The aim of this module is to introduce the student to multiple linear and generalised linear regression models. The statistical theory regarding these models, point and interval estimation for parameters and predicted responses is covered. Model building techniques are critically examined. Methods for residual and influence diagnostics are introduced. The R software system (or equivalent) will be explored as a tool for fitting these models.
Motivation and formulation of the multiple regression model. Least squares (LS) and the multiple linear regression model. Variance of parameter estimates and fitted values, confidence intervals and hypothesis testing. General linear hypotheses and ANOVA.
Model building techniques, residual and inference diagnostics and their role in model appraisal. Including categorical predictors in regression.
Generalised linear models (GLM): the exponential family; likelihood for GLMs including the linear, logistic and Poisson regression models. Fitting GLMs. Interpretation of model parameters; general linear hypotheses of parameters. Wald's and likelihood ratio tests; model building techniques.
Lectures supported by problem-solving sessions and the use of the R statistical software package (or equivalent).
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