Machine Learning 101 P4: Polynomial Linear Regression (a special case of Linear Regression)

Introduction

Polynomial Linear Regression is a variation of linear regression in which the relationship between the independent variable x and the dependent variable y is modeled as an n-degree polynomial. Key characteristics of polynomial linear regression include:

• Still a version of linear regression, just a special case.
• Modeling non-linearity: The model is used when variables exhibit a non-linear or curved relationship.
• Transforming features: Original features get transformed into polynomial features, while still using the principles of linear regression to find the coefficients.

Mathematical concepts of polynomial linear regression

Polynomial Linear Regression equation is illustrated as follows.

Where:

• y: dependent variable.
• X: independent variable.
• b0,b1,b2,…,bn: coefficients of the polynomial.
• n: degree of the polynomial.
• ϵ: error.

Feature transformation

• Features are transformed into polynomial one with n degree of the polynomial.
• For multivariate data with more features (x1, x2,…, xk), the transformation includes combinations of these…