# 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

Here are the practical solutions:

Everything else is here.

## Links