Assignments/Week #2/Homework.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "fbb7cfde",
   "metadata": {},
   "source": [
    "In this homework, we will use the California Housing Prices from Kaggle.\n",
    "\n",
    "Here's a wget-able link:\n",
    "\n",
    "wget https://raw.githubusercontent.com/alexeygrigorev/datasets/master/housing.csv\n",
    "\n",
    "The goal of this homework is to create a regression model for predicting housing prices (column 'median_house_value').\n",
    "\n",
    "\n",
    "EDA\n",
    "\n",
    "    Load the data.\n",
    "    Look at the median_house_value variable. Does it have a long tail?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2c18dc2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "--2022-09-19 17:44:32--  https://raw.githubusercontent.com/alexeygrigorev/datasets/master/housing.csv\n",
      "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.110.133, 185.199.111.133, ...\n",
      "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 1423529 (1.4M) [text/plain]\n",
      "Saving to: 'housing.csv'\n",
      "\n",
      "     0K .......... .......... .......... .......... ..........  3% 4.71M 0s\n",
      "    50K .......... .......... .......... .......... ..........  7% 14.6M 0s\n",
      "   100K .......... .......... .......... .......... .......... 10% 8.95M 0s\n",
      "   150K .......... .......... .......... .......... .......... 14% 12.1M 0s\n",
      "   200K .......... .......... .......... .......... .......... 17% 14.6M 0s\n",
      "   250K .......... .......... .......... .......... .......... 21% 10.7M 0s\n",
      "   300K .......... .......... .......... .......... .......... 25% 14.5M 0s\n",
      "   350K .......... .......... .......... .......... .......... 28% 21.9M 0s\n",
      "   400K .......... .......... .......... .......... .......... 32% 6.82M 0s\n",
      "   450K .......... .......... .......... .......... .......... 35% 20.6M 0s\n",
      "   500K .......... .......... .......... .......... .......... 39% 16.7M 0s\n",
      "   550K .......... .......... .......... .......... .......... 43% 47.5M 0s\n",
      "   600K .......... .......... .......... .......... .......... 46% 45.6M 0s\n",
      "   650K .......... .......... .......... .......... .......... 50% 12.8M 0s\n",
      "   700K .......... .......... .......... .......... .......... 53% 12.9M 0s\n",
      "   750K .......... .......... .......... .......... .......... 57% 32.0M 0s\n",
      "   800K .......... .......... .......... .......... .......... 61% 13.2M 0s\n",
      "   850K .......... .......... .......... .......... .......... 64% 41.7M 0s\n",
      "   900K .......... .......... .......... .......... .......... 68% 26.9M 0s\n",
      "   950K .......... .......... .......... .......... .......... 71% 13.3M 0s\n",
      "  1000K .......... .......... .......... .......... .......... 75% 10.8M 0s\n",
      "  1050K .......... .......... .......... .......... .......... 79% 40.5M 0s\n",
      "  1100K .......... .......... .......... .......... .......... 82% 50.6M 0s\n",
      "  1150K .......... .......... .......... .......... .......... 86% 38.9M 0s\n",
      "  1200K .......... .......... .......... .......... .......... 89% 28.7M 0s\n",
      "  1250K .......... .......... .......... .......... .......... 93% 29.3M 0s\n",
      "  1300K .......... .......... .......... .......... .......... 97% 12.2M 0s\n",
      "  1350K .......... .......... .......... ..........           100% 60.0M=0.09s\n",
      "\n",
      "2022-09-19 17:44:33 (15.7 MB/s) - 'housing.csv' saved [1423529/1423529]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget https://raw.githubusercontent.com/alexeygrigorev/datasets/master/housing.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fb64df17",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\anaconda3\\envs\\ml-zoomcamp\\lib\\site-packages\\scipy\\__init__.py:146: UserWarning: A NumPy version >=1.16.5 and <1.23.0 is required for this version of SciPy (detected version 1.23.2\n",
      "  warnings.warn(f\"A NumPy version >={np_minversion} and <{np_maxversion}\"\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a19960c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c8a11b80",
   "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>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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"housing.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "171c2781",
   "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": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5751503f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20640, 10)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f3e3aca5",
   "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(data.median_house_value, bins=40, color='black', alpha=0.25)\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Price')\n",
    "plt.title('Distribution of prices')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b289dfd3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_price = np.log1p(data['median_house_value'])\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "sns.histplot(log_price, bins=100, color='black', alpha=0.25)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Log(Price + 1)')\n",
    "plt.title('Distribution of prices after log tranformation')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4eaae6ed",
   "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": 9,
   "id": "ad80b2d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "housing = data.drop([\"ocean_proximity\"], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e3514936",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['longitude', 'latitude', '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": [
    "housing.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61fcf8b1",
   "metadata": {},
   "source": [
    "# Question 1 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91d19e1d",
   "metadata": {},
   "source": [
    "Find a feature with missing values. How many missing values does it have?\n",
    "\n",
    "    207\n",
    "    307\n",
    "    408\n",
    "    508"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "96f54d89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "longitude               0\n",
       "latitude                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": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63f997b4",
   "metadata": {},
   "source": [
    "total_bedrooms has **207 missing values**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fda2aa77",
   "metadata": {},
   "source": [
    "## Question 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f4d5c29",
   "metadata": {},
   "source": [
    "What's the median (50% percentile) for variable 'population'?\n",
    "\n",
    "    1133\n",
    "    1122\n",
    "    1166\n",
    "    1188"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4e7a5f24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1166.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing.population.median() # housing['population'].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0de1f69a",
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c2d5b85a",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "n = housing.shape[0]  # Length of the dataframe\n",
    "\n",
    "n_val = int(0.2 * n) # 20% of length of the dataframe\n",
    "n_test = int(0.2 * n) # 20% of length of the dataframe\n",
    "n_train = n - (n_val + n_test) # 60% of length of the dataframe \n",
    "\n",
    "idx = np.arange(n) # Generate indices for dataframe \n",
    "np.random.shuffle(idx) \n",
    "\n",
    "df_shuffled = housing.iloc[idx] # Shuffled dataframe generated \n",
    "\n",
    "df_train = df_shuffled.iloc[:n_train].copy() # Train Data\n",
    "df_val = df_shuffled.iloc[n_train:n_train+n_val].copy() # Validation Data\n",
    "df_test = df_shuffled.iloc[n_train+n_val:].copy() # Test Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8c97fcbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_orig = df_train['median_house_value'].values\n",
    "y_val_orig = df_val['median_house_value'].values\n",
    "y_test_orig = df_test['median_house_value'].values\n",
    "\n",
    "y_train = np.log1p(y_train_orig)\n",
    "y_val = np.log1p(y_val_orig)\n",
    "y_test = np.log1p(y_test_orig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "18fa683d",
   "metadata": {},
   "outputs": [],
   "source": [
    "del df_train['median_house_value']\n",
    "del df_val['median_house_value']\n",
    "del df_test['median_house_value']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d82629c2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "9ae3d682",
   "metadata": {},
   "source": [
    "## Question 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9617b612",
   "metadata": {},
   "source": [
    "- 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 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",
    "\n",
    "    With 0\n",
    "    With mean\n",
    "    Both are equally good"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6f1b8dc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['longitude', 'latitude', 'housing_median_age', 'total_rooms',\n",
       "       'total_bedrooms', 'population', 'households', 'median_income'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols = df_train.columns\n",
    "cols"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d9eb2b5",
   "metadata": {},
   "source": [
    "### Function Definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3b9b9614",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Preparation (Filling NaN with values considering selected columns)\n",
    "def prepare_X(df, cols, fill_value):\n",
    "    df_num = df[cols]\n",
    "    df_num = df_num.fillna(fill_value, axis=0)\n",
    "    X = df_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f4e43b79",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Linear Regression Function Definition\n",
    "def train_linear_regression(X, y):\n",
    "    ones = np.ones(X.shape[0])\n",
    "    X = np.column_stack([ones, X])\n",
    "\n",
    "    XTX = X.T.dot(X)\n",
    "    XTX_inv = np.linalg.inv(XTX)\n",
    "    w = XTX_inv.dot(X.T).dot(y)\n",
    "    \n",
    "    return w[0], w[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "288d3928",
   "metadata": {},
   "outputs": [],
   "source": [
    "# RMSE Function Definition\n",
    "def rmse(y, y_pred):\n",
    "    error = y_pred - y\n",
    "    mse = (error ** 2).mean()\n",
    "    return np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf858cf0",
   "metadata": {},
   "source": [
    "### Train model using Linear Regression with data prepared by using fill_value with 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "97c65e02",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.34\n"
     ]
    }
   ],
   "source": [
    "# Train model using Linear Regression with data prepared by using fill_value with 0\n",
    "\n",
    "x_train_0 = prepare_X(df_train, cols, 0)\n",
    "w_0, w = train_linear_regression(x_train_0, y_train)\n",
    "\n",
    "y_pred_0 = w_0 + x_train_0.dot(w)\n",
    "\n",
    "train_rmse_0 = round(rmse(y_train, y_pred_0), 2)\n",
    "print(train_rmse_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "15c47b6d",
   "metadata": {
    "scrolled": false
   },
   "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(y_train, label='target', color='#222222', alpha=0.6, bins=40)\n",
    "sns.histplot(y_pred_0, label='prediction', color='#aaaaaa', alpha=0.8, bins=40)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Log(Price + 1)')\n",
    "plt.title('Predictions vs actual distribution')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9bdc608c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33\n"
     ]
    }
   ],
   "source": [
    "# Validate the model\n",
    "x_val_0 = prepare_X(df_val, cols, 0)\n",
    "y_val_pred_0 = w_0 + x_val_0.dot(w)\n",
    "\n",
    "val_rmse_0 = round(rmse(y_val, y_val_pred_0), 2)\n",
    "print(val_rmse_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "71211976",
   "metadata": {
    "scrolled": false
   },
   "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(y_val, label='target', color='#222222', alpha=0.6, bins=40)\n",
    "sns.histplot(y_val_pred_0, label='prediction', color='#aaaaaa', alpha=0.8, bins=40)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Log(Price + 1)')\n",
    "plt.title('Predictions vs actual distribution')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63ac7c03",
   "metadata": {},
   "source": [
    "### Train model using Linear Regression with data prepared by using fill_value = df_train's mean\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6f373521",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "533.4803317730147"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bedroom_mean =  df_train['total_bedrooms'].mean()\n",
    "bedroom_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "030bc129",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.34\n"
     ]
    }
   ],
   "source": [
    "# Train model using Linear Regression with data prepared by using fill_value with 0\n",
    "\n",
    "x_train_fill_mean = prepare_X(df_train, cols, bedroom_mean)\n",
    "w_0, w = train_linear_regression(x_train_fill_mean, y_train)\n",
    "\n",
    "y_pred_fill_mean = w_0 + x_train_fill_mean.dot(w)\n",
    "\n",
    "train_rmse_fill_mean = round(rmse(y_train, y_pred_fill_mean), 2)\n",
    "print(train_rmse_fill_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b19147d2",
   "metadata": {
    "scrolled": false
   },
   "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(y_train, label='target', color='#222222', alpha=0.6, bins=40)\n",
    "sns.histplot(y_pred_fill_mean, label='prediction', color='#aaaaaa', alpha=0.8, bins=40)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Log(Price + 1)')\n",
    "plt.title('Predictions vs actual distribution')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ded55f3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33\n"
     ]
    }
   ],
   "source": [
    "# Validate the model\n",
    "x_val_fill_mean = prepare_X(df_val, cols, bedroom_mean)\n",
    "y_val_pred_fill_mean = w_0 + x_val_fill_mean.dot(w)\n",
    "\n",
    "val_rmse_fill_mean = round(rmse(y_val, y_val_pred_fill_mean), 2)\n",
    "print(val_rmse_fill_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "8263ba50",
   "metadata": {
    "scrolled": false
   },
   "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(y_val, label='target', color='#222222', alpha=0.6, bins=40)\n",
    "sns.histplot(y_val_pred_fill_mean, label='prediction', color='#aaaaaa', alpha=0.8, bins=40)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Log(Price + 1)')\n",
    "plt.title('Predictions vs actual distribution')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "21f3311b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33\n"
     ]
    }
   ],
   "source": [
    "print(val_rmse_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "279016dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33\n"
     ]
    }
   ],
   "source": [
    "print(val_rmse_fill_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbf5ec66",
   "metadata": {},
   "source": [
    " Both options i.e. fill it with 0 or with the mean of this variable are **equally good**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf7ddc88",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "5162d9cc",
   "metadata": {},
   "source": [
    "## Question 4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4973ba12",
   "metadata": {},
   "source": [
    "- 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",
    "\n",
    "    0\n",
    "    0.000001\n",
    "    0.001\n",
    "    0.0001"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "922a1f59",
   "metadata": {},
   "source": [
    "### Function Definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f292cdf7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Preparation (Filling NaN with 0 considering selected columns)\n",
    "def prepare_X(df, cols):\n",
    "    df_num = df[cols]\n",
    "    df_num = df_num.fillna(0, axis=0)\n",
    "    X = df_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "629e03e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regularized Linear Regression Function Definition\n",
    "def train_linear_regression_reg(X, y, r=0.0):\n",
    "    ones = np.ones(X.shape[0])\n",
    "    X = np.column_stack([ones, X])\n",
    "\n",
    "    XTX = X.T.dot(X)\n",
    "    reg = r * np.eye(XTX.shape[0])\n",
    "    XTX = XTX + reg\n",
    "\n",
    "    XTX_inv = np.linalg.inv(XTX)\n",
    "    w = XTX_inv.dot(X.T).dot(y)\n",
    "    \n",
    "    return w[0], w[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b0fc61ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "# RMSE Function Definition\n",
    "def rmse(y, y_pred):\n",
    "    error = y_pred - y\n",
    "    mse = (error ** 2).mean()\n",
    "    return np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b72c12bc",
   "metadata": {},
   "source": [
    "### Train model using Regularized Linear Regression with data prepared by using 0 to fill NaN values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "01071af2",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = prepare_X(df_train, cols)\n",
    "X_val = prepare_X(df_val, cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "de29fe9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " r: 0\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.33\n",
      "\n",
      " r: 1e-06\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.33\n",
      "\n",
      " r: 0.0001\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.33\n",
      "\n",
      " r: 0.001\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.33\n",
      "\n",
      " r: 0.01\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.33\n",
      "\n",
      " r: 0.1\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.33\n",
      "\n",
      " r: 1\n",
      " Train RMSE: 0.35\n",
      " Val RMSE: 0.33\n",
      "\n",
      " r: 5\n",
      " Train RMSE: 0.35\n",
      " Val RMSE: 0.34\n",
      "\n",
      " r: 10\n",
      " Train RMSE: 0.35\n",
      " Val RMSE: 0.34\n",
      "\n"
     ]
    }
   ],
   "source": [
    "train_rmse = list()\n",
    "val_rmse = list()\n",
    "\n",
    "for r in [0, 0.000001, 0.0001, 0.001, 0.01, 0.1, 1, 5, 10]:\n",
    "    w_0, w = train_linear_regression_reg(X_train, y_train, r=r)\n",
    "    \n",
    "    # Train RMSE\n",
    "    y_train_pred_r =  w_0 + X_train.dot(w)\n",
    "    train_rmse.append((r, round(rmse(y_train, y_train_pred_r), 2)))\n",
    "    \n",
    "    # Validation RMSE\n",
    "    y_val_pred_r =  w_0 + X_val.dot(w)\n",
    "    val_rmse.append((r, round(rmse(y_val, y_val_pred_r), 2)))\n",
    "    \n",
    "    print(f\" r: {train_rmse[-1][0]}\")\n",
    "    print(f\" Train RMSE: {train_rmse[-1][1]}\")\n",
    "    print(f\" Val RMSE: {val_rmse[-1][1]}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd3e70c4",
   "metadata": {},
   "source": [
    "**r = 0** gives the smallest Validation RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42024c46",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "96fed6aa",
   "metadata": {},
   "source": [
    "## Question 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf3aa9b0",
   "metadata": {},
   "source": [
    "- 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. If it's low, then all values are approximately the same. If it's high, the values are different. If standard deviation of scores is low, then our model is stable.\n",
    "\n",
    "Options:\n",
    "\n",
    "    0.16\n",
    "    0.00005\n",
    "    0.005\n",
    "    0.15555"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0898ca4",
   "metadata": {},
   "source": [
    "### Function Definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c86a625f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def split_data(seed):\n",
    "    np.random.seed(seed)\n",
    "\n",
    "    n = housing.shape[0]  # Length of the dataframe\n",
    "\n",
    "    n_val = int(0.2 * n) # 20% of length of the dataframe\n",
    "    n_test = int(0.2 * n) # 20% of length of the dataframe\n",
    "    n_train = n - (n_val + n_test) # 60% of length of the dataframe \n",
    "\n",
    "    idx = np.arange(n) # Generate indices for dataframe \n",
    "    np.random.shuffle(idx) \n",
    "\n",
    "    df_shuffled = housing.iloc[idx] # Shuffled dataframe generated \n",
    "\n",
    "    df_train = df_shuffled.iloc[:n_train].copy() # Train Data\n",
    "    df_val = df_shuffled.iloc[n_train:n_train+n_val].copy() # Validation Data\n",
    "    df_test = df_shuffled.iloc[n_train+n_val:].copy() # Test Data\n",
    "    \n",
    "    y_train_orig = df_train['median_house_value'].values\n",
    "    y_val_orig = df_val['median_house_value'].values\n",
    "    y_test_orig = df_test['median_house_value'].values\n",
    "\n",
    "    y_train = np.log1p(y_train_orig)\n",
    "    y_val = np.log1p(y_val_orig)\n",
    "    y_test = np.log1p(y_test_orig)\n",
    "\n",
    "    del df_train['median_house_value']\n",
    "    del df_val['median_house_value']\n",
    "    del df_test['median_house_value']\n",
    "    \n",
    "    return (df_train, y_train), (df_val, y_val), (df_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "e8e25076",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Preparation (Filling NaN with values considering selected columns)\n",
    "def prepare_X(df, cols):\n",
    "    df_num = df[cols]\n",
    "    df_num = df_num.fillna(0, axis=0)\n",
    "    X = df_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "0bf6bc2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Linear Regression Function Definition\n",
    "def train_linear_regression(X, y):\n",
    "    ones = np.ones(X.shape[0])\n",
    "    X = np.column_stack([ones, X])\n",
    "\n",
    "    XTX = X.T.dot(X)\n",
    "    XTX_inv = np.linalg.inv(XTX)\n",
    "    w = XTX_inv.dot(X.T).dot(y)\n",
    "    \n",
    "    return w[0], w[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "bde1e301",
   "metadata": {},
   "outputs": [],
   "source": [
    "# RMSE Function Definition\n",
    "def rmse(y, y_pred):\n",
    "    error = y_pred - y\n",
    "    mse = (error ** 2).mean()\n",
    "    return np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4fdb5a9",
   "metadata": {},
   "source": [
    "### Train the Model and calculate RMSE Standard Deviation for the given seed values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "e355178a",
   "metadata": {},
   "outputs": [],
   "source": [
    "seed_values = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "79fd95e8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Seed: 0\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.34\n",
      "\n",
      " Seed: 1\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.34\n",
      "\n",
      " Seed: 2\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.33\n",
      "\n",
      " Seed: 3\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.34\n",
      "\n",
      " Seed: 4\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.34\n",
      "\n",
      " Seed: 5\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.34\n",
      "\n",
      " Seed: 6\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.35\n",
      "\n",
      " Seed: 7\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.34\n",
      "\n",
      " Seed: 8\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.35\n",
      "\n",
      " Seed: 9\n",
      " Train RMSE: 0.34\n",
      " Val RMSE: 0.34\n",
      "\n"
     ]
    }
   ],
   "source": [
    "seed_val_rmse = list()\n",
    "\n",
    "for seed in seed_values:\n",
    "    \n",
    "    print(f\" Seed: {seed}\")\n",
    "    \n",
    "    train, val, test = split_data(seed)\n",
    "    X_train = prepare_X(train[0], train[0].columns)\n",
    "    y_train = train[1]\n",
    "    w_0, w = train_linear_regression(X_train, y_train)\n",
    "\n",
    "    # Train RMSE\n",
    "    y_train_pred =  w_0 + X_train.dot(w)\n",
    "    print(f\" Train RMSE: {round(rmse(y_train, y_train_pred), 2)}\")\n",
    "    \n",
    "    \n",
    "    # Validation RMSE\n",
    "    X_val = prepare_X(val[0], val[0].columns)\n",
    "    y_val = val[1]\n",
    "    y_val_pred =  w_0 + X_val.dot(w)\n",
    "    seed_val_rmse.append(round(rmse(y_val, y_val_pred),2))\n",
    "    \n",
    "    print(f\" Val RMSE: {seed_val_rmse[-1]}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "b67e2ce6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.34, 0.34, 0.33, 0.34, 0.34, 0.34, 0.35, 0.34, 0.35, 0.34]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seed_val_rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "1fddf28d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005385164807134491"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seed_val_rmse_std = np.array(seed_val_rmse).std()\n",
    "seed_val_rmse_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3171eb9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6296a64e",
   "metadata": {},
   "source": [
    "### Question 6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ded489cc",
   "metadata": {},
   "source": [
    "- 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",
    "\n",
    "    0.35\n",
    "    0.135\n",
    "    0.450\n",
    "    0.245"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "64991d2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 9\n",
    "\n",
    "np.random.seed(seed)\n",
    "\n",
    "n = housing.shape[0]  # Length of the dataframe\n",
    "\n",
    "n_test = int(0.2 * n) # 20% of length of the dataframe\n",
    "n_train = n - (n_test) # 80% of length of the dataframe \n",
    "\n",
    "idx = np.arange(n) # Generate indices for dataframe \n",
    "np.random.shuffle(idx) \n",
    "\n",
    "df_shuffled = housing.iloc[idx] # Shuffled dataframe generated \n",
    "\n",
    "df_train = df_shuffled.iloc[:n_train].copy() # Train Data\n",
    "df_test = df_shuffled.iloc[n_train:].copy() # Test Data\n",
    "\n",
    "y_train_orig = df_train['median_house_value'].values\n",
    "y_test_orig = df_test['median_house_value'].values\n",
    "\n",
    "y_train = np.log1p(y_train_orig)\n",
    "y_test = np.log1p(y_test_orig)\n",
    "\n",
    "del df_train['median_house_value']\n",
    "del df_test['median_house_value']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56da18c8",
   "metadata": {},
   "source": [
    "### Function Definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "93c46eb0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Preparation (Filling NaN with values considering selected columns)\n",
    "def prepare_X(df, cols):\n",
    "    df_num = df[cols]\n",
    "    df_num = df_num.fillna(0, axis=0)\n",
    "    X = df_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2ebda99b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regularized Linear Regression Function Definition\n",
    "def train_linear_regression_reg(X, y, r):\n",
    "    ones = np.ones(X.shape[0])\n",
    "    X = np.column_stack([ones, X])\n",
    "\n",
    "    XTX = X.T.dot(X)\n",
    "    reg = r * np.eye(XTX.shape[0])\n",
    "    XTX = XTX + reg\n",
    "\n",
    "    XTX_inv = np.linalg.inv(XTX)\n",
    "    w = XTX_inv.dot(X.T).dot(y)\n",
    "    \n",
    "    return w[0], w[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "3947d3e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# RMSE Function Definition\n",
    "def rmse(y, y_pred):\n",
    "    error = y_pred - y\n",
    "    mse = (error ** 2).mean()\n",
    "    return np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d25e504",
   "metadata": {},
   "source": [
    "### Train the model and Calculate Test RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "7990b2cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = prepare_X(df_train, df_train.columns)\n",
    "X_test = prepare_X(df_test, df_test.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "a78d4c97",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r: 0.001\n",
      "Train RMSE: 0.34\n",
      "Test RMSE: 0.35\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_rmse = 0\n",
    "r=0.001\n",
    "\n",
    "print(f\"r: {r}\")\n",
    "\n",
    "w_0, w = train_linear_regression_reg(X_train, y_train, r)\n",
    "    \n",
    "# Train RMSE\n",
    "y_train_pred_r =  w_0 + X_train.dot(w)\n",
    "print(f\"Train RMSE: {round(rmse(y_train, y_train_pred_r), 2)}\")\n",
    "\n",
    "# Test RMSE\n",
    "y_test_pred_r =  w_0 + X_test.dot(w)\n",
    "test_rmse = round(rmse(y_test, y_test_pred_r), 2)\n",
    "    \n",
    "print(f\"Test RMSE: {test_rmse}\")\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12dd280e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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