Course content

• Simple and multiple linear regression models – estimation, tests and confidence regions. Simultaneous testing methods- Bonferroni method etc.
• Analysis of Variance for simple and multiple regression models. Analysis of residuals. Lack of fit tests. Checks (graphical procedures and tests) for model assumptions: Normality, homogeneity of errors, independence, correlation of covariates and errors. Multicollinearity, outliers, leverage and measures of influence.
• Model selection (stepwise, forward and backward, best subset selection) and model validation.
• Discussion of algorithms for model selection. Regression models with indicator variables. Polynomial regression models. Regression models with interaction terms. Transformation of response variables and covariates.
• Variance stabilizing transformations, Box-Cox method. Ridge`s regression. Weighted Regression.

References

• Draper, N. and Smith,H. Applied Regression Analysis, 3rd Edition, John Wiley and Sons Series in Probability and Statistics, New York, 1998.
• Montgomery, D., Peck, E., Vining, G. Introduction to Linear Regression Analysis, 5th Edition, John Wiley, New York, 2013
• Sen, A. and Srivastava, M. Regression Analysis Theory, Methods & Applications, 1st Edition, Springer-Verlag Berlin Heidelberg, New York, 1990.
• Kutner, M., Nachtsheim, C., Neter, J. and Li, W. Applied Linear Statistical Models, 5th Edition, McGraw-Hill Companies, Boston, 2005.