Department assigned to the subject: Department of Statistics
ECTS Credits: 5.0 ECTS
Students are expected to have completed
Foundations of Statistics
Competences and skills that will be acquired and learning results.
The aim of the course is to review, at an intermediate level, the basic concepts and methods of Linear Regression. Emphasis is both in theory and applications.
Description of contents: programme
** 1.1 Formulation and meaning of a statistical regression problem.
** 1.2 Regression models. Goals of a regression analysis.
** 1.3 Data in a regression analysis.
** 1.4 Regression software.
2. THE MULTIPLE LINEAR REGRESSION MODEL: ESTIMATION.
** 2.1 Definition and matrix expression.
** 2.2 Least squares estimation.
** 2.3 Analysis of variance.
** A.1 The multivariate normal distribution.
3.THE MULTIPLE LINEAR REGRESSION MODEL: HYPOTHESIS
TESTING AND CONFIDENCE REGIONS.
** 3.1 The F-test for the general linear hypothesis.
** 3.2 Confidence regions.
** 3.3 Prediction intervals.
** A.1 Indicator variables.
4. MULTICOLLINEARITY, RESIDUAL ANALYSIS, AND DIAGNOSTIC
** 4.1 Multicollinearity: description and consequences.
** 4.2 Residual analysis.
** 4.3 Outliers and extreme cases.
5. GENERALIZED LEAST SQUARES THEORY.
** 5.1 Cases of known and unknown covariance matrix.
** 5.2 Heteroscedasticity.
** 5.3 Transformations.
** 5.4 Serial correlation.
6. TIME SERIES MODELS
** 6.1 Autoregressive (AR) and moving average (MA) models.
** 6.2 ARMA and ARIMA models.
Learning activities and methodology
There will be computer classes, in which the statistical package R will be used with the purpose of illustrating the derivations of the theoretical classes. Teaching will be divided in online sessions, that will be recorded, and face-to-face standard lecture classes.
% end-of-term-examination 40
% of continuous assessment (assigments, laboratory, practicals...) 60
CHATERJEE, S. and HADI, A. . Regression Analysis by Example, 5th Edn. John Wiley. 2012
FREES, E.W.. Regression Modeling with Actuarial and Financial Applications. Cambridge University Press. 2010
KABACOFF, R. L.. R in action: Data analysis and graphics with R, 2nd Edn. . Manning Publications. 2015
BROCKWELL P. J. and DAVIS, R. A. . Introduction to Time Series and Forecasting, 3rd Edn.. Springer Verlag. 2016
JAMES, G., WITTEN, D., HASTIE, T. and TIBSHIRANI, R.. An Introduction to Statistical Learning with Applications in R . Springer Verlag. 2013
KUTNER, M. H., NACHSTEIM, C., and NETER, J.. Applied Linear Statistical Models 4th Edition.. McGraw Hill. 2004
MATLOFF, N.. The Art of R programming: A Tour of Statistical Software Design. No Starch Press. 2011
RAWLINGS, J. O., PANTULA, S. G. and DICKEY, D. A.. Applied Regression Analysis: A Research Tool, 2nd Edn.. Springer Verlag. 1998
WEISBERG, S.. Applied Linear Regression, 4th Edition. Wiley . 2014
The course syllabus and the academic weekly planning may change due academic events or other reasons.