Original article was published on Artificial Intelligence on Medium
Normal Equation is as follow :
Polynomial Regression :
Hypothesis Function For Polynomial Regression :
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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