Linear Models (repetitive) (8 ECTS)

Introduction to regression, fitting, estimating the coefficients. Coefficient estimator properties, mean value, variance, confidence intervals,. Predicted values, ANOVA, R^2, F test (definition via SS_Regr and SS_error).
Introduction to multivariate normal distribution, quadratic forms, quadratic forms mean, distributions, independence. Multiple Regression definition and examples. Design matrix, introduction to dummy variables, linear model general form, LS estimations and properties. Unbiased variance estimation. Predicted values estimation, error estimation, properties, maximum likelihood estimation, LRT, general linear hypothesis, examples. Multiple correlation coefficient, ANOVA, partial F-tests. Examples. Simple residuals, standardized residuals, studentized residuals, normality test, Q-Q plots, basic model hypothesis testing graphs, added variable plot, other diagrams and model hypotheses testing. Simple transformations, influence statistics, the concept of multilinearity, diagnostic tests. One way analysis of variance. Sum to zero parameterization, corner point parameterization, design matrix, estimated coefficients, model ANOVA.
Two way analysis of variance, saturated and cumulative model. Parameterization explanation, design matrix, estimated ANOVA model parameters. Choosing the optimal regression model, forward, backward, stepwise methods, all possible regressions.

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

(old title: Introduction to Linear Regression)

(prerequisite for 6014 - Analysis of Variance and Experimental Design, 6176 - Generalized Linear Models and 6005 - Data Analysis)