Linear Models - recursive (8 ECTS)

Introduction to regression, straight line fitting, model coefficients estimates. Properties of estimated coefficients, mean value, variance, confidence intervals, hypothesis testing, estimation of conditional variance. Predicted values, simple linear regression ANOVA, R^2, F-test (note: definition through SS_Regr and SS_error).

Introduction to multivariate normal distribution. Multiple regression definition, examples. Design matrix, introduction to pseudo variables, general form of linear model, LS estimates and properties (through matrices). Unbiased variance estimate. Maximum likelihood estimation. Multiple correlation coefficient, model ANOVA, partial F-tests, recursive f-tests. Examples. Simple residuals, standardized and studentized residuals, normality test, Q-Q plots, simple hypothesis testing plots, added variable plots, other plots and hypothesis testing for the model.  Simple transformations, influence statistics and diagnostic tests, multicollinearity. Model choice, forward, backward, stepwise methods, all possible regressions, model choice using AIC, BIC, Μallows Cp.

Recommended Reading

• Draper N.R. and Smith, H. (1997). Εφαρμοσμένη Ανάλυση Παλινδρόμησης, Παπαζήσης
• Κούτρας, Μ. Και Ευαγγελάρας, Χ. (2010). Ανάλυση Παλινδρόμησης: Θεωρία και Εφαρμογές, Σταμούλης
• Montgomery, D.C., Peck, E.A. and Vining, G.G. (2012). Introduction to Linear Regression Analysis, Wiley.
• Weisberg, S. (2014). Applied Linear Regression, Wiley