codes/ML/linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PIBzTWnCk94D"
   },
   "source": [
    "                                    All rights reserved © Global AI Hub 2020 \n",
    "![](img/global.jpeg)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xAFYL8FOC3EX"
   },
   "source": [
    "# What is Regression?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ObZajM_LDfze"
   },
   "source": [
    "Regression analysis is one of the most important fields in statistics and machine learning. There are many regression methods available. Linear regression is one of them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tp0RCvw-D0jq"
   },
   "source": [
    "Regression searches for relationships among variables. For example, you can observe several employees of some company and try to understand how their salaries depend on the features, such as experience, level of education, role, city they work in, and so on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "t7TUcDz4HyB4"
   },
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pcJ2U0sUIAzn"
   },
   "source": [
    "Linear regression is probably one of the most important and widely used regression techniques. It’s among the simplest regression methods. One of its main advantages is the ease of interpreting results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Fh3LdXkTI2Ns"
   },
   "source": [
    "When implementing linear regression of some dependent variable 𝑦 on the set of independent variables 𝐱 = (𝑥₁, …, 𝑥ᵣ), where 𝑟 is the number of predictors, you assume a linear relationship between 𝑦 and 𝐱: 𝑦 = 𝛽₀ + 𝛽₁𝑥₁ + ⋯ + 𝛽ᵣ𝑥ᵣ + 𝜀. This equation is the regression equation. 𝛽₀, 𝛽₁, …, 𝛽ᵣ are the regression coefficients, and 𝜀 is the random error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gBea82xsJZuh"
   },
   "source": [
    "## Simple Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "CDXdTosaJfFJ"
   },
   "source": [
    "Simple or single-variate linear regression is the simplest case of linear regression with a single independent variable, 𝐱 = x. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "HJMakg8FJ0oi"
   },
   "source": [
    "![image.png](data:image/png;base64,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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DesNbbSCK7iA"
   },
   "source": [
    "The estimated regression function (red line) has the equation:\n",
    "$$f(x) = b_o + 𝑏_1x$$ \n",
    "\n",
    "Our goal is to calculate the optimal values of the predicted weights 𝑏₀ and 𝑏₁ that minimize the sum of squared residuals (SSR) and determine the estimated regression function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cBlpRHffLQTp"
   },
   "source": [
    "## Multiple Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JTXLFFmILXvG"
   },
   "source": [
    "Multiple or multivariate linear regression is a case of linear regression with two or more independent variables.\n",
    "\n",
    "If there are just two independent variables, the estimated regression function is:   \n",
    "$$f(x_1,x_2) = b_0 + b_1x_1 + b_2x_2$$\n",
    "It represents a regression plane in a three-dimensional space. The goal of regression is to determine the values of the weights 𝑏₀, 𝑏₁, and 𝑏₂ such that this plane is as close as possible to the actual responses and yield the minimal SSR."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](lin1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nM-uW1kShW0b"
   },
   "source": [
    "## Polynomial Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SrKnG8HMhZE3"
   },
   "source": [
    "You can regard polynomial regression as a generalized case of linear regression. You assume the polynomial dependence between the output and inputs and, consequently, the polynomial estimated regression function.\n",
    "\n",
    "In other words, in addition to linear terms like 𝑏₁𝑥₁, your regression function 𝑓 can include non-linear terms such as 𝑏₂𝑥₁², 𝑏₃𝑥₁³, or even 𝑏₄𝑥₁𝑥₂, 𝑏₅𝑥₁²𝑥₂, and so on.\n",
    "\n",
    "\n",
    "The simplest example of polynomial regression has a single independent variable, and the estimated regression function is a polynomial of degree 2:\n",
    "$$ f(x) = b_o + b_1x + b_2x^2$$\n",
    "\n",
    "- Kernel Trick\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QrisOngVj_Gm"
   },
   "source": [
    "## Simple Linear Regression With scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8FrcERYtmqOW"
   },
   "source": [
    "### Create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 141
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 946,
     "status": "ok",
     "timestamp": 1600455328617,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "FqECs48CC0Tg",
    "outputId": "8a823499-d4ad-4da9-c550-76783a1486d3"
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression\n",
    "\n",
    "X, y = make_regression(n_samples=100, n_features=1, noise=5,random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x138d8204b50>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD4CAYAAAAEhuazAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAay0lEQVR4nO3dcZCc9X3f8fdHx4JXdsqRWrXRgSLcYjEQEqm+we5onA6YWNiNjaCJgbZuXDJVPGM6gXqUkUImEDseNJUT6NROXLn2NFMTI2rgrBY7AgITT5nI4eSTEQKUAsbAQfE5oNhBhzjdffvH7R57e8+zt3u3zz7P3vN5zdxw+zy79/zYge/+9vt8f9+fIgIzMyuXVXkPwMzMes/B38yshBz8zcxKyMHfzKyEHPzNzErolLwH0I63v/3tsX79+ryHYWbWVw4ePPjjiFiTdK4vgv/69esZHR3NexhmZn1F0g/TzjntY2ZWQg7+ZmYl5OBvZlZCDv5mZiXk4G9mVkJ9Ue1jZlY2I2Pj7N5/lBePTbJ2sMr2LRvYummoa3/fwd/MrGBGxsbZefdhJqemARg/NsnOuw8DdO0DwGkfM7OC2b3/6Fzgr5ucmmb3/qNdu0amM39JG4C9DYfeBfweMAj8e2Cidvx3IuJbWY7FzKxbsk7JvHhssqPjS5Fp8I+Io8BGAEkDwDhwD/DvgFsj4vNZXt/MrNt6kZJZO1hlPCHQrx2sduXvQ2/TPh8Ano6I1OXGZmZF14uUzPYtG6hWBuYdq1YG2L5lQ9eu0cvgfzXw9YbH10l6VNJXJZ3R/GRJ2ySNShqdmJhoPm1mlotepGS2bhrilisvZGiwioChwSq3XHlhV1NL6sUevpJOBV4ELoiIlyW9A/gxEMBngTMj4tq01w8PD4cbu5lZEWze9WBiSmZosMrDOy7JYUTpJB2MiOGkc72a+X8I+F5EvAwQES9HxHREzABfBi7q0TjMzJYlKSVTGRCvvHaC9TvuZf2Oe9n0mfsYGRvPaYTt6VXwv4aGlI+kMxvOXQE81qNxmJktS3NK5ozVFaang8mpmbnnvHp8iu3f+H6hPwAyT/tIeivwHPCuiPi72rH/wWwVUADPAr8ZES+l/Q2nfcysqNLSQJB/KqhV2ifzFb4R8RrwD5uOfTzr65qZ9UKrG73dvAncbV7ha2a2DK1q77tZl99tDv5mZsuwfcsGKqu04HhlQF2ty+82N3YzM1uGeu39zfuOcGxyCpi9CXzTRy7oal1+tzn4m5k1WErfnq2bhgod6JM4+JuZ1bTTt6f5w+Hi89bw0JMTmTV5y0pPVvgul0s9zawXFlu92/zhkETM1rAPFeCDoAgrfM3MCm+xvj1JTd2a1afT9W8NRV3o5eBvZlaTVppZP95p3X63u312k4O/mVnNYq2Ul1K3X9SFXg7+ZmY1i7VSTvpwWExRF3q52sfMrEGrss368aRqn/Fjk3M3e+u6vQFLNzn4m5l1oNWHQ9Z7+3aTg7+ZWZf002Iv5/zNzErIwd/MrIQc/M3MSsjB38yshDK/4SvpWeCnwDRwMiKGJf0ssBdYz+w2jh+LiFezHouZmc3q1cz/4ojY2NBgaAfwFxFxLvAXtcdmZtYjeaV9Lgf+tPb7nwJbcxqHmVkp9aLOP4D7JAXwXyNiD/COiHipdv7/Ae9ofpGkbcA2gHXr1vVgmGZWZGkLqPppYVWRZN7PX9JQRIxL+kfA/cB/APZFxGDDc16NiDPS/ob7+ZuVW1If/WplgH/5niHuOji+4HhjP54ya9XPP/OZf0SM1/75I0n3ABcBL0s6MyJeknQm8KOsx2Fm/ac+q0/aYGVyapqvf/d5ppsmsPU2yg7+rWWa85f0Vkk/U/8d+CDwGLAP+PXa034d+GaW4zCz/lOf7ScF/rrmwF9X1DbKRZL1zP8dwD2S6tf6s4j4c0mPAHdK+g3gh8DHMh6HmRVUWs6+nV2zVglmEuJ/UdsoF0mmwT8ingF+MeH43wIfyPLaZlZ8rTZMb2f2ftopqwAtyPkXtY1ykXiFr5nlJml2X8/ZtzN7f31qpuXmK5bOLZ3NLDetNky/9aqNCyp8mq0drPZVG+UicfA3s55qzPGnqQd1YK7ap592yeoHDv5m1jNJ9frNKqs0F9QbZ/VezNVdzvmbWc+0U8HztreckhjUt24a4uEdl3DrVRsBuGHvITbvepCRsfEshrriOfibWc+0U8Fz7PhU6rnG2v9gtjro+r2H2PSZ+/wh0CEHfzPrmXYqeAZXV1LPpX1zePX4FDvvPuwPgA44+JtZz2zfsoFqZaDlc/7+9ZOpQbzVN4d6iai1xzd8zawn6jdsJ6emGZCYjlhQwQMwNRNzQbz5Bu/awWrLdg9u69A+z/zNLHPNfXqmI6hWBhYE/rr6St/G3P7Ouw9z8XlrWn5zcFuH9jn4m1nm0lbyDsz2/VpgQEp8/kNPTnDLlRcyWF14X8B1/51x8DezzKWlY+rfABpVKwMtu3Vu3TTEoZs+yG1XbXRbh2Vwzt/MuippMVZarn6odr75+Wk9/BvTOm7rsDwO/mbWNWldOtN23Kqv0k0K4kk7dzmt0z1O+5hZ16Tl9uu5+nbTNFs3DblbZ8Y88zezrmnVpbPTNI3TOtnyzN/Muiat1NIlmMWTWfCXdLakhyQ9LumIpN+qHb9Z0rikQ7WfD2c1BjPrnZGxcY6/cXLBcefqiynLtM9J4NMR8b3aJu4HJd1fO3drRHw+w2ubWQ+ltWoerFa4+aMXOH1TQJkF/4h4CXip9vtPJT0B+L8As4JaTr/8tIZrbz0tuT2z5a8nOX9J64FNwHdrh66T9Kikr0o6I+U12ySNShqdmJjoxTDNSiupVXInXTJb3ei1Ysq82kfS24C7gOsj4ieS/gT4LLP9nD4L/CFwbfPrImIPsAdgeHg4rQWImS1R40x/Va3RWqN6l8zGmXvat4O0RVy+0Vtcmc78JVWYDfy3R8TdABHxckRMR8QM8GXgoizHYGYLNc/0W7VTSHtN47eDpFbNvtFbbFlW+wj4CvBERPxRw/EzG552BfBYVmMws2TtbKcI82fuN+87kriAq/7twIuy+kuWaZ/NwMeBw5IO1Y79DnCNpI3Mpn2eBX4zwzGYWYJWPfHrGjdSHxkb59hk8vaK9W8HXpTVX7Ks9vk/QFK/1m9ldU0za89AQo6/WeNG6q12yHJevz95ha9ZCS0W+GH+Ruqtqnac1+9PDv5mJTTUxmy9cUafNrs/Y3XFqZ4+5eBvVkKLzdbV9Jykah4Brx6fYvOuB9teD2DF4eBvVkJbNw1xxuqFWyHW/ev3rZs3o2+s5gHmbbze6YIwKwYHf7MSGhkbJyntL+DfvG8df7D1wgXntm4a4uEdlzA0WF2w8Xq95NP6h4O/WcnUF2s1l26u0uxs/qEnJ1rO4t3KYWXwZi5mK1xzS4bXTpxMXOA1U5vO19M4QOLNXLdyWBk88zdboUbGxtn4+/dx/d5D81oypC3WatQqjeNWDiuDZ/5mfao+ox8/Njm3aGuo1mwNFm6A3qm0NE7jwq+ltH+2YnDwN+tDzZun1Bdt1VM2p52yalmBH1qncdzKof85+Jv1oaQma3WTU9MdB/5VejPnD07jlIGDv1mfadVkbalOr1ZYfeopTuOUiIO/WZ9pp57+jNUVXp+aafsbwLHjU4z93geXOzTrIw7+ZgXXXKq5WDvmamWAmz5yAfDmTdnB1RX+/vWTTM0kN3RzmWb5OPibFVjzjd3xY5PzWis0E/BP153O7/+vI7xa68o5WK3MfRjcvO/IgpSR8/vl5Dp/swJL2nErSN4oo37u4adfmQv8AMcmp9j+P78PwKGbPshtV230jluW38xf0mXAfwYGgP8WEbvyGotZUTSmeAZXV+YF8UaLd+Ofb2om5rZbdJmmQU7BX9IA8EXgl4EXgEck7YuIx/MYj1kRNKd40gI/vNmPv53tGOvce8ca5TXzvwh4KiKeAZB0B3A54OBvpdO4UrcdjTn65lW8re4H+KauNcor+A8Bzzc8fgF4b+MTJG0DtgGsW7eudyMz66Hm2X47mnP0jZVAF5+3hr2PPM/U9PyPgMbN2M2gwNU+EbEH2AMwPDzcaYrTLHPNJZitFkal9eE5/kZyh800g9U3t01Mu/7wz/3sgmqfmz96gfP8Nk9ewX8cOLvh8Vm1Y2Z9IakEM60Ncqs+PJ167Y2Tc732W13fgd4Wk1fwfwQ4V9I5zAb9q4F/ldNYzDqWVILZ2Aa5nf75i2nutwMwNR1z10i7vgO/tSOXOv+IOAlcB+wHngDujIgjeYzFbCnSKmfqM/BO++c3qlYGuO2qjYnbLNav7d20bLlyW+QVEd+KiHdHxD+OiM/lNQ6zpUirnBmQOp7lq2HF1mC1MndDN+0aawerLc+ZtcMrfM2WIG03q+m06XoLjS85cXJm0Wts37LBu2nZsjn4my3B1k1D3HLlhQvaJAx1MPMe0MImDY33DdKuUb+hm3bOrB2KJcxUem14eDhGR0fzHoZZSyNj4/NKLJdKwA92/YvuDMpKTdLBiBhOOlfYOn+zImuusb/4vDXcdXC8o3x/vd6/mfP21gsO/mYdSqrxv/3Acx03W5uOoFoZmPeB4by99Ypz/mYdSmuz3KnG+wTO21uveeZv1qFOa+mTmq1VBjTXjsHB3vLgmb9ZhzrNyZ9erTBYrcw9PmN1hd2/+osO+pYrz/zNOrR9y4YFnTibc/eNjk1O8ayrd6xgPPM361CnNf6CuWZsZkXhmb+VWidtmRsl5epHf/gKXzvw3ILnBrjhmhWOg7+VVjttmTv5cHjoyYnUa7nhmhWN0z5WWou1Za5/ODR26Lxh7yF+d+Rw4t9rFeBXSZyz414273rQKSArBAd/K61WbZFHxsa5Ye+hxHr+rx14LvEDoFUV0HTE3AfIzrsP+wPAcufgb6WVFqzfUlnF9XsPtVy4dfuB5xYE8KROm0kav12Y5cXB30orKVhXVonJqZmUV7ypfhO3UVIVUBrfA7C8+YavlVb9xm39hu7p1Qo/eb39jpxJAby5CmjzrgcT9+p18zbLWyYzf0m7JT0p6VFJ90garB1fL2lS0qHaz5eyuL5Zu7ZuGuLhHZdw61UbOXFyZsGeua20E8C96YoVVVZpn/uBn4+IXwD+BtjZcO7piNhY+/lkRtc360hS5U8rA6vUVgD3pitWVJmkfSLivoaHB4BfzeI6Zt3SaQ5+ZibaDuBu3mZF1IsbvtcC3254fI6kMUl/Ken9aS+StE3SqKTRiYn0xTNm3dBpDr74+9+Ztbbk4C/pAUmPJfxc3vCcG4GTwO21Qy8B6yJiE/AfgT+T9A+S/n5E7ImI4YgYXrNmzVKHaSvcyNg4m3c9uOwFVNu3bGDhjrrpkvbfNesnS077RMSlrc5L+gTwK8AHorZRcEScAE7Ufj8o6Wng3YA36LWOtdOeofn5za0a4M1qn05m89e89+xlj98sT5nk/CVdBvw28M8j4njD8TXAKxExLeldwLnAM1mMwVa+Vu0ZmoN/0gfF9m98HwKmFinxeeupA7w+NcN0BAMS17z3bP5g64Xd/Zcx67Gs6vy/AJwG3K/Zr8cHapU9vwR8RtIUMAN8MiJeyWgMtsK1as/QaGRsnE/f+f0Fm6VPTS8+169WBvjcFa7OsZUnq2qff5Jy/C7griyuaeWzdrC66AKq+oy/OfAvRrW/026LZ7N+4xW+1rfSdtRqrL/vtH4fZmvxH95xSdfGaVZEDv7Wt5rbMyTN1JO+GbTi1bdWFg7+1tdaLaAaGRtHtF+TP+Q0j5WIg7+tWLv3H+0o8DvVY2Xils62YrXbssGpHisjB39bsdJaNpyxuuJGa1Z6TvtY7jrZJL0TadVAN33kAgd7Kz1Fh/XPeRgeHo7RUXeAWImaV94Cczdpu3EDNqsPFrN+IOlgRAwnnfPM33KVVIdfn4409+ppFcjTzrmdslkyB3/L1WI3ZRs3O09r4tbqnAO/WTIHf8tVWouGRi8em2zZxK3+e9I5B3+zZK72sVwl7XHbbO1gtWUTt3YbvJnZmxz8LRf1TVhu2HuIt1RWMVitACzYUKVeg59Wtrl2sNrynJklc9rHeq65wufV41NUKwPcdtVGIL1XT6smbos1eDOz+Rz8LROtKnNa5e8f3nFJYp6+nSZuLuk0a5+Dv3XdYtsrLjVH36ps0yWdZp1xzt+6brHKHOfozfKXWfCXdLOkcUmHaj8fbji3U9JTko5K2pLVGCwfi83skyp8nKM3662s0z63RsTnGw9IOh+4GrgAWAs8IOndEdHZdktWWIttr9hO/t7MspVHzv9y4I6IOAH8QNJTwEXAX+UwFluGtJu6aQ3VLj5vDZt3PeiAb1YAWQf/6yT9W2AU+HREvAoMAQcanvNC7dg8krYB2wDWrVuX8TCtU4vd1IX5M/uLz1vDXQfH3YLBrCCW1dVT0gPAOxNO3chsgP8xs326PgucGRHXSvoCcCAivlb7G18Bvh0R30i7jrt6Fs/mXQ8mpnbSdsTq9PlmtnyZdfWMiEvbHMCXgf9dezgOnN1w+qzaMesjnZZrugWDWbFkWe1zZsPDK4DHar/vA66WdJqkc4Bzgb/OahyWjXbLNettHNK+X7q80ywfWdb5/ydJhyU9ClwM3AAQEUeAO4HHgT8HPuVKn/7TTrlm/b5AWtdOl3ea5SezG74R8fEW5z4HfC6ra1v22m230LzYq64bu3SZ2dK5vYMt2WItFdLy+QLf5DXLmds7WGbcxsGsuBz8LTNu42BWXE772KJatWduxW0czIrLwd8WaAz2p1crvPbGSaamZ4s1O12Z61bLZsXktI/N87sjh7lh7yHGj00SwLHJqbnAX9fYntnM+pODv80ZGRvn9gPPpS7IauSVuWb9zcHf5uzef7StwA+u2DHrdw7+Nqfd2XxllVyxY9bnHPxtTruz+be95RTfxDXrcw7+NiepLj/JseNTPRiNmWXJpZ42p7kuf5XEdMJ+D873m/U/B3+bp7Euv3m3LvAKXbOVwsF/BVjqCtzFeIWu2crl4N/n2tlLdzm8QtdsZfIN3z6X1DPfK3DNbDEO/n3Oe+Oa2VJkEvwl7ZV0qPbzrKRDtePrJU02nPtSFtcvk7TKmwA273qQkbHx3g7IzPpCJjn/iLiq/rukPwT+ruH00xGxMYvrltH2LRsWVOTUdTv/b2YrR6ZpH0kCPgZ8PcvrlNnWTUPccuWFDKV8A3D+38ySZJ3zfz/wckT834Zj50gak/SXkt6f9kJJ2ySNShqdmJjIeJj9beumIR7ecQlKOe/8v5k1W3LaR9IDwDsTTt0YEd+s/X4N82f9LwHrIuJvJb0HGJF0QUT8pPmPRMQeYA/A8PBwu80mS23tYJXxhEDvFblm1mzJwT8iLm11XtIpwJXAexpecwI4Ufv9oKSngXcDo0sdh70pKf/vFblmliTLRV6XAk9GxAv1A5LWAK9ExLSkdwHnAs9kOIZS8YpcM2tXlsH/ahbe6P0l4DOSpoAZ4JMR8UqGY+hrS2nb4BW5ZtaOzIJ/RHwi4dhdwF1ZXXMlybptg5mVm3v7FER9lj9+bJKBlFbK9bJNB38zWy4H/wJonuUnBf46l22aWTe4t08BJDVnS+OyTTPrBgf/Amh3Nu+yTTPrFgf/AmhnNj80WOWWKy90vt/MusLBvwBabZxerQxw21UbeXjHJQ78ZtY1vuFbAI2LsxqrfYa8SMvMMuLgXxBenGVmveS0j5lZCTn4m5mVkIO/mVkJOfibmZWQg7+ZWQk5+JuZlZCDv5lZCTn4m5mVkIO/mVkJLSv4S/o1SUckzUgabjq3U9JTko5K2tJw/LLasack7VjO9c3MbGmWO/N/DLgS+E7jQUnnM7uH7wXAZcAfSxqQNAB8EfgQcD5wTe25ZmbWQ8vq7RMRTwBIaj51OXBHRJwAfiDpKeCi2rmnIuKZ2uvuqD338eWMw8zMOpNVzn8IeL7h8Qu1Y2nHF5C0TdKopNGJiYmMhmlmVk6LzvwlPQC8M+HUjRHxze4PaVZE7AH2AAwPD6dvamtmZh1bNPhHxKVL+LvjwNkNj8+qHaPFcTMz65Gs0j77gKslnSbpHOBc4K+BR4BzJZ0j6VRmbwrvy2gMZmaWYlk3fCVdAfwXYA1wr6RDEbElIo5IupPZG7kngU9FxHTtNdcB+4EB4KsRcWRZ/wZmZtYxRRQ/nT48PByjo6N5D8PMrK9IOhgRw0nnvMLXzKyEHPzNzErIwd/MrIQc/M3MSsjB38yshJZV6ll0I2Pj7N5/lBePTbJ2sMr2LRvYuimxm4SZWams2OA/MjbOzrsPMzk1DcD4sUl23n0YwB8AZlZ6Kzbts3v/0bnAXzc5Nc3u/UdzGpGZWXGs2OD/4rHJjo6bmZXJig3+awerHR03MyuTFRv8t2/ZQLUyMO9YtTLA9i0bchqRmVlxrNgbvvWbuq72MTNbaMUGf5j9AHCwNzNbaMWmfczMLJ2Dv5lZCTn4m5mVkIO/mVkJOfibmZVQX2zjKGkC+GHe4+iBtwM/znsQBeL3Yz6/H/P5/Zgv6f34uYhYk/Tkvgj+ZSFpNG2/zTLy+zGf34/5/H7M1+n74bSPmVkJOfibmZWQg3+x7Ml7AAXj92M+vx/z+f2Yr6P3wzl/M7MS8szfzKyEHPzNzErIwb9gJO2W9KSkRyXdI2kw7zHlSdKvSToiaUZSKcv6JF0m6aikpyTtyHs8eZP0VUk/kvRY3mMpAklnS3pI0uO1/1d+q53XOfgXz/3Az0fELwB/A+zMeTx5ewy4EvhO3gPJg6QB4IvAh4DzgWsknZ/vqHL334HL8h5EgZwEPh0R5wPvAz7Vzn8jDv4FExH3RcTJ2sMDwFl5jidvEfFERBzNexw5ugh4KiKeiYg3gDuAy3MeU64i4jvAK3mPoygi4qWI+F7t958CTwCLbmTi4F9s1wLfznsQlqsh4PmGxy/Qxv/YVk6S1gObgO8u9twVvZNXUUl6AHhnwqkbI+KbtefcyOzXudt7ObY8tPN+mFlrkt4G3AVcHxE/Wez5Dv45iIhLW52X9AngV4APRAkWYiz2fpTcOHB2w+OzasfM5kiqMBv4b4+Iu9t5jdM+BSPpMuC3gY9GxPG8x2O5ewQ4V9I5kk4Frgb25TwmKxBJAr4CPBERf9Tu6xz8i+cLwM8A90s6JOlLeQ8oT5KukPQC8M+AeyXtz3tMvVS7+X8dsJ/ZG3l3RsSRfEeVL0lfB/4K2CDpBUm/kfeYcrYZ+DhwSS1mHJL04cVe5PYOZmYl5Jm/mVkJOfibmZWQg7+ZWQk5+JuZlZCDv5lZCTn4m5mVkIO/mVkJ/X+MIxyoPHe+gwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dwT8MuDxmi8v"
   },
   "source": [
    "### Import Scikit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LQUftsJ6C0e1"
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7lgOFL7xmw6I"
   },
   "source": [
    "### Create a model & fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "c9pvWB2xC0HP"
   },
   "outputs": [],
   "source": [
    "model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 907,
     "status": "ok",
     "timestamp": 1600455412483,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "Z6ZSZku6Cz7p",
    "outputId": "8eb7e5e0-3468-466b-d940-a3ac54703ce6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sooWWsmqm6RP"
   },
   "source": [
    "### Get Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1004,
     "status": "ok",
     "timestamp": 1600455441876,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "mFxmTaseCzu_",
    "outputId": "ff14a536-3cf6-4608-f92c-a607bef255d3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of determination (R2): 0.9872919587211263\n"
     ]
    }
   ],
   "source": [
    "r_sq = model.score(X, y)\n",
    "print('Coefficient of determination (R2):', r_sq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 52
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 882,
     "status": "ok",
     "timestamp": 1600455495680,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "obl0Qm53Czfx",
    "outputId": "f55ae184-bb4e-4869-8cf7-fe9c9ddf289b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: 0.5825576602634861\n",
      "slope: [43.08913515]\n"
     ]
    }
   ],
   "source": [
    "print('intercept:', model.intercept_)\n",
    "print('slope:', model.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "L3CUuxm0nBb3"
   },
   "source": [
    "### Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 52
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 917,
     "status": "ok",
     "timestamp": 1600455553379,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "b8Jb11mTCzMV",
    "outputId": "e54c5f07-4136-49cb-e731-c8066fe192ea"
   },
   "outputs": [],
   "source": [
    "X_test, y_test = make_regression(n_samples=100, n_features=1, noise=20 ,random_state=42)\n",
    "y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x138d952c5b0>"
      ]
     },
     "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": [
    "plt.scatter(X, y)\n",
    "plt.scatter(X_test, y_pred, color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error, mean_absolute_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard deviation 46.11025462073194 \n",
      "\n",
      "Mean squared error: 327.33384901136503\n",
      "Mean absolute error: 14.795675980173698\n"
     ]
    }
   ],
   "source": [
    "mse = mean_squared_error(y_test, y_pred)\n",
    "mae = mean_absolute_error(y_test, y_pred)\n",
    "\n",
    "print('Standard deviation', y_test.std(), \"\\n\")\n",
    "\n",
    "print('Mean squared error:', mse)\n",
    "print('Mean absolute error:', mae)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of determination (R2) of test: 0.8460442632197438\n"
     ]
    }
   ],
   "source": [
    "r_t = model.score(X_test, y_test)\n",
    "print('Coefficient of determination (R2) of test:', r_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "icAi86X1nJLc"
   },
   "source": [
    "## Multiple Linear Regression With scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "H0xTkmm_nVJ9"
   },
   "source": [
    "### Provide Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 176
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 780,
     "status": "ok",
     "timestamp": 1600456172877,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "Diw806hRl1A_",
    "outputId": "c65a73ab-25ae-49d7-d252-8eca3500a059"
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression\n",
    "X_m, y_m = make_regression(n_samples=100, n_features=2, noise=20,random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "otpUMvJZn1kM"
   },
   "source": [
    "### Create a model & fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3CHiKIZZl1K6"
   },
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(X_m, y_m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kLOWx40on-L0"
   },
   "source": [
    "### Get Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 70
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 910,
     "status": "ok",
     "timestamp": 1600456293410,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "iBt3pM-hl1S4",
    "outputId": "77ac4fff-59d2-4598-c567-1bcbbf13861f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficient of determination: 0.959604849170989\n",
      "intercept: 0.4327161689219041\n",
      "slope: [84.26785337 74.15664645]\n"
     ]
    }
   ],
   "source": [
    "r_sq = model.score(X_m, y_m)\n",
    "print('coefficient of determination:', r_sq)\n",
    "print('intercept:', model.intercept_)\n",
    "print('slope:', model.coef_)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TY6mePg5oSBE"
   },
   "source": [
    "### Predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 70
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1542,
     "status": "ok",
     "timestamp": 1600456327996,
     "user": {
      "displayName": "Adem Tekin",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gjji3ec_q6_sWOPCSacyEQOavzHeGZCtJpnBwD9=s64",
      "userId": "01835850446278926637"
     },
     "user_tz": -180
    },
    "id": "6ViFtCWfl1a5",
    "outputId": "27a58f97-7a0f-4896-a3e5-a275700519ef",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted response:\n",
      "[ -53.2618421   -81.47203332  182.21191983 -185.91510539  -48.19449499\n",
      "  -30.58967254 -142.85219232  -89.69922222  -68.68904094 -149.21585472\n",
      "  -41.44798528   90.09462956  -73.17883242 -174.86416876 -114.62008988\n",
      "  -36.66153161   11.33844031  111.89967811   25.61613614  176.80558272]\n"
     ]
    }
   ],
   "source": [
    "Xm_test, ym_test = make_regression(n_samples=20, n_features=2, noise=20, random_state=42)\n",
    "\n",
    "ym_pred = model.predict(Xm_test)\n",
    "print('predicted response:', ym_pred, sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of determination (R2) of test: 0.9587826719061529\n"
     ]
    }
   ],
   "source": [
    "print('Coefficient of determination (R2) of test:', model.score(Xm_test,ym_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9587826719061529"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "r2_score(ym_test, ym_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0t2bMe0DruXG"
   },
   "source": [
    "## Cost Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "h0d9Gg4Sr_JD"
   },
   "source": [
    "It is a function that measures the performance of a Machine Learning model for given data. Cost Function quantifies the error between predicted values and expected values and presents it in the form of a single real number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3KrPoOTJjDpS"
   },
   "source": [
    "$$MSE = \\frac{1}{m}\\sum_{n=1}^{m} (y_p-y)^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "b-CqFQ0cmijD"
   },
   "source": [
    "#### Mean Square Error (MSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "327.33384901136503"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "327.33384901136503"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((y_test - y_pred)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean Square Error (MAE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.552246565706957"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_absolute_error\n",
    "mean_absolute_error(y,y_pred)"
   ]
  }
 ],
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