Module_4_Model_Build_Performance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.facebook.com/codemakerz\"><img src=\"https://scontent.ffjr1-4.fna.fbcdn.net/v/t1.0-9/36189148_736466693143793_2172101683281133568_n.png?_nc_cat=107&_nc_eui2=AeHzxv3SUcQBOfijLP-cEnHkX4z9XQXdeau__2MlErWZ1x07aZ1zx1PzJUDDxL6cpr7oPqYiifggXDptgtP8W5iCoDRjcdILDBYZ5Ig40dqi8Q&_nc_oc=AQmMCNXdzelFB2rdtpk8wN8nC410Wm2yKupYfYS1FxHNejTF0Jhr1G3WIZORKRF3TvFpohMB8Puw29Txxan8CW05&_nc_ht=scontent.ffjr1-4.fna&oh=7b13627e991a4d1b508923041bd7bc22&oe=5D8A7B03\" />\n",
    "</a>\n",
    "\n",
    "\n",
    "You can download:\n",
    "> Datasets at: https://raw.githubusercontent.com/martandsingh/datasets/master/cars/automobile_preprocessed.csv<br/>\n",
    "> Git Repo for dataset: https://github.com/martandsingh/datasets.git <br/>\n",
    "> Jupyter Notebook(Code): https://github.com/martandsingh/dataanalytics <br/>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this module we will understand how to make a basic regression model and try to understand:\n",
    "1. Linear Regression\n",
    "2. Multiple regression (Coming Soon)\n",
    "3. Polynomial regression (Coming Soon) \n",
    "4. Perfomrmance of the model (Coming Soon)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import & load db as discussed earlier\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "# CSV file path. IT can be any resource.\n",
    "file_name = 'https://raw.githubusercontent.com/martandsingh/datasets/master/cars/automobile_preprocessed.csv'\n",
    "df = pd.read_csv(file_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['symboling', 'normalized-losses', 'make', 'aspiration', 'num-of-doors',\n",
       "       'body-style', 'drive-wheels', 'engine-location', 'wheel-base', 'length',\n",
       "       'width', 'height', 'curb-weight', 'engine-type', 'num-of-cylinders',\n",
       "       'engine-size', 'fuel-system', 'bore', 'stroke', 'compression-ratio',\n",
       "       'horsepower', 'peak-rpm', 'city-mpg', 'highway-mpg', 'price',\n",
       "       'city-L/100km', 'horsepower-binned', 'diesel', 'gas'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head() # We are ready to go.\n",
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>What is Regression?</h2>\n",
    "Ans. Regression analysis is a set of statistical processes for estimating the relationships among variables (Wikipedia)\n",
    "\n",
    "In simple words, in our database we have different columns. So regression analysis tell your the relationship between\n",
    "two or more variables.\n",
    "for example: In general lets say we have a database of cars and there two different columns engine-capacity and mileage. By using regression on both the columns we can find how engine-capacity affects the mileage of cars. \n",
    "\n",
    "Usually people say high HP will result you in less mileage... How can they say that?\n",
    "So if you have that kind of dataset, you can actually find the relationship between engine-capacity and mileage using regression methods.\n",
    "\n",
    "<h2>What is Linear Regression?</h2>\n",
    "Ans. Linear regression is the regresion analysis between two variable, just like our above case.\n",
    "\n",
    "<h2>What is Multiple Regression?</h2>\n",
    "Ans. Sometimes one variable or feature is not enough to predict the value of target variable. In that case we need to add more features or columns to calculate the result. The case where we use regression analysis is done by more than one feature or columns is called multiple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now lets do some code..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# As we told linear regression is the regression analysis or finding relationship between two variables.\n",
    "# Or you can say in this case we show the relationship between a single feature and target value.\n",
    "# we all in our schools have seen equation of line:\n",
    "#. Y = mx + c\n",
    "# Where m = coefficient , c = intercept, x = independent variable/predictor, y = target variable/dependent variable.\n",
    "# So is linear regression a line or what?\n",
    "\n",
    "# As name suggest, linear regression will help you to find relationship between two variable in form of a line.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To use linear regression we will use and inbuit library sklearn.\n",
    "from sklearn.linear_model import LinearRegression # Class imported"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "lm_obj = LinearRegression() # Object of Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[[\"engine-size\"]] # Independent Variable\n",
    "Y = df[\"price\"] # Target/dependent variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_obj.fit(X,Y) # We need to fit first. Fit is like you are training your model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13728.4631336 , 13728.4631336 , 17399.38347881, 10224.40280408,\n",
       "       14729.62322775])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_pred = lm_obj.predict(X) # We are predicting the price for all the given horsepower. We already have prices but \n",
    "# we are predicting prices for the same values so thatwe could compare them.\n",
    "Y_pred[0:5] # Y_pred is the array containing all the predicted values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.86001569])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Remember y = mx+c\n",
    "# how to get value of m(coeff) & c(intercept)\n",
    "lm_obj.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7963.338906281049"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_obj.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# our equation is now:\n",
    "Y = 166.86001569*X + (-7963.338906281049)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56389.094889036096)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now we got the values and equation but still the concept is not clear?\n",
    "# Because we can see values but we can not obviously compare 1000 or more variables one by one. \n",
    "# For this we should take help of visualization. It helps you to understand exactly what your model just did?\n",
    "\n",
    "width = 12 # width of the visualization\n",
    "height = 10 # height of the visualization\n",
    "plt.figure(figsize=(width, height)) # Setting width and height with mtplotlib.pyplot obj\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df) # visualizing using seaborn\n",
    "plt.title('Engine Size VS Price') # Visualization title\n",
    "plt.xlabel('engine-size') # x-axis label\n",
    "plt.ylabel('Price (in dollars)') # y-axis label\n",
    "plt.ylim(0,) # settin the minimum value of y axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we can see the blue line is our regression line, which is increasing as X increases, This show we have a\n",
    "# positive regression between engine-size and price. This means as engine-size increases, price also increases.\n",
    "# See now you have mathemetical proof to argue with someone.\n",
    "\n",
    "# One more thing we should notice, all dots are real values. So you should observer whether your ral values are\n",
    "# uniformely distrubuted around regression line or not. In this case dots are distributed around line, which shows\n",
    "# our regression is good. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "326"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"engine-size\"].max() # max value of engine-size is 326"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([58780.66737029])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets predict a value which is not there in our dataframe.\n",
    "# lets calculate price for engine-size 400 which is not there in above dataframe\n",
    "lm_obj.predict([[400]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SO you can see the price of car with engine-size around 300 is somewhere between 40000 to 50000, now we just\n",
    "# calculated for engine-size 400 which is 58780.66 which shows a positive linear behaviour which somewhere is \n",
    "# correct as per our model.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Multiple Linear Regression </h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As name suggests, It is also a kind of linear regression but in this case there can be more than one predictor.\n",
    "e.g. price of car may depend on color, company, engine-size, mileage and many other predictors. Lets predict price of the car with more than one predictors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[[\"engine-size\", \"highway-mpg\"]]\n",
    "Y = df[\"price\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_obj.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2903.795260341656"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_obj.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 139.83785426, -242.40836682])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_obj.coef_ # now you can see there are two coefficient because we had two predictors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y = c + m1X1+m2X2....MnXn\n",
    "So equation will be\n",
    "Y = (139.83785426*X1)+(-242.40836682*X2) + 2903.795260341656"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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