Multiple Linear Regression

This post is a continuation of Linear Regression. Introduction In multiple linear regression we extend the notion developed in linear regression to use multiple descriptive values in order to estimate the dependent variable, which effectively allows us to write more complex functions such as higher order polynomials ($y = \sum_{i_0}^{k} w_ix^i$), sinusoids ($y = w_1 sin(x) + w_2 cos(x)$) or a mix of functions ($y = w_1 sin(x_1) + w_2 cos(x_2) + x_1x_2$).

Linear Regression with NumPy

Introduction Linear regression is a method used to find a relationship between a dependent variable and a set of independent variables. In its simplest form it consist of fitting a function $ \boldsymbol{y} = w.\boldsymbol{x}+b $ to observed data, where $\boldsymbol{y}$ is the dependent variable, $\boldsymbol{x}$ the independent, $w$ the weight matrix and $b$ the bias. Illustratively, performing linear regression is the same as fitting a scatter plot to a line.