This course introduces students to predictive models for regression and classification.

The course mostly consists of asynchronous teaching material.

Linear Models 3

Statistics 3L: Linear Models

Regression Models (Level M)

-/-

100% Continuous Assessment

The continuous assessment will typically be made up of one class test, a report, and three homework exercises, including online quizzes. Full details are provided in the programme handbook.

The aims of this course are:

■ to introduce students to predictive modelling using multiple linear regression as a showcase;

■ to present some of the distributional theory underpinning the normal linear models and the associated methods for testing and interval estimation;

■ to explain how the design matrix of a linear model can be constructed to accommodate categorical covariates or, through basis expansions, non-linear effects;

■ to describe and contrast several common methods for model assessment as well as variable and model selection;

■ to show students how to implement these statistical methods using the R computer package.

By the end of this course students will be able to:

■ formulate normal linear models in vector-matrix notation and apply general results to derive ordinary least squares estimators in particular contexts;

■ construct a design matrix incorporating categorical covariates or covariates with a nonlinear effect;

■ derive, evaluate and interpret point and interval estimates of model parameters;

■ conduct and interpret hypothesis tests in the context of the Normal Linear Model;

■ derive, evaluate and interpret confidence and prediction intervals for the response at particular values of the explanatory variables;

■ assess the assumptions of a normal linear model using residual plots and diagnostics;

■ make use of and critique different methods for assessing the performance of a predictive model such R2 or AIC/BIC and use these for model or variable selection;

■ identify scenarios where data may be considered to be smooth functions and apply suitable data analysis techniques;

■ implement these statistical methods using the R computer package;

■ frame statistical conclusions clearly.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.