Study-Unit Description

Study-Unit Description


CODE SOR3221

 
TITLE Regression Models

 
UM LEVEL 03 - Years 2, 3, 4 in Modular Undergraduate Course

 
MQF LEVEL 6

 
ECTS CREDITS 4

 
DEPARTMENT Statistics and Operations Research

 
DESCRIPTION - Multiple regression models
- Properties of least squares and maximum likelihood estimates
- Cramer Rao Lower bound
- Distribution theory
- ANOVA regression models
- ANCOVA regression models
- Hypothesis Testing on regression parameters
- Confidence Intervals and Prediction Intervals
- Criteria for Choice of Best Model
- Multicollinearity
- Model Checking and Residuals
- Residual Plots to Detect Model Misspecifications
- The Hat Matrix and Leverage
- Detection of influential data points (Cook’s Distance)
- Detection of outliers (Studentized Residuals)
- Weighted Least Squares Estimation

Study-unit Aims

- Familiarize with different Regression Models that accommodate both covariates and factors.
- Carry out estimation by ordinary least squares, maximum likelihood and weighted least squares
- Use diagnostic tools to identify model misspecifications, outliers, influential data points and collinearity.

Learning Outcomes

1. Knowledge & Understanding: By the end of the study-unit the student will be able to:

- Test the assumptions of Regression Models including the normality assumption of the responses, independence of the predictors and linearity.
- Understand the limitation of Regression Models when the normality assumption is violated.
- Understand that Regression Models are a subset of a more general framework that accommodate other error distributions.

2. Skills (including transferable [generic] skills): By the end of the study-unit the student will be able to:

- Fit Normal Linear Regression Models using at least two statistical packages.
- Use these Regression Models for prediction.
- Assess goodness of model fit and identify model misspecifications.

Main Text/s and any supplementary readings

- Clarke, G.M. and Kempson, R.E. (1997) Introduction to the Design and Analysis of Experiment, Wiley
- Dean, A. and Voss, D. (1999) Design and Analysis of Experiments, Springer
- Draper, N. R. and Smith, H. (1981) Applied Regression Analysis – Second Edition, Wiley
- Freund, R. J. and Wilson, W.J. (1998) Regression Analysis, Academic
- Johnson, R.A. and Wichern, D.W. (1992) Applied Multivariate Statistical Analysis, Prentice Hall Inc.
- Montgomery, D. C. and Peck, E. A. (1991) Introduction to Linear Regression Analysis, Wiley
- Sahai H. and Ageel M. (2000) The Analysis of Variance: Fixed, Random and Mixed Models, Springer
- Scheffé, H. (1999) Analysis of Variance, Wiley
- Seber, G. A. F. (1977) Linear Regression Analysis, Wiley
- Weisberg, S. (1985) Applied Linear Regression, Wiley

 
ADDITIONAL NOTES Pre-requisite Study-units: SOR1110, SOR2211, SOR2221

 
STUDY-UNIT TYPE Lecture and Practical

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Sept. Asst Session Weighting
Computer-Assisted Examination (2 Hours) SEM2 Yes 100%

 
LECTURER/S Liberato Camilleri

 

 
The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit