Regression Data Analysis

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Department of Mathematics

Synopsis:

1.Simple linear regression: least squares estimation, properties of parameter estimates, hypotheses tests and confi-dence intervals for parameters of the model, model-based prediction, analysis of residuals

2.Multiple linear regression: general linear model, least squares estimation, analytical and numerical solutions of the normal equations, properties of parameter estimates, coefficient of determination, F-test, prediction intervals

3.Residuals, diagnostics and transformations: residuals and residual plots, normality tests, detection of outlying and influential observations, hat matrix, Cooks distance, transformations of dependent and independent varia-ble, Box-Cox transformation

4.Selection of a regression model: criteria functions, R2 statistics, Mallows Cp statistics, Akaike and Bayes infor-mation criteria, stepwise regression and backward elimination

5.Multicollinearity: impact of multicollinearity on precision of the parameter estimates, detecting and combatting multicollinearity, ridge regression

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Key references:

[1] Golberg, M. Cho, H.A.: Introduction to Regression Analysis. WITpress, Southampton 2010.

[2] Olive, D.: Linear Regression. Springer, 2017.

Recommended references:

[3] Weisberg, S.: Applied Linear Regression. John Wiley & Sons, New Jersey 2014.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikované matematicko-stochastické metody (compulsory course in the program)