# Introduction **Polynomial Regression is** an extension where the relationship between variables is non-linear. Polynomial regression transforms input variables to higher powers (e.g., $$x2,x3x^2, x^3x2,x3$$) but remains a linear model concerning the parameters, making it suitable for more complex patterns. In polynomial regression, we aim to model a non-linear relationship by transforming the input variable x to include higher powers. The model equation for a polynomial regression of degree $$d$$ is: $$y = \beta\_0 + \beta\_1 x + \beta\_2 x^2 + \beta\_3 x^3 + \dots + \beta\_d x^d + \epsilon$$\ \ where: • $$y$$ is the dependent variable, • $$\beta\_0, \beta\_1, \beta\_2, \dots, \beta\_d$$ are the coefficients, • $$x, x^2, x^3, \dots, x^d$$ represent the transformed input features up to the $$d$$-th degree, • $$\epsilon$$ is the error term. This transformation allows the model to fit a curve that better matches non-linear patterns in the data. **Example:** Predicting energy consumption based on home size.