# MATH3714 — Linear Regression and Robustness

In this module we will study how linear regression can be used to describe and analyse the relationship between explanatory variables $x_1, \ldots, x_n$ (input) and a response variable $y$ (output). The models we will consider are of the form

$y = \beta_0 + x_1 \beta_1 + \cdots + x_p \beta_p + \varepsilon$,
where the coefficients $\beta_i$ describe how strongly the response depends on the feature $x_i$, and the residual $\varepsilon$ represents the noise, i.e. the component of the data not explicitly described by the model. We will consider the following questions:
• How to estimate the coefficients $\beta_0, \ldots, \beta_p$ from data?
• How much of the variance in $y$ is described by the $x_i$? How much by the noise $\varepsilon$?
• Is a linear model appropriate for the data?
• What happens if there are outliers in the data?

## Contents

Everything is here.