Normal Equation Using Python

Dikshit Kathuria
Jan 29 · 5 min read


Linear Regression with One Variable

Necessary Imports

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

Reading and Plotting the Data

x = np.array([1,2,3,4,5])
y = np.array([7,9,12,15,16])
dataset = pd.read_csv('Salary_Data.csv')
x = dataset.iloc[:, 0].values #Feature matrix
y = dataset.iloc[:, 1].values #Criterion Matrix

Understanding Normal Equation

Source : Google Images
ŷͥ = Ɵ˳ + Ɵࢭx
# Ɵ˳ is the intercept and Ɵࢭ is the slope of the line.
Source : Google Images

Python Code

x _ bias = np.ones((m,1)) #m is number of records in the dataset.
#shape of x can be calculated by 
print(x.shape) #which turns out to be (5,) for our sample dataset.
#We need to convert it to (5,1) for successful
#addition as np.ones yields us with an array
#of (5,1) dimension. Click here to know more.
x = np.reshape(x,(m,1))
updated_x = np.append(x_bias,x,axis=1) #axis=1 to join matrix using
x_transpose = np.transpose(x)   #calculating transpose
x_transpose_dot_x = # calculating dot product
temp_1 = np.linalg.inv(x_transpose_dot_x) #calculating inverse
temp_2 =  
Ɵ =
Fitting Regression line to our Sample Dataset
Regression Line for our Salary VS Exp. Dataset
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
# x = np.array([1,2,3,4,5]) #Uncomment this when using Sample Dataset# y = np.array([7,9,12,15,16]) #Uncomment this when using Sample Dataset# dataset = pd.read_csv('Salary_Data.csv') #Uncomment this when using SalaryVsExp Dataset# x = dataset.iloc[:, 0].values #Uncomment this when using SalaryVsExp Dataset# y = dataset.iloc[:, 1].values #Uncomment this when using SalaryVsExp Datasetplt.scatter(x,y,color='red')x_bias = np.ones((5,1))x = np.reshape(x,(5,1))x = np.append(x_bias,x,axis=1)x_transpose = np.transpose(x)x_transpose_dot_x = = np.linalg.inv(x_transpose_dot_x) y = 4.6 + 2.4*x #Uncomment this when using Sample Dataset# y = 25792.2 + 9449.96*x #Uncomment this when using SalaryVsExp Datasetplt.plot(x,y,color='blue')

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