Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn.metrics import r2_score, mean_absolute_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Calculates cost with regularization </h2>\n",
    "<h2> Note that $ \\theta_{0} $ is not included in the calculation of cost for regularization in the second summation</h2>\n",
    "<h1> $$ \\frac{1}{2m}( \\sum_{i=1}^m (h_{\\theta}(x^{(i)})-y^{(i)})^2) + \\frac{\\lambda}{2m} \\sum_{j=1}^n \\theta_j^2 $$ </h1>\n",
    "<h3> where m = number of training examples, $y^{(i)}$ and $x^{(i)}$ are training example i, $\\lambda$ is regularization constant </h3>\n",
    "<h3> $$h_{\\theta}(x^{(i)}) = \\theta_{0}+\\theta_{1}x^{(i)}_{1}+...+\\theta_{n}x^{(i)}_{n}$$ </h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_cost(theta, X, y, lbd): # theta is dimensions n x 1, X is dimensions m x n, y is dimensions m x 1\n",
    "    m = X.shape[0]\n",
    "    cost = (1/(2*m))*(np.square((np.matmul(X,theta.transpose()) - y))).sum() + (lbd/(2*m)) * np.square(theta).sum() # vectorized implementation of mean squared error as cost function\n",
    "    cost -= (lbd/(2*m)) * theta[0] ** 2 # theta zero is not regularized\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Vectorized implementation gradient calculation together with regularization </h2>\n",
    "<h2> Note that for $\\theta_{0}$, regularization is not needed </h2>\n",
    "<h1> $$ \\frac{\\partial J}{\\partial \\theta_{j}} = \\frac{1}{m} \\sum_{i=1}^m (h_{\\theta}(x^{(i)})-y^{(i)})x_{j}^{(i)} + \\frac{\\lambda}{m} \\theta_{j}$$ </h1>\n",
    "<h3> for j = 1,2,...,n where n is the number of weights theta, and m is the number of training examples </h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_grad(theta, X, y, lbd): # theta is dimensions n x 1, X is dimensions m x n, y is dimensions m x 1\n",
    "    m = X.shape[0]\n",
    "    grad = (1/m)*(np.matmul(np.matmul(X,theta.transpose()) - y,X) + lbd*theta) # vectorized implementation of gradient\n",
    "    grad[0] -= (1/m)*lbd*theta[0] # theta_zero is not regularized\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_reg(X_train, y_train, alpha, lbd, iterations, X_test=None, y_test=None): # X is dimensions m x n, y is dimensions m x 1, alpha is learning rate\n",
    "    theta = np.random.rand(X_train.shape[1]) # randomly initiates weights\n",
    "    m = X_train.shape[0]\n",
    "    costs_train = []\n",
    "    costs_test = []\n",
    "    for i in range(iterations):\n",
    "        costs_train.append(calculate_cost(theta, X_train, y_train, lbd))\n",
    "        theta -= alpha * calculate_grad(theta, X_train ,y_train, lbd)\n",
    "        if (X_test is not None and y_test is not None):\n",
    "            costs_test.append(calculate_cost(theta, X_test, y_test, lbd))\n",
    "    x_graph = np.arange(0,iterations,1);    \n",
    "    plt.plot(x_graph,costs_train, label='train') \n",
    "    if (X_test is not None and y_test is not None):\n",
    "        plt.plot(x_graph,costs_test, label='test')\n",
    "    plt.legend()\n",
    "    return theta    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(X,theta):\n",
    "    return np.matmul(X,theta.transpose())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_cost(X, y, theta):\n",
    "    pred = predict(X,theta)\n",
    "    plt.scatter(X[:,1],y)\n",
    "    plt.plot(X[:,1],pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(X, mean, std):\n",
    "    return (X-mean) / std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Applying linear regression model on data from kaggle </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>Gender</th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Index</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Male</td>\n",
       "      <td>174</td>\n",
       "      <td>96</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Male</td>\n",
       "      <td>189</td>\n",
       "      <td>87</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Female</td>\n",
       "      <td>185</td>\n",
       "      <td>110</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Female</td>\n",
       "      <td>195</td>\n",
       "      <td>104</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Male</td>\n",
       "      <td>149</td>\n",
       "      <td>61</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>Female</td>\n",
       "      <td>150</td>\n",
       "      <td>153</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>Female</td>\n",
       "      <td>184</td>\n",
       "      <td>121</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>Female</td>\n",
       "      <td>141</td>\n",
       "      <td>136</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>Male</td>\n",
       "      <td>150</td>\n",
       "      <td>95</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>Male</td>\n",
       "      <td>173</td>\n",
       "      <td>131</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Gender  Height  Weight  Index\n",
       "0      Male     174      96      4\n",
       "1      Male     189      87      2\n",
       "2    Female     185     110      4\n",
       "3    Female     195     104      3\n",
       "4      Male     149      61      3\n",
       "..      ...     ...     ...    ...\n",
       "495  Female     150     153      5\n",
       "496  Female     184     121      4\n",
       "497  Female     141     136      5\n",
       "498    Male     150      95      5\n",
       "499    Male     173     131      5\n",
       "\n",
       "[500 rows x 4 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/kaggle_height_weight_data.csv\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xd17fe2f160>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_height_weight = df.loc[df[\"Index\"] == 2,['Height','Weight']] # get height and weight for normal bmi\n",
    "df_height_weight.plot.scatter(x=\"Height\", y=\"Weight\", alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "height = df_height_weight['Height'].values\n",
    "weight = df_height_weight['Weight'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_height_weight['Height'].values\n",
    "normalized_X = normalize(X, X.mean(axis=0), X.std(axis=0))\n",
    "x_ones = np.ones(X.shape[0])\n",
    "normalized_X = np.stack((x_ones, normalized_X), 1)\n",
    "y = df_height_weight['Weight'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = linear_reg(normalized_X, y, 0.1, 0.1, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xd17ff9d8e0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred = predict(normalized_X,theta)\n",
    "plt.scatter(X,y)\n",
    "plt.plot(X,pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.284440470562946\n"
     ]
    }
   ],
   "source": [
    "print(mean_absolute_error(pred,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "68.20180950283819\n"
     ]
    }
   ],
   "source": [
    "height = (173-X.mean(axis=0)) / X.std(axis=0)\n",
    "print(predict(np.array([1,height]),theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>No</th>\n",
       "      <th>X1 transaction date</th>\n",
       "      <th>X2 house age</th>\n",
       "      <th>X3 distance to the nearest MRT station</th>\n",
       "      <th>X4 number of convenience stores</th>\n",
       "      <th>X5 latitude</th>\n",
       "      <th>X6 longitude</th>\n",
       "      <th>Y house price of unit area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2012.917</td>\n",
       "      <td>32.0</td>\n",
       "      <td>84.87882</td>\n",
       "      <td>10</td>\n",
       "      <td>24.98298</td>\n",
       "      <td>121.54024</td>\n",
       "      <td>37.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2012.917</td>\n",
       "      <td>19.5</td>\n",
       "      <td>306.59470</td>\n",
       "      <td>9</td>\n",
       "      <td>24.98034</td>\n",
       "      <td>121.53951</td>\n",
       "      <td>42.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>2013.583</td>\n",
       "      <td>13.3</td>\n",
       "      <td>561.98450</td>\n",
       "      <td>5</td>\n",
       "      <td>24.98746</td>\n",
       "      <td>121.54391</td>\n",
       "      <td>47.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2013.500</td>\n",
       "      <td>13.3</td>\n",
       "      <td>561.98450</td>\n",
       "      <td>5</td>\n",
       "      <td>24.98746</td>\n",
       "      <td>121.54391</td>\n",
       "      <td>54.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2012.833</td>\n",
       "      <td>5.0</td>\n",
       "      <td>390.56840</td>\n",
       "      <td>5</td>\n",
       "      <td>24.97937</td>\n",
       "      <td>121.54245</td>\n",
       "      <td>43.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>409</th>\n",
       "      <td>410</td>\n",
       "      <td>2013.000</td>\n",
       "      <td>13.7</td>\n",
       "      <td>4082.01500</td>\n",
       "      <td>0</td>\n",
       "      <td>24.94155</td>\n",
       "      <td>121.50381</td>\n",
       "      <td>15.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>410</th>\n",
       "      <td>411</td>\n",
       "      <td>2012.667</td>\n",
       "      <td>5.6</td>\n",
       "      <td>90.45606</td>\n",
       "      <td>9</td>\n",
       "      <td>24.97433</td>\n",
       "      <td>121.54310</td>\n",
       "      <td>50.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>411</th>\n",
       "      <td>412</td>\n",
       "      <td>2013.250</td>\n",
       "      <td>18.8</td>\n",
       "      <td>390.96960</td>\n",
       "      <td>7</td>\n",
       "      <td>24.97923</td>\n",
       "      <td>121.53986</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>412</th>\n",
       "      <td>413</td>\n",
       "      <td>2013.000</td>\n",
       "      <td>8.1</td>\n",
       "      <td>104.81010</td>\n",
       "      <td>5</td>\n",
       "      <td>24.96674</td>\n",
       "      <td>121.54067</td>\n",
       "      <td>52.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>413</th>\n",
       "      <td>414</td>\n",
       "      <td>2013.500</td>\n",
       "      <td>6.5</td>\n",
       "      <td>90.45606</td>\n",
       "      <td>9</td>\n",
       "      <td>24.97433</td>\n",
       "      <td>121.54310</td>\n",
       "      <td>63.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>414 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      No  X1 transaction date  X2 house age  \\\n",
       "0      1             2012.917          32.0   \n",
       "1      2             2012.917          19.5   \n",
       "2      3             2013.583          13.3   \n",
       "3      4             2013.500          13.3   \n",
       "4      5             2012.833           5.0   \n",
       "..   ...                  ...           ...   \n",
       "409  410             2013.000          13.7   \n",
       "410  411             2012.667           5.6   \n",
       "411  412             2013.250          18.8   \n",
       "412  413             2013.000           8.1   \n",
       "413  414             2013.500           6.5   \n",
       "\n",
       "     X3 distance to the nearest MRT station  X4 number of convenience stores  \\\n",
       "0                                  84.87882                               10   \n",
       "1                                 306.59470                                9   \n",
       "2                                 561.98450                                5   \n",
       "3                                 561.98450                                5   \n",
       "4                                 390.56840                                5   \n",
       "..                                      ...                              ...   \n",
       "409                              4082.01500                                0   \n",
       "410                                90.45606                                9   \n",
       "411                               390.96960                                7   \n",
       "412                               104.81010                                5   \n",
       "413                                90.45606                                9   \n",
       "\n",
       "     X5 latitude  X6 longitude  Y house price of unit area  \n",
       "0       24.98298     121.54024                        37.9  \n",
       "1       24.98034     121.53951                        42.2  \n",
       "2       24.98746     121.54391                        47.3  \n",
       "3       24.98746     121.54391                        54.8  \n",
       "4       24.97937     121.54245                        43.1  \n",
       "..           ...           ...                         ...  \n",
       "409     24.94155     121.50381                        15.4  \n",
       "410     24.97433     121.54310                        50.0  \n",
       "411     24.97923     121.53986                        40.6  \n",
       "412     24.96674     121.54067                        52.5  \n",
       "413     24.97433     121.54310                        63.9  \n",
       "\n",
       "[414 rows x 8 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "No                                        0\n",
       "X1 transaction date                       0\n",
       "X2 house age                              0\n",
       "X3 distance to the nearest MRT station    0\n",
       "X4 number of convenience stores           0\n",
       "X5 latitude                               0\n",
       "X6 longitude                              0\n",
       "Y house price of unit area                0\n",
       "dtype: int64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/kaggle_real_estate_prices.csv\",index_col=None)\n",
    "display(df)\n",
    "display(df.isnull().sum()) # check for nan values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "train=df.sample(frac=0.9,random_state=0) #random state is a seed value\n",
    "test=df.drop(train.index)\n",
    "\n",
    "train_x = train.loc[:,df.columns != \"Y house price of unit area\"]\n",
    "train_y = train.loc[:,\"Y house price of unit area\"]\n",
    "test_x = test.loc[:,df.columns != \"Y house price of unit area\"]\n",
    "test_y = test.loc[:,\"Y house price of unit area\"]\n",
    "\n",
    "train_mean = train_x.mean(axis=0) # mean normalization\n",
    "train_std = train_x.std(axis=0)\n",
    "train_x = normalize(train_x,train_mean ,train_std)\n",
    "test_x = normalize(test_x,train_mean ,train_std )\n",
    "\n",
    "train_x.insert(0, 'One', 1) # adding column of ones for theta that is independent of features\n",
    "test_x.insert(0, 'One', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([38.06033037, -0.59095602,  1.29302486, -3.44991947, -4.84111204,\n",
       "        2.6980591 ,  3.57121424,  0.52307292])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = linear_reg(train_x.values, train_y.values, 0.05, 0, 200, test_x.values, test_y.values)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = predict(test_x.values, theta)\n",
    "print(mean_absolute_error(pred,test_y))\n",
    "print(max(test_y) - min(test_y))\n",
    "print('r2 Score : ', r2_score(test_y, pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "reg = LinearRegression()\n",
    "reg.fit (train_x.values, train_y.values)\n",
    "y_pred = reg.predict(test_x)\n",
    "print('r2 Score : ', r2_score(test_y, y_pred))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}