Linear Models (8 ECTS)

    Course Code: 
    6023
    Semester: 
    4th
    Compulsory Courses
    Διδάσκων: 

    PAPASTAMOULIS PANAGIOTIS

    Introduction to regression, fitting a straight line, and coefficient estimates. Properties of estimated coefficients, mean and variance, confidence intervals, hypothesis testing, and estimation of the variance of the data. Predicted values. ANOVA for the straight-line model, (R^2), and the F-test. Introduction to the multivariate normal distribution, quadratic forms, expected values of quadratic forms, distributions of quadratic forms, and independence of quadratic forms. Definition of multiple regression and examples. Design matrix, introduction to dummy variables, general form of the linear model, least-squares (LS) estimates, properties of estimators (using matrix notation). Unbiased estimation of the unknown variance. Estimates of predicted values, error estimates, and their properties (using projection matrices), maximum likelihood estimation, likelihood ratio test (LRT), and the general linear hypothesis (R\beta=r), with examples. Multiple correlation coefficient, ANOVA for the model, partial F-tests, sequential F-tests, and examples. Ordinary residuals, standardized residuals, studentized residuals, tests for normality, Q-Q plots, basic diagnostic plots for checking model assumptions, added-variable plots, and other diagnostic plots and tests for model assumptions. Simple transformations, influence statistics, the concept of multicollinearity, and diagnostic tests. One-way analysis of variance. Sum-to-zero parameterization, corner-point parameterization, design matrix, estimated coefficients, and ANOVA for the model. Two-way analysis of variance: the saturated and additive models. Explanation of parameterizations, design matrix, estimated coefficients, and ANOVA for the model. Selection of the best regression model: forward, backward, stepwise, and all-possible-regressions methods.

    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 6176 - Generalized Linear Models and 6005 - Data Analysis)