Regression Data Analysis

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Key words:

Regression model, cross-sectinal and panel data, classical and robust estimators.

Requirements:

Syllabus of lectures:

Linear model, the least squares, estimator minimizing sum of absolute values of residuals. The best linear unbiased estimator of regression coefficients - orthogonality condition and sphericality (homoscedasticity), consistency. Asymptotic normality of the estimator of regression coefficients. The best unbiased estimator of regression coefficients. Coefficient of determination, role of intercept, significance of explonatory variables. Confidence intervals testing submodels, Chow test. Statistical packages, possibilities, inputs and outputs, reliability, interpretation of results, White test of heteroscedasticity, index plot. Normality test, Theil residuals, tests of good fit, K-S test, normal plot. Colinearity, condition number, Farrar-Glauber test, redundancy, ridge regression, estimator with linear restrictions. AR, MA, AR(I)MA, invertibilty and stationarity conditions. Smoothing the linear envelope of trends, moving averages. Seasonal and cyclic components, randomness test. Efficient estimate of AR(1), MA(1), AR(2), MA(2), Prais-Winston, ochrane-Orcutt. Robust regression, M-estimators, qualitative and quantitative robustness, influence function, influential points (outliers, leverage points). The least median of squares, the trimmed least squares and the least trimmed squares, the weighted least squares and the least weighted squares, algorithms, aplications. Philosophical ideas of mathematical modelling.

Syllabus of tutorials:

Exercises in regression will be held in agreement with the lecture and its aim is the application of the regression methods in R.

Introduction to R, linear model, Least Squares estimation, residuals, sub-model, ANOVA, tests of model assumptions, normality, independence, QQ plots, multicollinearity, logistic regression, nonlinear regression, transformations, robust methods in regression

Study Objective:

Acquired knowledge:

To continue in statistical lectures and to offer one of the most powerful tool for data modelling. To make students familiar with theoretical and practical aspects of topic and open them the point of view of statistician and econometrician, classical and robust approach.

Acquired skills:

Independent application of regression methods to epmirical data.

Study materials:

Key references:

[1] Statistical data analysis, in Czech. Publishing house of the Czech Technical University in Prague, 1997. (187 pages, ISBN 80-01-01735-4)

Recommended references:

[2] Atkinson, A.C. (1985): Plots, Transformations and Regression: An Introduction to Graphical Methods of Diagnostic Regression Analysis. Oxford: Claredon Press.

[3] Baltagi, B. H. (2001): A Companion to Theoretical Econometrics,Massachusetts, Oxford: Blackwell.

[4] Drapper, N. R., Smith, H (1998): Applied Regression Analysis, New York: J.Wiley.

[5] Judge, G. G., W. E. Griffiths, R. C. Hill, H. Lütkepohl, T. C. Lee (1982): Introduction to the Theory and Practice of Econometrics. New York: J.Wiley.

[6] Wooldridge,J.M. (2001): Econometric Analysis of Cross section and Panel Data. The MIT Press, Cambridge, Massachusetts, U.S.A. and London, England.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematické inženýrství (elective course)