Simple_linear_regression_example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting sklearn\n",
      "Requirement already satisfied: scikit-learn in /anaconda3/lib/python3.6/site-packages (from sklearn) (0.21.1)\n",
      "Requirement already satisfied: joblib>=0.11 in /anaconda3/lib/python3.6/site-packages (from scikit-learn->sklearn) (0.13.2)\n",
      "Requirement already satisfied: numpy>=1.11.0 in /anaconda3/lib/python3.6/site-packages (from scikit-learn->sklearn) (1.16.3)\n",
      "Requirement already satisfied: scipy>=0.17.0 in /anaconda3/lib/python3.6/site-packages (from scikit-learn->sklearn) (1.3.0)\n",
      "Installing collected packages: sklearn\n",
      "Successfully installed sklearn-0.0\n"
     ]
    }
   ],
   "source": [
    "!pip install sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([5, 15, 25, 35, 45, 55]).reshape(-1, 1)\n",
    "y = np.array([5, 20, 14, 32, 22, 38])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5],\n",
       "       [15],\n",
       "       [25],\n",
       "       [35],\n",
       "       [45],\n",
       "       [55]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 1)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5, 20, 14, 32, 22, 38])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_sq = model.score(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficient of determination: 0.7158756137479542\n"
     ]
    }
   ],
   "source": [
    "print('coefficient of determination:', r_sq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sklearn.linear_model.base.LinearRegression"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: 5.633333333333329\n"
     ]
    }
   ],
   "source": [
    "print('intercept:', model.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope: [0.54]\n"
     ]
    }
   ],
   "source": [
    "print('slope:', model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted response:\n",
      "[ 8.33333333 13.73333333 19.13333333 24.53333333 29.93333333 35.33333333]\n"
     ]
    }
   ],
   "source": [
    "print('predicted response:', y_pred, sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model.intercept_ + model.coef_ * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33.75555555555555"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(y, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted response:\n",
      "[[ 8.33333333]\n",
      " [13.73333333]\n",
      " [19.13333333]\n",
      " [24.53333333]\n",
      " [29.93333333]\n",
      " [35.33333333]]\n"
     ]
    }
   ],
   "source": [
    "print('predicted response:', y_pred, sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#In practice, regression models are often applied for forecasts. \n",
    "#This means that you can use fitted models to calculate the outputs based on some other, new inputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_new = np.arange(5).reshape((-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0]\n",
      " [1]\n",
      " [2]\n",
      " [3]\n",
      " [4]]\n"
     ]
    }
   ],
   "source": [
    "print(x_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_new = model.predict(x_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.63333333 6.17333333 6.71333333 7.25333333 7.79333333]\n"
     ]
    }
   ],
   "source": [
    "print(y_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Here .predict() is applied to the new regressor x_new and yields the response y_new. \n",
    "#This example conveniently uses arange() from numpy to generate an array with the elements from 0 (inclusive) to 5 (exclusive), that is 0, 1, 2, 3, and 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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