Complete Guide On Linear Regression Vs. Polynomial Regression With Implementation In Python

Original article was published on Artificial Intelligence on Medium

Normal Equation is as follow :

Polynomial Regression :

Hypothesis Function For Polynomial Regression :

Where,

beta_0 , beta_1, …. are the coefficients that we need to find.

x,x²,x³ are features of our dataset.

Let’s code :

(1) Import required libraries :

(2) Generate data points :

(3) Initialize x,x²,x³ vectors :

(4) Column-1 of X matrix :

(5) Form the complete x matrix :

(6) Transpose of matrix :

(7) Matrix multiplication :

(8) Inverse of a matrix :

(9) Matrix multiplication :

(10) Coefficient values :

(11) Store the coefficients in variables :

(12) Plot the data with curve :

(13) Prediction function :

(14) Error function :

(15) Calculate the error :

Here you can see that the error is significantly lower than the error in linear regression.

So we can say that it has done a pretty good work. So in conclusion we can say that if our dataset if following curve trends then we can use polynomial regression for better results and accuracy.

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