1. Introduction
1.1. Regression models.
1.2. Simple linear regression.
1.2.1. Formulation of the model.
1.2.2. Model assumptions.
1.2.3. Parameter estimation.
1.2.4. The F test.
1.2.5. Prediction.
1.3. Statistical Software R.
2. Multiple linear regression: estimation, confidence regions and hypothesis testing.
2.1. The general linear model.
2.1.1. Formulation of the model.
2.1.2. Analysis of variance (ANOVA) model.
2.1.3. Model assumptions.
2.2. Parameter estimation.
2.3. Inference about the parameters.
2.4. Variability decomposition. The F test.
2.5. Prediction.
3. Validation of a regression model.
3.1. The determination coefficient.
3.2. Model diagnosis.
3.3. Regression transformations.
4. Diagnosis of outliers or influential observations. Construction of regression models.
4.1. Diagnostic techniques.
4.1.1. Leverages.
4.1.2. Detection of outliers and influential observations.
4.1.3. Dealing with outliers or influential observations.
4.2. Construction of regression models.
4.2.1. Polynomial regression.
4.2.2. Interactions.
4.2.3. Collinearity.
4.2.4. Variable selection methods.
5. Generalized least squares.
5.1. Introduction.
5.2. Generalized least squares.
5.3. Weighted least squares.
5.4. Iteratively reweighted least squares.
5.5. Feasible generalized least squares.
6. Time series models.
6.1. Autoregressive (AR) and moving average (MA) models.
6.2. ARMA and ARIMA models.
Learning activities and methodology
The course is organized in theoretical classes, whose materials are slides, and computer classes, where R will be used in order to illustrate and consolidate the contents.
Assessment System
% end-of-term-examination 50
% of continuous assessment (assigments, laboratory, practicals...) 50
