linear-regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject\n",
      "  return f(*args, **kwds)\n",
      "/opt/anaconda/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject\n",
      "  return f(*args, **kwds)\n",
      "/opt/anaconda/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject\n",
      "  return f(*args, **kwds)\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined_data = pd.read_csv('data/combined_data/cleaned_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T</th>\n",
       "      <th>TM</th>\n",
       "      <th>Tm</th>\n",
       "      <th>H</th>\n",
       "      <th>PP</th>\n",
       "      <th>VV</th>\n",
       "      <th>V</th>\n",
       "      <th>VM</th>\n",
       "      <th>PM_2_5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>23.4</td>\n",
       "      <td>30.3</td>\n",
       "      <td>19.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.3</td>\n",
       "      <td>4.3</td>\n",
       "      <td>5.4</td>\n",
       "      <td>284.795833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>22.4</td>\n",
       "      <td>30.3</td>\n",
       "      <td>16.9</td>\n",
       "      <td>57.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.9</td>\n",
       "      <td>3.3</td>\n",
       "      <td>7.6</td>\n",
       "      <td>239.695455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>24.0</td>\n",
       "      <td>31.8</td>\n",
       "      <td>16.9</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.9</td>\n",
       "      <td>2.8</td>\n",
       "      <td>5.4</td>\n",
       "      <td>182.187500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>22.8</td>\n",
       "      <td>30.2</td>\n",
       "      <td>17.6</td>\n",
       "      <td>55.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.7</td>\n",
       "      <td>3.7</td>\n",
       "      <td>7.6</td>\n",
       "      <td>264.064286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>23.1</td>\n",
       "      <td>30.6</td>\n",
       "      <td>17.4</td>\n",
       "      <td>46.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.9</td>\n",
       "      <td>3.3</td>\n",
       "      <td>5.4</td>\n",
       "      <td>223.208333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      T    TM    Tm     H   PP   VV    V   VM      PM_2_5\n",
       "0  23.4  30.3  19.0  59.0  0.0  6.3  4.3  5.4  284.795833\n",
       "1  22.4  30.3  16.9  57.0  0.0  6.9  3.3  7.6  239.695455\n",
       "2  24.0  31.8  16.9  51.0  0.0  6.9  2.8  5.4  182.187500\n",
       "3  22.8  30.2  17.6  55.0  0.0  7.7  3.7  7.6  264.064286\n",
       "4  23.1  30.6  17.4  46.0  0.0  6.9  3.3  5.4  223.208333"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = combined_data.iloc[:, :-1]\n",
    "y = combined_data.iloc[:, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=43)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Coefficient of determination R^2 on train set 0.40130070313506305'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Coefficient of determination R^2 on train set {lin_reg.score(X_train, y_train)}'\n",
    "# must be close to 1, 1 is perfect fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Coefficient of determination R^2 on test set 0.32029156453105967'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Coefficient of determination R^2 on test set {lin_reg.score(X_test, y_test)}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-15.84230876,  -0.72209799,  -2.51152075,  -1.38818232,\n",
       "        -0.84155463,  -9.35371295, -11.32087403,   0.5496871 ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "763.0768032875101"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "score = cross_val_score(lin_reg, X, y, cv = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2838598029575895"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "        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>Coeff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>T</td>\n",
       "      <td>-15.842309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>TM</td>\n",
       "      <td>-0.722098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Tm</td>\n",
       "      <td>-2.511521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>H</td>\n",
       "      <td>-1.388182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>PP</td>\n",
       "      <td>-0.841555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>VV</td>\n",
       "      <td>-9.353713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>V</td>\n",
       "      <td>-11.320874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>VM</td>\n",
       "      <td>0.549687</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Coeff\n",
       "T  -15.842309\n",
       "TM  -0.722098\n",
       "Tm  -2.511521\n",
       "H   -1.388182\n",
       "PP  -0.841555\n",
       "VV  -9.353713\n",
       "V  -11.320874\n",
       "VM   0.549687"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(lin_reg.coef_, X.columns, columns=['Coeff'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Holding all other features fixed a 1 unit increase in T is associated with decrease of val in AQI PM2.5\n",
      "Holding all other features fixed a 1 unit increase in TM is associated with decrease of val in AQI PM2.5\n",
      "Holding all other features fixed a 1 unit increase in Tm is associated with decrease of val in AQI PM2.5\n",
      "Holding all other features fixed a 1 unit increase in H is associated with decrease of val in AQI PM2.5\n",
      "Holding all other features fixed a 1 unit increase in PP is associated with decrease of val in AQI PM2.5\n",
      "Holding all other features fixed a 1 unit increase in VV is associated with decrease of val in AQI PM2.5\n",
      "Holding all other features fixed a 1 unit increase in V is associated with decrease of val in AQI PM2.5\n",
      "Holding all other features fixed a 1 unit increase in VM is associated with increase of val in AQI PM2.5\n"
     ]
    }
   ],
   "source": [
    "c = 0\n",
    "for val in lin_reg.coef_:\n",
    "    effect = 'increase' if val>0 else 'decrease'\n",
    "    print(f'Holding all other features fixed a 1 unit increase in {X.columns[c]} is associated with {effect} of val in AQI PM2.5')\n",
    "    c = c+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = lin_reg.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f884a8b8d50>"
      ]
     },
     "execution_count": 18,
     "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": [
    "sns.distplot(y_test - pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Abs Error: 55.12183806894883\n",
      "Mean Sq Error: 5157.1723387446555\n",
      "Root Mean Error: 71.81345513721405\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "print(f\"Mean Abs Error: {metrics.mean_absolute_error(y_test, pred)}\")\n",
    "print(f\"Mean Sq Error: {metrics.mean_squared_error(y_test, pred)}\")\n",
    "print(f\"Root Mean Error: {np.sqrt(metrics.mean_squared_error(y_test, pred))}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "pickle.dump(lin_reg, open('linreg.pkl', 'wb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}