Foundations of Statistical Modelling

Cod: 22112

Department: DCET

Department: DCET

ECTS: 10

Scientific area: Statistics

Scientific area: Statistics

Total working hours: 260

Total contact time: 40

Total contact time: 40

The aim of this course is to provide students a deep understanding of concepts and statistical models, particularly regarding the regression models. It is intended that the student acquire skills that will enable him to build knowledge, develop and interpret statistical models, where there are dependencies that can be modeled by a mathematical expression involving probabilistic notions. The student will show proficiency in applying regression models using generalized linear models, as well as on the respective graphical interpretation and exploitation, aiming at the adjustment to data from a wide range of scientific areas.

Statistical Modelling

Regression Models

Generalized Linear Models

Residual Analysis

Regression Models

Generalized Linear Models

Residual Analysis

At the end of this course students should have acquired skills to allow:

- Feeling able to work with regression models, adjusting them to real problems.

- Reveal proficiency in interpretation, exploration and graphical analysis of results.

- Select and know how to apply the best models to real data in their professional areas.

- Validate models using the graphical analysis of residuals.

- Getting benefit from the capabilities of software suitable for statistical modelling, namely the language R.

- Feeling able to work with regression models, adjusting them to real problems.

- Reveal proficiency in interpretation, exploration and graphical analysis of results.

- Select and know how to apply the best models to real data in their professional areas.

- Validate models using the graphical analysis of residuals.

- Getting benefit from the capabilities of software suitable for statistical modelling, namely the language R.

1 - Introduction to statistical modeling: principles, concepts and goals

2 - Characterization of the regression models

3 - Multiple regression models and inference

4 - Prediction and collinearity

5 - Introduction to Generalized Linear Models: concepts, examples and parameter estimation

6 - Logistic regression and probit models and log-linear

7 - Residuals graphical analysis, model selection and validation

8 - Introduction to Mixed Models

2 - Characterization of the regression models

3 - Multiple regression models and inference

4 - Prediction and collinearity

5 - Introduction to Generalized Linear Models: concepts, examples and parameter estimation

6 - Logistic regression and probit models and log-linear

7 - Residuals graphical analysis, model selection and validation

8 - Introduction to Mixed Models

[2] Faraway, J. J. (2006) Extending the Linear Model with R; Generalized Linear, Mixed Effects and Nonparametric Regression Models. Chapman & Hall.

[3] Fox, J (2008). Applied Regression Analysis and Generalized Linear Models. Sage Publications.

[4] Hosmer, D.W, Lemeshow, S. (2000). Applied Logistic Regression, 2nd Ed., Wiley.

[5] Kutner, M.H., Nachtsheim, C.J., Neter, J. (2004) . Applied Linear Regression Models, 4th Ed., McGraw-Hill/Irwin.

[6] Neter, J., Kutner, M.H.,Li, W.,Nachtsheim, C. J. (2005 ): Applied Linear Statistical Models, 5th Ed. Mcgraw-Hill Professi.

[7] Turkman, M.A.A.& Silva, G.L. (2000). Modelos Lineares Generalizados. Edições SPE (Sociedade Portuguesa de Estatística)

[8] Weisberg, S. (2005). Applied Linear Regression. Wiley Series in Probability and Statistics.

[9] Fox, J (2008). Applied Regression Analysis and Generalized Linear Models. Sage Publications.

E-learning

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and
final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.