Module Descriptors

Statistics

ST313: Applied Regression Models (5 ECTS)

An introduction to the theory and application of regression models. Topics covered include the simple linear model, least-squares estimation, multiple linear regression, inference, model checking, model choice and variable selection, and the use of Minitab for practical applications. This module is built on the statistical inference methods demonstrated in pre-requisite module ST236.

Taught in Semester(s) I. Examined in Semester(s) I.

Workload: 120 hours (24 Lecture hours, 10 Tutorial hours, 6 Lab hours, 80 Self study hours).

Module Learning Outcomes. On successful completion of this module the learner should be able to:

  1. calculate and interpret correlations between variables and make inferences about relationships;
  2. calculate regression diagnostics and use these to check model assumptions, including linearity, normality, constant variance, independence and the presence of outliers and influential points;
  3. formulate a multiple regression model and specify this in matrix form;
  4. derive least-squares estimates for a multiple regression model;
  5. interpret output from a Minitab regression procedure and use this to test hypotheses on the overall model, individual terms, and make model comparisons;
  6. use regression model diagnostic output to check model assumptions and model adequacy and explore the need for transformations of response and explanatory variables;
  7. interpret and use output from variable selection procedures to choose adequate models;
  8. incorporate categorical variables in regression models using indicator variables and interpret and test associated parameters;

Indicative Content

This course gives a basic introduction to regression modelling. The topics covered include:

  1. Populations and samples, correlation and association, response and explanatory variables.
  2. Simple linear regression: estimation using least-squares, properties of estimators, inference on parameter estimates, construction and use of ANOVA table, confidence and prediction intervals, residuals and model diagnostics.
  3. Multiple regression: matrix formulation of general linear model, least-squares estimation, properties of estimators, inference on parameter estimates, ANOVA table, fitted values, residuals, the hat-matrix, predictions, diagnostics and model checking.
  4. Model choice and variable selection: testing of nested models, varaible selection criteria, stepwise and best subsets variable selection methods.
  5. Categorical explanatory variables: use of indicator variables for categoprical variables, test of overall significance, analysis of covariance, interaction.
  6. Practical computer lab sessions: Use of Minitab statistical software to fit regression models, statistical report writing, including a group project and presentation.

Module Resources

Textbook: Applied Linear Regression Models by Kutner, Nachtsheim & Neter; McGraw Hill

Reference: STAT2: building models for a world of data by Ann R. Cannon et al.

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