## Polynomial Regression and Features-Extension of Linear Regression

Priliminaries A Simple Linear Regression Least Squares Estimation Extending Linear Regression with Features1 The original linear regression is in the form: \begin{aligned} y(\mathbf{x})&= b + \mathbf{w}^T \mathbf{x}\\ &=w_01 + w_1x_1+ w_2x_2+\cdots + w_{m+1}x_{m+1} \end{aligned}\tag{1} where the input vector $$\mathbf{x}$$ and parameter $$\mathbf{w}$$ are $$m$$-dimension vectors whose first components are $$1$$ and bias $$w_0=b$$ respectively. This equation is linear for both the input vector and parameter vector. Then an idea come to us, if we set $$x_i=\phi_i(\mathbf{x})$$ then equation (1) convert to:...

February 15, 2020 · (Last Modification: April 30, 2022) · Anthony Tan