Regression 8. Basis Functions for Non-linear Regression

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Introduction

For polynomial curve fitting, you can use basis functions to model the relationship between the input features and the output variable. 

General Form

The general form of a polynomial regression equation with basis functions is:


Each term in the equation is the product of a weight and a basis function evaluated at the input x. The basis functions capture the polynomial terms of different degrees, allowing the model to fit more complex curves to the data.


Quadratic and cubic Polynomials for Scalar x



Polynomial for Vectors


The basis functions are : 


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