## Regression Analysis

 Unit code: MATH38141 Credit Rating: 10 Unit level: Level 3 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

Prerequisite

None.

#### Aims

• To familiarise students with the methodology and applications of standard techniques of regression analysis and analysis of variance.
• To explore some of the wide range of real-life situations occurring in different fields that can be investigated using regression statistical models.

#### Overview

In many areas of science, technology and medicine one often wishes to explore the relationship between one observable random response and a number of explanatory variables, which may influence simultaneously the response. The required statistical principles and techniques are established and used to select a suitable model for a given dataset.

#### Learning outcomes

On successful completion of this course unit students will be able to:

• formulate, estimate, use and test for lack of fit regression linear models that are suitable for relevant statistical studies;
• formulate statistical hypotheses in terms of the model parameters and test such hypotheses;
• obtain confidence intervals for linear combinations of the model parameters;
• state the implications of orthogonality and collinearity between regressors;
• obtain a best-fitting model in a systematic and pragmatic way;
• use R to implement methods covered in the course.

#### Assessment methods

• Other - 20%
• Written exam - 80%

#### Assessment Further Information

• Coursework: weighting 20%
• End of semester examination: two hours weighting 80%

#### Syllabus

• Regression models. Assumptions. Matrix representation. Least squares estimators and their properties. Fitted values. Residuals. Estimating 2. [4]
• Vector random variables. Gauss-Markov theorem. Multivariate normal distribution.
• Distribution of estimators and residuals. [3]
• Orthogonality. Multicolinearity. Indicator variables. Overparameterisation. [2]
• Estimating 2 from replication. Weighted least squares. Testing model fit with and without replication. Checking model assumptions. Plots of residuals.[3]
• Model building and model selection. Deleting predictor variables. The general linear hypothesis. Stepwise regression. Penalised likelihood. AIC, AICc, BIC. Comparison of nested and not nested models. [3]
• One and two way analysis of variance. [4]

• Draper, D. N. R. and Smith, H., Applied Regression, (third edition).  Wiley.
• Faraway, J. J. (2015). Linear Models with R., (second edition). Chapman and Hall/CRC.
• Montgomery, D. C. and Peck, E. A., (2011). Introduction to Linear Regression Analysis, Wiley.
• Weisberg, S., (2013). Applied Linear Regression (fourth edition). Wiley.

#### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

#### Study hours

• Lectures - 22 hours
• Practical classes & workshops - 11 hours
• Independent study hours - 67 hours

#### Teaching staff

Alexander Donev - Unit coordinator