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
- How to estimate the coefficients $\beta_0, \ldots, \beta_p$ from
- 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?
Everything is here.