{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import the libraries and packages we need\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#we are going to create two arrays that have our data. These should be the same length\n",
    "\n",
    "x = np.array([10,40,25,30,55,18,7]).reshape(-1,1) #we have to use reshape because we are required to pass in x \n",
    "                                                  #as a 2-dimensional array. One column and as many rows as necessary\n",
    "y = np.array([5,18,22,45,60,34,19])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10]\n",
      " [40]\n",
      " [25]\n",
      " [30]\n",
      " [55]\n",
      " [18]\n",
      " [ 7]]\n",
      "[ 5 18 22 45 60 34 19]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 1)\n",
      "(7,)\n"
     ]
    }
   ],
   "source": [
    "print(x.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#we now create our model instance. We are just going to use the default parameters\n",
    "#we also are going to fit the model\n",
    "#this calculates the values for the slope and intercept in our regression equation\n",
    "model = LinearRegression().fit(x,y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-squared:  0.5034536744482078\n"
     ]
    }
   ],
   "source": [
    "#now we can see the results\n",
    "#first our r-squared\n",
    "r_sq = model.score(x,y)\n",
    "print(\"r-squared: \",r_sq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept:  8.420731707317064\n",
      "slope:  [0.77867502]\n"
     ]
    }
   ],
   "source": [
    "#we can also find our intercept and slope\n",
    "intercept = model.intercept_\n",
    "slope = model.coef_\n",
    "print(\"intercept: \",intercept)\n",
    "print(\"slope: \",slope)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#now we can find our predicted values\n",
    "y_predicted = model.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16.20748187, 39.56773237, 27.88760712, 31.7809822 , 51.24785761,\n",
       "       22.436882  , 13.87145682])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#we can now create our regression equation\n",
    "y_predicted = intercept + slope*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1114dcd0>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#now we can plot the \n",
    "fig,ax = plt.subplots(figsize=(10,10))\n",
    "plt.scatter(x,y)\n",
    "plt.plot(x,y_predicted)"
   ]
  },
  {
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}