8DNy/kF59R+577//vhjOoGjc3d1x8eJFnD59Wla+fv16qFQq6Xxzzv/cuXOyert37873+A0aNMDnn38OZ2dn6TM8PDxgaGiIq1ev5trXhb1dwKvfQWRkJG7evFnk+3T07NkTz58/z/dqEk9PTwghcOfOnVzb7ezsrLePSqVC8+bNsWTJElSrVk2vr4tKpVJJN0vMkZCQoHc1EAAYGBhg2LBh2LlzJ44dO4bo6Gi96S5PT08kJSUhKysr13Nr2LBhvm0RQuj9bP/www+yixLykt+IoUql0jvu3r17cefOnQKPSy9wZOUtFxsbi8zMTL3yevXqwcrKCk+fPsXAgQPh4OCA4OBgGBsbY+vWrWjVqhVGjhwpjZz07t0bixcvxpAhQ/Cf//wHSUlJ+Oabb3L9zay8Gj58OJYsWYKhQ4fiyy+/RP369bFv3z4cOHAAAPIdWlcCHx8fbNu2DZ06dcLkyZPRrFkzZGdn49atWwgLC8PUqVPRtm1bdO/eHZ06dYKvry+ePn2KNm3a4Pfffy9U8GzUqBHq1auHGTNmQAgBCwsL/PLLL7JL3Evb5MmTsX79evTu3Rvz589HnTp1sHfvXgQHB+Pjjz9GgwYNALyYXunatSsCAgJQvXp11KlTB7/99pvsiirgRZgZP348BgwYAEdHRxgbG+PQoUM4d+6c9Bu3vb095s+fj1mzZuHatWvo0aMHqlevjnv37uHUqVMwMzOTbhCWn+joaHz00UcYMGAA4uLiMGvWLNja2uZ5tU9BBg8ejLVr12Ls2LG4dOkSOnfujOzsbPzxxx9o3LgxBg0ahA4dOuA///kPRo4ciejoaHTq1AlmZmaIj4/H8ePH4ezsjI8//hh79uxBcHAw3n//fdStWxdCCGzfvh0PHz6UXSX4Jjw9PbF9+3aMGzcO//73vxEXF4cvvvgC1tbWelf+AC+mghYuXIghQ4bA1NRU70q9QYMGYdOmTejVqxcmTZqEd999F0ZGRrh9+zYOHz6Mfv364V//+leubalatSo6deqEr7/+GjVq1IC9vT0iIiKwZs2aQo1+mJubo06dOti1axfc3d1hYWEhHcfT0xMhISFo1KgRmjVrhpiYGHz99ddFvp9UREQE3N3dMWfOnAqzboVh5S2Xc0nfq1avXo2PPvoIY8eOxa1btxAVFQUzMzMAQN26dfHDDz9gwIABCAoKgo+PD7p06YIff/wRCxcuRJ8+fWBra4vRo0ejZs2a8Pb2Ls1TKjFmZmY4dOgQfHx84OvrC5VKhe7duyM4OBi9evVS/HCtmZkZjh07hgULFmDVqlW4fv06TE1NUbt2bXTt2lUaWahUqRJ2796NKVOmIDAwEOnp6ejQoQN+/fXXXO92/DIjIyP88ssvmDRpEsaMGQNDQ0N07doVBw8elC1+Lk1WVlaIjIzEzJkzMXPmTDx69Ah169ZFYGAgpkyZIqu7YcMGTJgwAdOnT0dWVhb69OmDLVu2yEZCdDod6tWrh+DgYMTFxUGlUqFu3bpYtGgRJkyYINWbOXMmmjRpgm+//VZaP6HT6fDOO+9g7NixhWr7mjVrsGHDBgwaNAhpaWno3Lkzvv32W711S4VlaGiIX3/9FQEBAdiyZQuCgoJgbm6O5s2byxaOf//992jXrh2+//57BAcHIzs7GzY2NujQoYO0KNbR0RHVqlVDYGAg7t69C2NjYzRs2FBvCvBNjBw5EomJiVi5ciV+/PFH1K1bFzNmzMDt27dzDXsNGjSAi4sLIiMj4eXlBY1GI9tuYGCA3bt349tvv8WGDRsQEBAAQ0ND1KpVC66urrmOGr1s8+bNmDRpEnx9fZGZmYkOHTogPDwcvXv3LtT5rFmzBp9++in69u2LtLQ0DB8+HCEhIfj2229hZGSEgIAAPHnyBK1atcL27dulWxu8LiEEsrKy9BZ+v81UQrxyRy8ikvH398fnn3+OW7duFfk3IaKXhYSEYOTIkYiKiip3d5gmKgscWSF6Sc6dfBs1aoSMjAwcOnQI3333HYYOHcqgQkRURhhWiF5SuXJlLFmyBDdu3EBaWhpq166N6dOnF3m4loiI3hyngYiIiEjRlH15AxEREVV4DCtERESkaAwrREREpGhcYFtI2dnZuHv3LszNzQt962siIiJ6cW+Yx48fF/jsqrwwrBTS3bt3YWdnV9bNICIiKrfi4uKKdBsIhpVCynkAVlxcHKpWrVrGrSEiIio/Hj16BDs7u3wfJpkfhpVCypn6qVq1KsMKERFRERR1GQUX2BIREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRovHZQERERBVIm3YuiE9IzLeOta4mok9GllKLCsawQkREVIHEJySi42cb8q1zzH9YKbWmcDgNRERERIrGsEJERESKxrBCREREilamYeXo0aPo06cPbGxsoFKpsHPnTtl2IQT8/PxgY2MDU1NTuLm54cKFC7I6aWlpmDBhAmrUqAEzMzP07dsXt2/fltVJTk7GsGHDoNFooNFoMGzYMDx8+LCEz46IiIiKQ5mGladPn6J58+ZYtmxZrtsDAwOxePFiLFu2DFFRUdDpdOjWrRseP34s1fHx8cGOHTsQGhqK48eP48mTJ/D09ERWVpZUZ8iQITh79iz279+P/fv34+zZsxg2TFmLh4iIiCh3ZXo1UM+ePdGzZ89ctwkhEBQUhFmzZqF///4AgHXr1kGr1WLz5s0YM2YMUlJSsGbNGmzYsAFdu3YFAGzcuBF2dnY4ePAgPDw88Ndff2H//v04efIk2rZtCwBYvXo12rdvj0uXLqFhw4alc7JERERUJIpds3L9+nUkJCSge/fuUplarYarqysiI19c+x0TE4OMjAxZHRsbGzg5OUl1Tpw4AY1GIwUVAGjXrh00Go1UJzdpaWl49OiR7EVERESlT7FhJSEhAQCg1Wpl5VqtVtqWkJAAY2NjVK9ePd86NWvW1Dt+zZo1pTq5CQgIkNa4aDQa2NnZvdH5EBERUdEoNqzkUKlUsvdCCL2yV71aJ7f6BR1n5syZSElJkV5xcXGv2XIiIiIqDooNKzqdDgD0Rj8SExOl0RadTof09HQkJyfnW+fevXt6x79//77eqM3L1Go1qlatKnsRERFR6VNsWHFwcIBOp0N4eLhUlp6ejoiICLi4uAAAWrduDSMjI1md+Ph4xMbGSnXat2+PlJQUnDp1Sqrzxx9/ICUlRapDREREylWmVwM9efIEV65ckd5fv34dZ8+ehYWFBWrXrg0fHx/4+/vD0dERjo6O8Pf3R+XKlTFkyBAAgEajgbe3N6ZOnQpLS0tYWFhg2rRpcHZ2lq4Oaty4MXr06IHRo0fj+++/BwD85z//gaenJ68EIiIiKgfKNKxER0ejc+fO0vspU6YAAIYPH46QkBD4+voiNTUV48aNQ3JyMtq2bYuwsDCYm5tL+yxZsgSGhoYYOHAgUlNT4e7ujpCQEBgYGEh1Nm3ahIkTJ0pXDfXt2zfPe7sQERGRsqiEEKKsG1EePHr0CBqNBikpKVy/QkRE5Zatff1CPXX5zo0r+dZ5HW/6b6hi16wQERERAQwrREREpHAMK0RERKRoDCtERESkaGV6NRBRRdamnQviExLz3G6tq4nok3k/v4qIqKJgWCEqI/EJifmuyD/mP6wUW0NEpFycBiIiIiJFY1ghIiIiRWNYISIiIkVjWCEiIiJFY1ghIiIiRWNYISIiIkVjWCEiIiJFY1ghIiIiRWNYISIiIkXjHWyJSkBBt9IHgAdJSaXUGiKi8o1hhagEFHQrfQDY5uNRSq0hIirfOA1EREREisawQkRERIrGsEJERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisbb7ZOiFPRMHWtdTUSfjCzFFhERUVljWCFFKeiZOsf8h5Via4iISAk4DURERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisZnAxG9oqCHKQJ8oCIRUWliWCF6RUEPUwT4QEUiotLEaSAiIiJSNIYVIiIiUjSGFSIiIlI0rlkhKscKWgzMhcBE9DZQdFjJzMyEn58fNm3ahISEBFhbW2PEiBH4/PPPUanSi0EhIQTmzZuHVatWITk5GW3btsXy5cvRtGlT6ThpaWmYNm0atmzZgtTUVLi7uyM4OBi1atUqq1OjElJaV/I8eHAftvb1896elPRGxy+sghYDcyEwEb0NFB1WFi5ciJUrV2LdunVo2rQpoqOjMXLkSGg0GkyaNAkAEBgYiMWLFyMkJAQNGjTAl19+iW7duuHSpUswNzcHAPj4+OCXX35BaGgoLC0tMXXqVHh6eiImJgYGBgZleYpUzErrSp7sbJHv52zz8XjjzyAiohcUHVZOnDiBfv36oXfv3gAAe3t7bNmyBdHR0QBejKoEBQVh1qxZ6N+/PwBg3bp10Gq12Lx5M8aMGYOUlBSsWbMGGzZsQNeuXQEAGzduhJ2dHQ4ePAgPD/6jQkREpGSKXmD73nvv4bfffsPff/8NAPjzzz9x/Phx9OrVCwBw/fp1JCQkoHv37tI+arUarq6uiIx8McwfExODjIwMWR0bGxs4OTlJdXKTlpaGR48eyV70Ztq0c4Gtff18X6U1fUJEROWHokdWpk+fjpSUFDRq1AgGBgbIysrCV199hcGDBwMAEhISAABarVa2n1arxc2bN6U6xsbGqF69ul6dnP1zExAQgHnz5hXn6VR4hZmi4fQJERG9StEjKz/99BM2btyIzZs34/Tp01i3bh2++eYbrFu3TlZPpVLJ3gsh9MpeVVCdmTNnIiUlRXrFxcUV/USIiIioyBQ9svLpp59ixowZGDRoEADA2dkZN2/eREBAAIYPHw6dTgcA0pVCORITE6XRFp1Oh/T0dCQnJ8tGVxITE+Hi4pLnZ6vVaqjV6pI4LSIiInoNih5ZefbsmXSJcg4DAwNkZ2cDABwcHKDT6RAeHi5tT09PR0REhBREWrduDSMjI1md+Ph4xMbG5htWiIiISBkUPbLSp08ffPXVV6hduzaaNm2KM2fOYPHixRg1ahSAF9M/Pj4+8Pf3h6OjIxwdHeHv74/KlStjyJAhAACNRgNvb29MnToVlpaWsLCwwLRp0+Ds7CxdHUSkRAXdywUovfu5EBGVJUWHlaVLl2L27NkYN24cEhMTYWNjgzFjxmDOnDlSHV9fX6SmpmLcuHHSTeHCwsKke6wAwJIlS2BoaIiBAwdKN4ULCQnhPVZI0Qq6lwvABclEVDEoOqyYm5sjKCgIQUFBedZRqVTw8/ODn59fnnVMTEywdOlSLF26tPgbSURERCVK0WtWiIiIiBhWiIiISNEYVoiIiEjRGFaIiIhI0RhWiIiISNEYVoiIiEjRGFaIiIhI0RhWiIiISNEYVoiIiEjRGFaIiIhI0RhWiIiISNEYVoiIiEjRGFaIiIhI0RhWiIiISNEYVoiIiEjRGFaIiIhI0RhWiIiISNEMy7oBRKXtwYP7sLWvn/f2pKRSbA0RERWEYYUqnOxsgY6fbchz+zYfj1JsDRERFYTTQERERKRoHFmhcoVTOEREFQ/DCpUrnMJ5PQWFOwCw1tVE9MnIUmoREdHrY1gheosVFO4A4Jj/sFJqDRFR0XDNChERESkawwoREREpGsMKERERKRrDChERESkawwoREREpGq8GokJp084F8QmJ+dbhJbBERFQSGFaoUOITEnkJLBERlQlOAxEREZGiMawQERGRonEaiIjeCNczEVFJY1ghojfC9UxEVNI4DURERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisawQkRERIrGsEJERESKxtvtE1G+Cnr2z4OkpFJsDRFVRAwrRJSvgp79s83HoxRbQ0QVkeKnge7cuYOhQ4fC0tISlStXRosWLRATEyNtF0LAz88PNjY2MDU1hZubGy5cuCA7RlpaGiZMmIAaNWrAzMwMffv2xe3bt0v7VIiIiKgIFB1WkpOT0aFDBxgZGWHfvn24ePEiFi1ahGrVqkl1AgMDsXjxYixbtgxRUVHQ6XTo1q0bHj9+LNXx8fHBjh07EBoaiuPHj+PJkyfw9PREVlZWGZwVERERvQ5FTwMtXLgQdnZ2WLt2rVRmb28v/b8QAkFBQZg1axb69+8PAFi3bh20Wi02b96MMWPGICUlBWvWrMGGDRvQtWtXAMDGjRthZ2eHgwcPwsODQ9hERERKpuiRld27d6NNmzYYMGAAatasiZYtW2L16tXS9uvXryMhIQHdu3eXytRqNVxdXREZGQkAiImJQUZGhqyOjY0NnJycpDq5SUtLw6NHj2QvIiIiKn1FCitdunTBw4cP9cofPXqELl26vGmbJNeuXcOKFSvg6OiIAwcOYOzYsZg4cSLWr18PAEhISAAAaLVa2X5arVbalpCQAGNjY1SvXj3POrkJCAiARqORXnZ2dsV2XkRERFR4RQorR44cQXp6ul758+fPcezYsTduVI7s7Gy0atUK/v7+aNmyJcaMGYPRo0djxYoVsnoqlUr2XgihV/aqgurMnDkTKSkp0isuLq7oJ0JERERF9lprVs6dOyf9/8WLF2UjE1lZWdi/fz9sbW2LrXHW1tZo0qSJrKxx48bYtm0bAECn0wF4MXpibW0t1UlMTJRGW3Q6HdLT05GcnCwbXUlMTISLi0uen61Wq6FWq4vtXIiIiKhoXiustGjRAiqVCiqVKtfpHlNTUyxdurTYGtehQwdcunRJVvb333+jTp06AAAHBwfodDqEh4ejZcuWAID09HRERERg4cKFAIDWrVvDyMgI4eHhGDhwIAAgPj4esbGxCAwMLLa2EhERUcl4rbBy/fp1CCFQt25dnDp1ClZWVtI2Y2Nj1KxZEwYGBsXWuMmTJ8PFxQX+/v4YOHAgTp06hVWrVmHVqlUAXkz/+Pj4wN/fH46OjnB0dIS/vz8qV66MIUOGAAA0Gg28vb0xdepUWFpawsLCAtOmTYOzs7N0dRAREREp12uFlZwRjezs7BJpzKveeecd7NixAzNnzsT8+fPh4OCAoKAgeHl5SXV8fX2RmpqKcePGITk5GW3btkVYWBjMzc2lOkuWLIGhoSEGDhyI1NRUuLu7IyQkpFiDFREREZWMIt9n5e+//8aRI0eQmJioF17mzJnzxg3L4enpCU9Pzzy3q1Qq+Pn5wc/PL886JiYmWLp0abFOURFR4T14cB+29vXz3G6tq4nok3nfSoCIKrYihZXVq1fj448/Ro0aNaDT6WRX1ahUqmINK0RU/mVni3yfL3TMf1gptoaIypsihZUvv/wSX331FaZPn17c7SEiIiKSKdJ9VpKTkzFgwIDibgsRERGRniKFlQEDBiAsLKy420JERESkp0jTQPXr18fs2bNx8uRJODs7w8jISLZ94sSJxdI4IiIioiKFlVWrVqFKlSqIiIhARESEbJtKpWJYISIiomJTpLBy/fr14m4HERERUa6KtGaFiIiIqLQUaWRl1KhR+W7/8ccfi9QYKt8KuvHXg6SkUmwNERG9LYoUVpKTk2XvMzIyEBsbi4cPH+b6gEOqGAq68dc2H49SbA0REb0tihRWduzYoVeWnZ2NcePGoW7dum/cKCIiIqIcRX420KsqVaqEyZMnw83NDb6+vsV1WColbdq5ID4hMc/tnMIhIqKyUmxhBQCuXr2KzMzM4jwklZL4hERO4RARkSIVKaxMmTJF9l4Igfj4eOzduxfDhw8vloYRERERAUUMK2fOnJG9r1SpEqysrLBo0aICrxQiIiIieh1FCiuHDx8u7nYQERER5eqN1qzcv38fly5dgkqlQoMGDWBlZVVc7SIiIiICUMQ72D59+hSjRo2CtbU1OnXqhI4dO8LGxgbe3t549uxZcbeRiIiIKrAihZUpU6YgIiICv/zyCx4+fIiHDx9i165diIiIwNSpU4u7jURERFSBFWkaaNu2bfj555/h5uYmlfXq1QumpqYYOHAgVqxYUVztI6IKoKBHNQCAta4mok9GllKLiEhJihRWnj17Bq1Wq1des2ZNTgMRlTNKeKZTQY9qAIBj/sNKvB1EpExFCivt27fH3LlzsX79epiYmAAAUlNTMW/ePLRv375YG0hEJYvPdCIipStSWAkKCkLPnj1Rq1YtNG/eHCqVCmfPnoVarUZYWFhxt5GIiIgqsCKFFWdnZ1y+fBkbN27Ef//7XwghMGjQIHh5ecHU1LS420hEREQVWJHCSkBAALRaLUaPHi0r//HHH3H//n1Mnz69WBpHREREVKRLl7///ns0atRIr7xp06ZYuXLlGzeKiIiIKEeRwkpCQgKsra31yq2srBAfH//GjSIiIiLKUaSwYmdnh99//12v/Pfff4eNjc0bN4qIiIgoR5HWrHz00Ufw8fFBRkYGunTpAgD47bff4OvryzvYEhERUbEqUljx9fXFP//8g3HjxiE9PR0AYGJigunTp2PmzJnF2kAiIiKq2IoUVlQqFRYuXIjZs2fjr7/+gqmpKRwdHaFWq4u7fURERFTBFSms5KhSpQreeeed4moLERERkZ43CitEROVJm3YuiE9IzHM7H5ZIpEwMK0RUYcQnJOb7HCQ+LJFImYp06TIRERFRaWFYISIiIkVjWCEiIiJFY1ghIiIiRWNYISIiIkXj1UBEVC48eHAftvb189zOy46J3l4MK0RULmRni3wvO94xpUe+YQYAHiQlFXeziKgUMKwQ0VuhoDADANt8PEqpNURUnLhmhYiIiBSNYYWIiIgUjWGFiIiIFI1hhYiIiBStXIWVgIAAqFQq+Pj4SGVCCPj5+cHGxgampqZwc3PDhQsXZPulpaVhwoQJqFGjBszMzNC3b1/cvn27lFtPRERERVFuwkpUVBRWrVqFZs2aycoDAwOxePFiLFu2DFFRUdDpdOjWrRseP34s1fHx8cGOHTsQGhqK48eP48mTJ/D09ERWVlZpnwYRERG9pnIRVp48eQIvLy+sXr0a1atXl8qFEAgKCsKsWbPQv39/ODk5Yd26dXj27Bk2b94MAEhJScGaNWuwaNEidO3aFS1btsTGjRtx/vx5HDx4sKxOiYiIiAqpXISVTz75BL1790bXrl1l5devX0dCQgK6d+8ulanVari6uiIy8sWdLGNiYpCRkSGrY2NjAycnJ6lObtLS0vDo0SPZi4iIiEqf4m8KFxoaipiYGERHR+ttS0hIAABotVpZuVarxc2bN6U6xsbGshGZnDo5++cmICAA8+bNe9PmExER0RtS9MhKXFwcJk2ahE2bNsHExCTPeiqVSvZeCKFX9qqC6sycORMpKSnSKy4u7vUaT0RERMVC0WElJiYGiYmJaN26NQwNDWFoaIiIiAh89913MDQ0lEZUXh0hSUxMlLbpdDqkp6cjOTk5zzq5UavVqFq1quxFREREpU/RYcXd3R3nz5/H2bNnpVebNm3g5eWFs2fPom7dutDpdAgPD5f2SU9PR0REBFxcXAAArVu3hpGRkaxOfHw8YmNjpTpERESkXIpes2Jubg4nJydZmZmZGSwtLaVyHx8f+Pv7w9HREY6OjvD390flypUxZMgQAIBGo4G3tzemTp0KS0tLWFhYYNq0aXB2dtZbsEtERETKo+iwUhi+vr5ITU3FuHHjkJycjLZt2yIsLAzm5uZSnSVLlsDQ0BADBw5Eamoq3N3dERISAgMDgzJsORERERVGuQsrR44ckb1XqVTw8/ODn59fnvuYmJhg6dKlWLp0ack2joiIiIqdotesEBERETGsEBERkaIxrBAREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRojGsEBERkaIxrBAREZGilbsHGRIRlZQHD+7D1r5+vnWsdTURfTKylFpERADDChGRJDtboONnG/Ktc8x/WCm1hohycBqIiIiIFI1hhYiIiBSN00BERK+hoHUtXNNCVPwYVoiIXkNB61q4poWo+HEaiIiIiBSNYYWIiIgUjWGFiIiIFI1hhYiIiBSNYYWIiIgUjWGFiIiIFI1hhYiIiBSN91khIqqA2rRzQXxCYr51eIM7UgqGFSKiCig+IZEPbaRyg9NAREREpGgMK0RERKRoDCtERESkaAwrREREpGgMK0RERKRoDCtERESkaAwrREREpGi8z0oFUJibPz1ISiql1hAREb0ehpUKoDA3f9rm41FKrSGi0lDQLyn8BYXKE4YVIqK3UEG/pPAXFCpPGFaIiMoZTu1SRcOwQkRUznBqlyoaXg1EREREisawQkRERIrGaSAiIoXhlTxEcgwrREQKwyt5iOQYVoiIShlHToheD8MKEVEp48gJ0ethWCEiKkYPHtyHrX39/Otw5ITotSg6rAQEBGD79u3473//C1NTU7i4uGDhwoVo2LChVEcIgXnz5mHVqlVITk5G27ZtsXz5cjRt2lSqk5aWhmnTpmHLli1ITU2Fu7s7goODUatWrbI4LSJ6i2VnC94DhaiYKfrS5YiICHzyySc4efIkwsPDkZmZie7du+Pp06dSncDAQCxevBjLli1DVFQUdDodunXrhsePH0t1fHx8sGPHDoSGhuL48eN48uQJPD09kZWVVRanRURERK9B0SMr+/fvl71fu3YtatasiZiYGHTq1AlCCAQFBWHWrFno378/AGDdunXQarXYvHkzxowZg5SUFKxZswYbNmxA165dAQAbN26EnZ0dDh48CA8P/oZDRESkZIoeWXlVSkoKAMDCwgIAcP36dSQkJKB79+5SHbVaDVdXV0RGRgIAYmJikJGRIatjY2MDJycnqU5u0tLS8OjRI9mLiIiISl+5CStCCEyZMgXvvfcenJycAAAJCQkAAK1WK6ur1WqlbQkJCTA2Nkb16tXzrJObgIAAaDQa6WVnZ1ecp0NERESFVG7Cyvjx43Hu3Dls2bJFb5tKpZK9F0Lolb2qoDozZ85ESkqK9IqLiytaw4mIiOiNKHrNSo4JEyZg9+7dOHr0qOwKHp1OB+DF6Im1tbVUnpiYKI226HQ6pKenIzk5WTa6kpiYCBcXlzw/U61WQ61WF/epEBGVGwVdhm2tq4nok3lPpxMVF0WHFSEEJkyYgB07duDIkSNwcHCQbXdwcIBOp0N4eDhatmwJAEhPT0dERAQWLlwIAGjdujWMjIwQHh6OgQMHAgDi4+MRGxuLwMDA0j0hIqJypKDLsI/5DyvF1lBFpuiw8sknn2Dz5s3YtWsXzM3NpTUmGo0GpqamUKlU8PHxgb+/PxwdHeHo6Ah/f39UrlwZQ4YMkep6e3tj6tSpsLS0hIWFBaZNmwZnZ2fp6iAiIiJSLkWHlRUrVgAA3NzcZOVr167FiBEjAAC+vr5ITU3FuHHjpJvChYWFwdzcXKq/ZMkSGBoaYuDAgdJN4UJCQmBgYFBap0JERERFpOiwIoQosI5KpYKfnx/8/PzyrGNiYoKlS5di6dKlxdg6IiIiKg3l5mogIiIiqpgYVoiIiEjRGFaIiIhI0RhWiIiISNEUvcCWiIiUq6CbxgG8cRwVD4YVIiIqkoJuGgfwxnFUPDgNRERERIrGkRUiIioxfL4QFQeGFSIiKjF8vhAVB04DERERkaIxrBAREZGiMawQERGRonHNChERKVqbdi6IT0jMczsX6b79GFaIiEjR4hMSuUi3guM0EBERESkawwoREREpGqeBiIiozBTm+UIPkpJKqTWkVAwrRERUZgrzfKFtPh6l1BpSKk4DERERkaIxrBAREZGicRqIiIjKtcKseymNe7HwfjAlh2GFiIjKtcKseymNe7HwfjAlh2GFiIjeegWNvnDUQ9kYVoiI6K1X0OgLRz2UjWGFiIioAAWtRwF4P5iSxLBCRERUgILWowC8H0xJ4qXLREREpGgcWSEiogqvoAW4nOIpWwwrRERU4RW0AJdTPGWL00BERESkaAwrREREpGicBiIiIioFSnksQHnEsPIWKOj6fy4MIyIqe0p5LEB5xLDyFijo+n8uDCMiovKMa1aIiIhI0TiyQkREVE4U5rb/b+O6F4YVIiIihSjMzen+tejXfI+xY0qPt+4GdwwrREREClEcN6d7G29wxzUrREREpGgMK0RERKRoDCtERESkaAwrREREpGgMK0RERKRoDCtERESkaAwrREREpGgMK0RERKRoFeqmcMHBwfj6668RHx+Ppk2bIigoCB07dizrZuWrMLdWLo93IyQiIiqsChNWfvrpJ/j4+CA4OBgdOnTA999/j549e+LixYuoXbt2mbWroDBSmFsrl8e7ERIRERVWhQkrixcvhre3Nz766CMAQFBQEA4cOIAVK1YgICCgzNoVn5D41t0WmYiIqDhViLCSnp6OmJgYzJgxQ1bevXt3REbm/mTKtLQ0pKWlSe9TUlIAAI8ePSrWtmVnZyMj9Wme24UQ+W4vTJ2KdIzy0s636RjlpZ1v0zHKSzvfpmOUl3YW1zGys7OL9d+7nGMJIYp2AFEB3LlzRwAQv//+u6z8q6++Eg0aNMh1n7lz5woAfPHFF1988cVXMb3i4uKK9O94hRhZyaFSqWTvhRB6ZTlmzpyJKVOmSO+zs7Pxzz//wNLSMtd9Hj16BDs7O8TFxaFq1arF2/AKjn1bcti3JYd9W3LYtyWrJPpXCIHHjx/DxsamSPtXiLBSo0YNGBgYICEhQVaemJgIrVab6z5qtRpqtVpWVq1atQI/q2rVqvzDU0LYtyWHfVty2Lclh31bsoq7fzUaTZH3rRD3WTE2Nkbr1q0RHh4uKw8PD4eLi0sZtYqIiIgKo0KMrADAlClTMGzYMLRp0wbt27fHqlWrcOvWLYwdO7asm0ZERET5qDBh5YMPPkBSUhLmz5+P+Ph4ODk54ddff0WdOnWK5fhqtRpz587VmzqiN8e+LTns25LDvi057NuSpcT+VQlR1OuIiIiIiEpehVizQkREROUXwwoREREpGsMKERERKRrDChERESkaw0oxCA4OhoODA0xMTNC6dWscO3asrJtUqo4ePYo+ffrAxsYGKpUKO3fulG0XQsDPzw82NjYwNTWFm5sbLly4IKuTlpaGCRMmoEaNGjAzM0Pfvn1x+/ZtWZ3k5GQMGzYMGo0GGo0Gw4YNw8OHD2V1bt26hT59+sDMzAw1atTAxIkTkZ6eLqtz/vx5uLq6wtTUFLa2tpg/f37Rn1dRwgICAvDOO+/A3NwcNWvWxPvvv49Lly7J6rB/i2bFihVo1qyZdOOr9u3bY9++fdJ29mvxCQgIgEqlgo+Pj1TG/i0aPz8/qFQq2Uun00nb39p+LdJN+kkSGhoqjIyMxOrVq8XFixfFpEmThJmZmbh582ZZN63U/Prrr2LWrFli27ZtAoDYsWOHbPuCBQuEubm52LZtmzh//rz44IMPhLW1tXj06JFUZ+zYscLW1laEh4eL06dPi86dO4vmzZuLzMxMqU6PHj2Ek5OTiIyMFJGRkcLJyUl4enpK2zMzM4WTk5Po3LmzOH36tAgPDxc2NjZi/PjxUp2UlBSh1WrFoEGDxPnz58W2bduEubm5+Oabb0qug96Ah4eHWLt2rYiNjRVnz54VvXv3FrVr1xZPnjyR6rB/i2b37t1i79694tKlS+LSpUvis88+E0ZGRiI2NlYIwX4tLqdOnRL29vaiWbNmYtKkSVI5+7do5s6dK5o2bSri4+OlV2JiorT9be1XhpU39O6774qxY8fKyho1aiRmzJhRRi0qW6+GlezsbKHT6cSCBQuksufPnwuNRiNWrlwphBDi4cOHwsjISISGhkp17ty5IypVqiT2798vhBDi4sWLAoA4efKkVOfEiRMCgPjvf/8rhHgRmipVqiTu3Lkj1dmyZYtQq9UiJSVFCCFEcHCw0Gg04vnz51KdgIAAYWNjI7Kzs4uxJ0pGYmKiACAiIiKEEOzf4la9enXxww8/sF+LyePHj4Wjo6MIDw8Xrq6uUlhh/xbd3LlzRfPmzXPd9jb3K6eB3kB6ejpiYmLQvXt3WXn37t0RGRlZRq1SluvXryMhIUHWR2q1Gq6urlIfxcTEICMjQ1bHxsYGTk5OUp0TJ05Ao9Ggbdu2Up127dpBo9HI6jg5OckelOXh4YG0tDTExMRIdVxdXWU3O/Lw8MDdu3dx48aN4u+AYpaSkgIAsLCwAMD+LS5ZWVkIDQ3F06dP0b59e/ZrMfnkk0/Qu3dvdO3aVVbO/n0zly9fho2NDRwcHDBo0CBcu3YNwNvdrwwrb+DBgwfIysrSexiiVqvVe2hiRZXTD/n1UUJCAoyNjVG9evV869SsWVPv+DVr1pTVefVzqlevDmNj43zr5LxX+ncmhMCUKVPw3nvvwcnJCQD7902dP38eVapUgVqtxtixY7Fjxw40adKE/VoMQkNDERMTg4CAAL1t7N+ia9u2LdavX48DBw5g9erVSEhIgIuLC5KSkt7qfq0wt9svSSqVSvZeCKFXVtEVpY9erZNb/eKoI/53sZfSv7Px48fj3LlzOH78uN429m/RNGzYEGfPnsXDhw+xbds2DB8+HBEREdJ29mvRxMXFYdKkSQgLC4OJiUme9di/r69nz57S/zs7O6N9+/aoV68e1q1bh3bt2gF4O/uVIytvoEaNGjAwMNBLiImJiXppsqLKWaWeXx/pdDqkp6cjOTk53zr37t3TO/79+/dldV79nOTkZGRkZORbJzExEYD+byNKMmHCBOzevRuHDx9GrVq1pHL275sxNjZG/fr10aZNGwQEBKB58+b49ttv2a9vKCYmBomJiWjdujUMDQ1haGiIiIgIfPfddzA0NMzzt2v27+szMzODs7MzLl++/Fb/3DKsvAFjY2O0bt0a4eHhsvLw8HC4uLiUUauUxcHBATqdTtZH6enpiIiIkPqodevWMDIyktWJj49HbGysVKd9+/ZISUnBqVOnpDp//PEHUlJSZHViY2MRHx8v1QkLC4NarUbr1q2lOkePHpVdXhcWFgYbGxvY29sXfwe8ISEExo8fj+3bt+PQoUNwcHCQbWf/Fi8hBNLS0tivb8jd3R3nz5/H2bNnpVebNm3g5eWFs2fPom7duuzfYpKWloa//voL1tbWb/fP7WstxyU9OZcur1mzRly8eFH4+PgIMzMzcePGjbJuWql5/PixOHPmjDhz5owAIBYvXizOnDkjXb69YMECodFoxPbt28X58+fF4MGDc72UrlatWuLgwYPi9OnTokuXLrleStesWTNx4sQJceLECeHs7JzrpXTu7u7i9OnT4uDBg6JWrVqyS+kePnwotFqtGDx4sDh//rzYvn27qFq1qiIvURRCiI8//lhoNBpx5MgR2aWKz549k+qwf4tm5syZ4ujRo+L69evi3Llz4rPPPhOVKlUSYWFhQgj2a3F7+WogIdi/RTV16lRx5MgRce3aNXHy5Enh6ekpzM3NpX9z3tZ+ZVgpBsuXLxd16tQRxsbGolWrVtJlpRXF4cOHBQC91/Dhw4UQLy6nmzt3rtDpdEKtVotOnTqJ8+fPy46Rmpoqxo8fLywsLISpqanw9PQUt27dktVJSkoSXl5ewtzcXJibmwsvLy+RnJwsq3Pz5k3Ru3dvYWpqKiwsLMT48eNll80JIcS5c+dEx44dhVqtFjqdTvj5+Snu8sQcufUrALF27VqpDvu3aEaNGiX9ubWyshLu7u5SUBGC/VrcXg0r7N+iyblvipGRkbCxsRH9+/cXFy5ckLa/rf2qEkKBt+gjIiIi+l9cs0JERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisawQkRERIrGsEJERESKxrBCREREisawQkT5cnNzg4+Pj/Te3t4eQUFBJfqZR44cgUqlwsOHD0v0c5QoJCQE1apVK+tmECmKYVk3gIjKl6ioKJiZmZV1M4ioAmFYIaLXYmVlVdZNIKIKhtNAROWQm5sbJkyYAB8fH1SvXh1arRarVq3C06dPMXLkSJibm6NevXrYt2+fbL+LFy+iV69eqFKlCrRaLYYNG4YHDx5I258+fYoPP/wQVapUgbW1NRYtWqT32a9OAy1evBjOzs4wMzODnZ0dxo0bhydPnkjbc6Y1Dhw4gMaNG6NKlSro0aOH7NHyeYmJiUGbNm1QuXJluLi44NKlS7LtK1asQL169WBsbIyGDRtiw4YN0rYbN25ApVLh7NmzUtnDhw+hUqlw5MgRAEBycjK8vLxgZWUFU1NTODo6Yu3atVL9O3fu4IMPPkD16tVhaWmJfv364caNG7m2NTs7G7Vq1cLKlStl5adPn4ZKpcK1a9cK1V+vGjFiBN5//31ZmY+PD9zc3KT3QggEBgaibt26MDU1RfPmzfHzzz/neUyi8oZhhaicWrduHWrUqIFTp05hwoQJ+PjjjzFgwAC4uLjg9OnT8PDwwLBhw/Ds2TMAQHx8PFxdXdGiRQtER0dj//79uHfvHgYOHCgd89NPP8Xhw4exY8cOhIWF4ciRI4iJicm3HZUqVcJ3332H2NhYrFu3DocOHYKvr6+szrNnz/DNN99gw4YNOHr0KG7duoVp06YVeI6zZs3CokWLEB0dDUNDQ4waNUratmPHDkyaNAlTp05FbGwsxowZg5EjR+Lw4cOF7sPZs2fj4sWL2LdvH/766y+sWLECNWrUkNrcuXNnVKlSBUePHsXx48eloJWenp5rPwwaNAibNm2SlW/evBnt27dH3bp1C91fr+vzzz/H2rVrsWLFCly4cAGTJ0/G0KFDERER8UbHJVKM135OMxGVOVdXV/Hee+9J7zMzM4WZmZkYNmyYVBYfHy8AiBMnTgghhJg9e7bo3r277DhxcXECgLh06ZJ4/PixMDY2FqGhodL2pKQkYWpqKiZNmiSV1alTRyxZsiTPtm3dulVYWlpK79euXSsAiCtXrkhly5cvF1qtNs9jHD58WAAQBw8elMr27t0rAIjU1FQhhBAuLi5i9OjRsv0GDBggevXqJYQQ4vr16wKAOHPmjLQ9OTlZABCHDx8WQgjRp08fMXLkyFzbsGbNGtGwYUPZ4+zT0tKEqampOHDgQK77nD59WqhUKnHjxg0hhBBZWVnC1tZWLF++PM9zza2/NBqN9H748OGiX79+sn0mTZokXF1dhRBCPHnyRJiYmIjIyEhZHW9vbzF48OA8P5eoPOHIClE51axZM+n/DQwMYGlpCWdnZ6lMq9UCABITEwG8mFI5fPgwqlSpIr0aNWoEALh69SquXr2K9PR0tG/fXjqGhYUFGjZsmG87Dh8+jG7dusHW1hbm5ub48MMPkZSUhKdPn0p1KleujHr16knvra2tpXYV9hytra1l5/PXX3+hQ4cOsvodOnTAX3/9VeBxc3z88ccIDQ1FixYt4Ovri8jISGlbTEwMrly5AnNzc6m/LCws8Pz5c1y9ejXX47Vs2RKNGjXCli1bAAARERFITEyUjV4Vpr9ex8WLF/H8+XN069ZN9t2uX78+z3YSlTdcYEtUThkZGcneq1QqWZlKpQLwYi1Fzn/79OmDhQsX6h3L2toaly9ffu023Lx5E7169cLYsWPxxRdfwMLCAsePH4e3tzcyMjLybasQosDj53c+L5flEEJIZZUqVZLKcrzcJgDo2bMnbt68ib179+LgwYNwd3fHJ598gm+++QbZ2dlo3bq13rQOkP8iYy8vL2zevBkzZszA5s2b4eHhIU0tFba/XlapUiW9vnq5bk5/7N27F7a2trJ6arU6z3YSlSccWSGqIFq1aoULFy7A3t4e9evXl73MzMxQv359GBkZ4eTJk9I+ycnJ+Pvvv/M8ZnR0NDIzM7Fo0SK0a9cODRo0wN27d0vjdNC4cWMcP35cVhYZGYnGjRsD+L9A8fJC3pcX2+awsrLCiBEjsHHjRgQFBWHVqlUAXvTX5cuXUbNmTb3+0mg0ebZryJAhOH/+PGJiYvDzzz/Dy8tL2laU/rKystJbjPzyeTRp0gRqtRq3bt3Sa6ednV2+xyYqLxhWiCqITz75BP/88w8GDx6MU6dO4dq1awgLC8OoUaOQlZWFKlWqwNvbG59++il+++03xMbGYsSIEdIIRW7q1auHzMxMLF26FNeuXcOGDRv0roYpKZ9++ilCQkKwcuVKXL58GYsXL8b27dulhbumpqZo164dFixYgIsXL+Lo0aP4/PPPZceYM2cOdu3ahStXruDChQvYs2ePFHa8vLxQo0YN9OvXD8eOHcP169cRERGBSZMm4fbt23m2y8HBAS4uLvD29kZmZib69esnbStKf3Xp0gXR0dFYv349Ll++jLlz5yI2Nlbabm5ujmnTpmHy5MlYt24drl69ijNnzmD58uVYt27da/crkRIxrBBVEDY2Nvj999+RlZUFDw8PODk5YdKkSdBoNFIg+frrr9GpUyf07dsXXbt2xXvvvYfWrVvnecwWLVpg8eLFWLhwIZycnLBp0yYEBASUyvm8//77+Pbbb/H111+jadOm+P7777F27VrZJb0//vgjMjIy0KZNG0yaNAlffvml7BjGxsaYOXMmmjVrhk6dOsHAwAChoaEAXqyzOXr0KGrXro3+/fujcePGGDVqFFJTU1G1atV82+bl5YU///wT/fv3h6mpqVRelP7y8PDA7Nmz4evri3feeQePHz/Ghx9+KKvzxRdfYM6cOQgICEDjxo3h4eGBX375BQ4ODoXpSiLFU4nCTBwTERERlRGOrBAREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRojGsEBERkaIxrBAREZGiMawQERGRov1/MxzlSusRIFsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "# sns.histplot(df.msrp[df.msrp < 100000], bins=40, color='black', alpha=1)\n",
    "sns.histplot(df[\"median_house_value\"], bins=50)\n",
    "\n",
    "plt.ylabel('count')\n",
    "plt.xlabel('median house value')\n",
    "plt.title('Examining if median house prices have a tail:')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "7b25b5df",
   "metadata": {},
   "source": [
    "#### Yes, It has a tail and a spike at an outlier location hmm\n",
    "Tail definition: \n",
    "\n",
    "- This kind of distribution is difficult for ML models, the values in the tail have very few samples\n",
    "- We want to get rid of the tail, and for that we pply natural logarithm to the median house value to make it more compact if possible\n",
    "- Use np.log1p, this function takes the log, but adds 1 before applying it (this is done to be sure that we don't get 0 values)\n",
    "- The new distribution should look more like a bell curve\n",
    "- Not all data will have a resemblance to normal distribution\n",
    "- Why is a normal distribution important? Because many ML algo assume that the underlying distribution is normal.\n",
    "- also, the data distribution is right skewed, i.e. data is clustered to the left, and tail moves to the right\n",
    "![image.png](attachment:image.png)\n",
    "image from: https://www.statisticshowto.com/probability-and-statistics/skewed-distribution/\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "392d0fb1",
   "metadata": {},
   "source": [
    "### Features\n",
    "\n",
    "For the rest of the homework, you'll need to use only these columns:\n",
    "\n",
    "* `'latitude'`,\n",
    "* `'longitude'`,\n",
    "* `'housing_median_age'`,\n",
    "* `'total_rooms'`,\n",
    "* `'total_bedrooms'`,\n",
    "* `'population'`,\n",
    "* `'households'`,\n",
    "* `'median_income'`,\n",
    "* `'median_house_value'`\n",
    "\n",
    "Select only them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6e18b8bf",
   "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>latitude</th>\n",
       "      <th>longitude</th>\n",
       "      <th>housing_median_age</th>\n",
       "      <th>total_rooms</th>\n",
       "      <th>total_bedrooms</th>\n",
       "      <th>population</th>\n",
       "      <th>households</th>\n",
       "      <th>median_income</th>\n",
       "      <th>median_house_value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>37.88</td>\n",
       "      <td>-122.23</td>\n",
       "      <td>41.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>129.0</td>\n",
       "      <td>322.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>8.3252</td>\n",
       "      <td>452600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>37.86</td>\n",
       "      <td>-122.22</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7099.0</td>\n",
       "      <td>1106.0</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>1138.0</td>\n",
       "      <td>8.3014</td>\n",
       "      <td>358500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.24</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1467.0</td>\n",
       "      <td>190.0</td>\n",
       "      <td>496.0</td>\n",
       "      <td>177.0</td>\n",
       "      <td>7.2574</td>\n",
       "      <td>352100.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1274.0</td>\n",
       "      <td>235.0</td>\n",
       "      <td>558.0</td>\n",
       "      <td>219.0</td>\n",
       "      <td>5.6431</td>\n",
       "      <td>341300.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1627.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>565.0</td>\n",
       "      <td>259.0</td>\n",
       "      <td>3.8462</td>\n",
       "      <td>342200.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   latitude  longitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
       "0     37.88    -122.23                41.0        880.0           129.0   \n",
       "1     37.86    -122.22                21.0       7099.0          1106.0   \n",
       "2     37.85    -122.24                52.0       1467.0           190.0   \n",
       "3     37.85    -122.25                52.0       1274.0           235.0   \n",
       "4     37.85    -122.25                52.0       1627.0           280.0   \n",
       "\n",
       "   population  households  median_income  median_house_value  \n",
       "0       322.0       126.0         8.3252            452600.0  \n",
       "1      2401.0      1138.0         8.3014            358500.0  \n",
       "2       496.0       177.0         7.2574            352100.0  \n",
       "3       558.0       219.0         5.6431            341300.0  \n",
       "4       565.0       259.0         3.8462            342200.0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selected_columns = [\"latitude\",\"longitude\",\"housing_median_age\",\"total_rooms\",\"total_bedrooms\",\n",
    "                             \"population\",\"households\",\"median_income\",\"median_house_value\"]\n",
    "\n",
    "\n",
    "df = df[selected_columns]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27276f52",
   "metadata": {},
   "source": [
    "### Question 1\n",
    "\n",
    "Find a feature with missing values. How many missing values does it have?\n",
    "- 207\n",
    "- 307\n",
    "- 408\n",
    "- 508\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "60b4da0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "latitude                0\n",
       "longitude               0\n",
       "housing_median_age      0\n",
       "total_rooms             0\n",
       "total_bedrooms        207\n",
       "population              0\n",
       "households              0\n",
       "median_income           0\n",
       "median_house_value      0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().sum(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66e231b4",
   "metadata": {},
   "source": [
    "It has 207 values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0d9cb80",
   "metadata": {},
   "source": [
    "### Question 2\n",
    "\n",
    "What's the median (50% percentile) for variable 'population'?\n",
    "- 1133\n",
    "- 1122\n",
    "- 1166\n",
    "- 1188\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a967e465",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1166.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.population.median()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34369794",
   "metadata": {},
   "source": [
    "### Split the data\n",
    "\n",
    "* Shuffle the initial dataset, use seed `42`.\n",
    "* Split your data in train/val/test sets, with 60%/20%/20% distribution.\n",
    "* Make sure that the target value ('median_house_value') is not in your dataframe.\n",
    "* Apply the log transformation to the median_house_value variable using the `np.log1p()` function.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6c6ac9fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['latitude', 'longitude', 'housing_median_age', 'total_rooms',\n",
       "       'total_bedrooms', 'population', 'households', 'median_income',\n",
       "       'median_house_value'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cd96b614",
   "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>latitude</th>\n",
       "      <th>longitude</th>\n",
       "      <th>housing_median_age</th>\n",
       "      <th>total_rooms</th>\n",
       "      <th>total_bedrooms</th>\n",
       "      <th>population</th>\n",
       "      <th>households</th>\n",
       "      <th>median_income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>37.88</td>\n",
       "      <td>-122.23</td>\n",
       "      <td>41.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>129.0</td>\n",
       "      <td>322.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>8.3252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>37.86</td>\n",
       "      <td>-122.22</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7099.0</td>\n",
       "      <td>1106.0</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>1138.0</td>\n",
       "      <td>8.3014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.24</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1467.0</td>\n",
       "      <td>190.0</td>\n",
       "      <td>496.0</td>\n",
       "      <td>177.0</td>\n",
       "      <td>7.2574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1274.0</td>\n",
       "      <td>235.0</td>\n",
       "      <td>558.0</td>\n",
       "      <td>219.0</td>\n",
       "      <td>5.6431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1627.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>565.0</td>\n",
       "      <td>259.0</td>\n",
       "      <td>3.8462</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   latitude  longitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
       "0     37.88    -122.23                41.0        880.0           129.0   \n",
       "1     37.86    -122.22                21.0       7099.0          1106.0   \n",
       "2     37.85    -122.24                52.0       1467.0           190.0   \n",
       "3     37.85    -122.25                52.0       1274.0           235.0   \n",
       "4     37.85    -122.25                52.0       1627.0           280.0   \n",
       "\n",
       "   population  households  median_income  \n",
       "0       322.0       126.0         8.3252  \n",
       "1      2401.0      1138.0         8.3014  \n",
       "2       496.0       177.0         7.2574  \n",
       "3       558.0       219.0         5.6431  \n",
       "4       565.0       259.0         3.8462  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = df.drop(columns='median_house_value')\n",
    "features.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a3d56a99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    452600.0\n",
       "1    358500.0\n",
       "2    352100.0\n",
       "3    341300.0\n",
       "4    342200.0\n",
       "Name: median_house_value, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target = df[\"median_house_value\"]\n",
    "target.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c4453c97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        13.022766\n",
       "1        12.789687\n",
       "2        12.771673\n",
       "3        12.740520\n",
       "4        12.743154\n",
       "           ...    \n",
       "20635    11.265758\n",
       "20636    11.252872\n",
       "20637    11.432810\n",
       "20638    11.346883\n",
       "20639    11.400887\n",
       "Name: median_house_value, Length: 20640, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_target = np.log1p(target)\n",
    "log_target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2d536f48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "# sns.histplot(df.msrp[df.msrp < 100000], bins=40, color='black', alpha=1)\n",
    "sns.histplot(log_target, bins=50)\n",
    "\n",
    "plt.ylabel('count')\n",
    "plt.xlabel('median house value')\n",
    "plt.title('Examining if median house prices have a tail after taking natural log:')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73615a51",
   "metadata": {},
   "source": [
    "looks more normal, the tail has disappeared, though not centered around 0 and there is still a spike at the right-most."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9406ef8e",
   "metadata": {},
   "source": [
    "#### Creating train-val-test sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3eedf622",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_train_val_test_split(features, log_target, seed=42, train_split = 0.6, val_split =0.2, test_split =0.2):\n",
    "\n",
    "    features_temp = features.sample(frac=1, random_state = seed, ignore_index =True).copy()\n",
    "    log_target_temp = log_target.sample(frac=1, random_state = seed, ignore_index =True).copy()\n",
    "    \n",
    "\n",
    "    x_train, x_val, x_test = np.split(features_temp, [int(len(features_temp)*train_split), int(len(features_temp)*(train_split+val_split))]) # split of 60:20:20\n",
    "    y_train, y_val, y_test = np.split(log_target_temp, [int(len(log_target_temp)*train_split), int(len(log_target_temp)*(train_split+val_split))])\n",
    "    \n",
    "    splits = (x_train, x_val, x_test)\n",
    "    \n",
    "#     Sanity check \n",
    "#     for i,split in enumerate (splits):\n",
    "#         print (\"length of spit %d is %0.2f of total df length\"\\\n",
    "#         %(i, len(split)/(len(x_train)+len(x_val)+len(x_test))))\n",
    "    \n",
    "    return x_train, x_val, x_test, y_train, y_val, y_test\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "22307233",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_val, x_test, y_train, y_val, y_test= create_train_val_test_split(features, log_target, seed = 42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b4091b7",
   "metadata": {},
   "source": [
    "### Question 3\n",
    "\n",
    "* We need to deal with missing values for the column from Q1.\n",
    "* We have two options: fill it with 0 or with the mean of this variable.\n",
    "* Try both options. For each, train a linear regression model without regularization using the code from the lessons.\n",
    "* For computing the mean, use the training [dataset] only!\n",
    "* Use the validation dataset to evaluate the models and compare the RMSE of each option.\n",
    "* Round the RMSE scores to 2 decimal digits using `round(score, 2)`\n",
    "* Which option gives better RMSE?\n",
    "\n",
    "Options:\n",
    "- With 0\n",
    "- With mean\n",
    "- Both are equally good\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c73db486",
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_isnull(df):\n",
    "#   print (df.isnull().sum(),\"\\n\")\n",
    "    return sum(df.isnull().sum(axis=0)>0)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "aa77e62f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def deal_with_missing_data(splits = [x_train, x_val, x_test], fill_with = 0):\n",
    "    \"\"\"\n",
    "    splits: expect 3 splits by default, but only x_train is call by name. Can only pass 2 splits\n",
    "            like train and val only\n",
    "    fillwith: Can be 0 or mean   \n",
    "    \n",
    "    \"\"\"\n",
    "\n",
    "    splits_alt = []\n",
    "    \n",
    "    # iterate through all of the x_train, x_val and x_test\n",
    "    for i, split in enumerate (splits):\n",
    "        \n",
    "        # check if any of the splits has columns with missing values\n",
    "        if (check_isnull(split) == True):\n",
    "            \n",
    "            # get column names, will return a numpy array\n",
    "            column_names = split.columns[split.isnull().any()].to_list()\n",
    "            \n",
    "            # create copy of original split\n",
    "            temp = split.copy()  \n",
    "                    \n",
    "            # for loop becuase columns with missing values might be more than 1\n",
    "            # for each column:\n",
    "            \n",
    "            for column in column_names:\n",
    "                \n",
    "                # check for mean, otherwise will use default fill_with =0\n",
    "                if fill_with == \"mean\":\n",
    "                        fill_value = x_train[column].mean()\n",
    "                elif fill_with == 0:                    \n",
    "                        fill_value = 0\n",
    "                        \n",
    "                temp[column].fillna(fill_value, inplace=True) \n",
    "                \n",
    "            # append to splits_alt for returning from function later\n",
    "            splits_alt.append(temp)\n",
    "            \n",
    "        else:\n",
    "            splits_alt.append(split.copy())\n",
    "        \n",
    "        # Check if each split has actually had it's missing values replaced\n",
    "        # print (\"split %d has %d columns with missing values\" %(i, sum(splits_alt[i].isnull().sum()>0)))\n",
    "\n",
    "        \n",
    "    # it will return a varibale list each time depending of how many splits were passed to the function\n",
    "    return splits_alt\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "30c3533d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# be careful while assigning, \n",
    "# if only x_train and x_val or x_test have been passed, it will return number of variables accordingly\n",
    "\n",
    "x_train_0, x_val_0, x_test_0 = deal_with_missing_data(splits = [x_train, x_val, x_test], fill_with =0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13f373cf",
   "metadata": {},
   "source": [
    "Yay. so we correctly replaced. We made copies to use the same train, val and test data for filling with mean \n",
    "of train dataset. Otherwise replacing with 0 would have overwritten.\n",
    "\n",
    "Creating copies of train,val and test data with NaN values filled with mean of train dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b420e181",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_mean, x_val_mean, x_test_mean = deal_with_missing_data(splits = [x_train, x_val, x_test], fill_with = \"mean\" )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4c280917",
   "metadata": {},
   "outputs": [],
   "source": [
    "#train and get predictions on val/test set:\n",
    "\n",
    "def train_linear_regression_reg(x_train,y_train,x_test, r=0):\n",
    "    X =x_train\n",
    "    y = y_train\n",
    "    \n",
    "    ones = np.ones(X.shape[0])\n",
    "    X = np.column_stack([ones, X])\n",
    "    \n",
    "    XTX = X.T.dot(X)\n",
    "    XTX = XTX + r*np.eye(XTX.shape[0])\n",
    "    XTX_inv = np.linalg.inv(XTX)\n",
    "    w_full = XTX_inv.dot(X.T).dot(y)\n",
    "\n",
    "    # getting trained weights\n",
    "    w0, w = w_full[0], w_full[1:]\n",
    "    # prediction\n",
    "    y_pred = w0 + x_test.dot(w)\n",
    "    \n",
    "    return y_pred\n",
    "\n",
    "# getting rmse scores from predicted values:\n",
    "\n",
    "def calculate_rmse(y_pred, y_test):\n",
    "    error = y_pred - y_test\n",
    "    mse = (error ** 2).mean()\n",
    "    rmse =np.sqrt(mse)\n",
    "    return rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "908a8613",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#getting predictions for missing values replaced with 0\n",
    "y_pred_val_0 = train_linear_regression_reg(x_train_0,y_train, x_val_0)\n",
    "\n",
    "# evaluating predictions\n",
    "rmse_0 = calculate_rmse(y_pred_val_0, y_val) \n",
    "round(rmse_0,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "fce912d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#getting predictions for missing values replaced with mean\n",
    "y_pred_val_mean = train_linear_regression_reg(x_train_mean,y_train, x_val_mean)\n",
    "\n",
    "\n",
    "# evaluating predictions\n",
    "rmse_mean = calculate_rmse(y_pred_val_mean, y_val) \n",
    "round(rmse_mean,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99bbc7fc",
   "metadata": {},
   "source": [
    "Both histograms look similar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8e96680e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='median_house_value', ylabel='Count'>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define plotting region (2 rows, 2 columns)\n",
    "fig, axes = plt.subplots(1, 2)\n",
    "\n",
    "sns.set(rc={'figure.figsize':(15,10)})\n",
    "#create boxplot in each subplot\n",
    "sns.histplot(y_pred_val_0, color=\"red\", alpha=0.5, bins=50, ax=axes[0])\n",
    "sns.histplot(y_val, color=\"blue\", alpha=0.5, bins=50, ax=axes[0])\n",
    "\n",
    "sns.histplot(y_pred_val_mean, color=\"red\", alpha=0.5, bins=50,ax=axes[1])\n",
    "sns.histplot(y_val, color=\"blue\", alpha=0.5, bins=50, ax=axes[1]) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba4d5538",
   "metadata": {},
   "source": [
    "It means in this case, replacing with 0 or the mean both give equal results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c15fd4fd",
   "metadata": {},
   "source": [
    "### Question 4\n",
    "\n",
    "* Now let's train a regularized linear regression.\n",
    "* For this question, fill the NAs with 0. \n",
    "* Try different values of `r` from this list: `[0, 0.000001, 0.0001, 0.001, 0.01, 0.1, 1, 5, 10]`.\n",
    "* Use RMSE to evaluate the model on the validation dataset.\n",
    "* Round the RMSE scores to 2 decimal digits.\n",
    "* Which `r` gives the best RMSE?\n",
    "\n",
    "If there are multiple options, select the smallest `r`.\n",
    "\n",
    "Options:\n",
    "- 0\n",
    "- 0.000001\n",
    "- 0.001\n",
    "- 0.0001\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7dc1c3bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RSME values are:  [0.33, 0.33, 0.33, 0.33, 0.33, 0.33, 0.33, 0.34, 0.34]\n",
      "Best regularization values are:  [0, 1e-06, 0.0001, 0.001, 0.01, 0.1, 1]\n",
      "The smallest best regularization value is:  0\n"
     ]
    }
   ],
   "source": [
    "regularization_values = [0, 0.000001, 0.0001, 0.001, 0.01, 0.1, 1, 5, 10]\n",
    "RMSE = []\n",
    "\n",
    "for r in regularization_values:\n",
    "    \n",
    "    y_pred_val_0 = train_linear_regression_reg(x_train_0, y_train, x_val_0, r = r)\n",
    "    rmse = calculate_rmse(y_pred_val_0, y_val) \n",
    "    RMSE.append(round(rmse,2))\n",
    "    \n",
    "best_RMSE = min(RMSE)\n",
    "index_list = [index for index in range(len(RMSE)) if RMSE[index] == best_RMSE]\n",
    "best_regularization_values = [regularization_values[index] for index in index_list]\n",
    "\n",
    "print(\"RSME values are: \", RMSE)\n",
    "print(\"Best regularization values are: \", best_regularization_values)\n",
    "print (\"The smallest best regularization value is: \", min(best_regularization_values))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a7e9ce5",
   "metadata": {},
   "source": [
    "### Question 5 \n",
    "\n",
    "* We used seed 42 for splitting the data. Let's find out how selecting the seed influences our score.\n",
    "* Try different seed values: `[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]`.\n",
    "* For each seed, do the train/validation/test split with 60%/20%/20% distribution.\n",
    "* Fill the missing values with 0 and train a model without regularization.\n",
    "* For each seed, evaluate the model on the validation dataset and collect the RMSE scores. \n",
    "* What's the standard deviation of all the scores? To compute the standard deviation, use `np.std`.\n",
    "* Round the result to 3 decimal digits (`round(std, 3)`)\n",
    "\n",
    "> Note: Standard deviation shows how different the values are.\n",
    "> If it's low, then all values are approximately the same.\n",
    "> If it's high, the values are different. \n",
    "> If standard deviation of scores is low, then our model is *stable*.\n",
    "\n",
    "Options:\n",
    "- 0.16\n",
    "- 0.00005\n",
    "- 0.005\n",
    "- 0.15555\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4831905d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation of all RMSE with different seeds split is:  0.004\n"
     ]
    }
   ],
   "source": [
    "# Create a function from previous ones:\n",
    "\n",
    "seeds = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
    "RMSE_seeds = []\n",
    "\n",
    "for seed in seeds:\n",
    "\n",
    "    x_train, x_val, _, y_train, y_val, _ = create_train_val_test_split(features, log_target, seed=seed)\n",
    "    x_train_0, x_val_0 = deal_with_missing_data(splits = [x_train, x_val], fill_with =0)\n",
    "\n",
    "    #getting predictions for missing values replaced with mean\n",
    "    y_pred_val_0 = train_linear_regression_reg(x_train_0, y_train, x_val_0, r=0)\n",
    "\n",
    "    # evaluating predictions\n",
    "    rmse_0 = calculate_rmse(y_pred_val_0, y_val) \n",
    "    RMSE_seeds.append(rmse_0)\n",
    "\n",
    "    \n",
    "print(\"standard deviation of all RMSE with different seeds split is: \",round(np.std(RMSE_seeds), 3))\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a82adbda",
   "metadata": {},
   "source": [
    "### Question 6\n",
    "\n",
    "* Split the dataset like previously, use seed 9.\n",
    "* Combine train and validation datasets.\n",
    "* Fill the missing values with 0 and train a model with `r=0.001`. \n",
    "* What's the RMSE on the test dataset?\n",
    "\n",
    "Options:\n",
    "- 0.35\n",
    "- 0.135\n",
    "- 0.450\n",
    "- 0.245\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9c5f0186",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The RMSE on the test set is:  0.345\n"
     ]
    }
   ],
   "source": [
    "x_train, x_val, x_test, y_train, y_val, y_test = create_train_val_test_split(features, log_target, seed= 9)\n",
    "x_train, x_val, x_test = deal_with_missing_data(splits = [x_train, x_val, x_test], fill_with =0)\n",
    "\n",
    "x_train_val = pd.concat([x_train, x_val])\n",
    "y_train_val = np.concatenate([y_train, y_val])\n",
    "\n",
    "#getting predictions for missing values replaced with mean\n",
    "y_pred = train_linear_regression_reg(x_train_val, y_train_val, x_test, r=0.001)\n",
    "\n",
    "# evaluating predictions\n",
    "rmse = calculate_rmse(y_pred, y_test) \n",
    "\n",
    "print(\"The RMSE on the test set is: \", round(rmse,3))"
   ]
  }
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