091562 - Métodos de Regresión (OPCIÓN ESTADÍSTICA E INVESTIGACIÓN OPERATIVA) - Curso 2011/2012
- Tipo: Materia Ordinaria RD 1497/1987
- Departamentos: Estadística e Investigación Operativa
- Áreas: Estadística e Investigación Operativa
- Centro: Facultad de Matemáticas
- Convocatoria: Primer Cuatrimestre
- Docencia y Matrícula: null
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Existen programas da materia para los siguientes idiomas:CastellanoGallegoInglésCourse objectives
The objectives of this course are that the students:
- Know the models describing the influence of certain variables (explanatory variables) over another one (response variable).
- Know how to perform model selection, and its application for inference and prediction.Contents
1. Simple linear regression model.
Elements of a regression model: the linear model. Least squares estimation. Estimators properties. Inference on the parameters. Variability decomposition. The F test. Prediction.
2. Regression model validation.
Coefficient of determination. Model diagnosis. Transformations.
3. Linear and quadratic operations over random vectors.
Random vectors: mean vector, covariance matrix, linear transformations and standardization. The multivariate normal distribution. Quadratic forms over a random sample of normal variables.
4. The general linear model: multiple regression.
The multiple linear regression model and the general lineal model. Parameter estimation. Interpretation of the parameters: partitioned regression and partial regression. Simple, multiple and partial correlation coefficients. Estimators properties. Inference on the parameters. Variability decomposition. The F test. Prediction.
5. Diagnosis of outliers and influential observations.
Introduction to outliers and influential observations. Leverage in simple regression and multiple regression. Normality diagnosis. Detection of influential observations: measures of influence. Rules to deal with outliers and influential observations.
6. Construction of a regression model.
Polynomial regression. Interactions. Linearized models. Validation of a multiple regression model. Colinearity. Variable selection methods.
7. Analysis of variance.
The analysis of variance model. Parametrization of a discrete explanatory variable. Variability decomposition. The F test. Multiple comparisons. Testing the equality of variances.
8. Analysis of covariance.
Model with a discrete and a continuous explanatory variables, with and without interactions. Testing principal effects and testing interaction.
9. Introduction to experimental design.
Basic concepts of experimental design. Randomized block design. Two-way analysis of variance. Nested variables.
10. Logistic regression.
Logistic regression model: odds and odds-ratio. Maximum likelihood parameter estimation. Estimation algorithms. Inference on the parameters based on their asymptotic distributions and by means of the profile likelihood. Model testing using the deviance. Introduction to the generalized linear models.Basic and complementary bibliography
Faraway, J.J. (2004). Linear models with R. Chapman and Hall.
Faraway, J.J. (2006). Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Chapman and Hall.
Sheather, S.J. (2009). A modern approach to regression with R. Springer.
Agresti, A. (1990). Categorical data analysis. Wiley.
Agresti, A. (1996). An introduction to categorical data analysis. Wiley.
Draper, N.R. and Smith, H. (1998). Applied Regression Analysis. Wiley.
Greene, W.H. (1999). Análisis econométrico. Prentice Hall.
Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning. Springer.
Hosmer, D.W. and Lemeshow, S. (1989). Applied logistic regression. Wiley.
Peña, D. (2002). Regresión y diseño de experimentos. Alianza Editorial.
Ryan, T.P. (1997). Modern Regression Methods. Wiley.
Venables, W.N. and Ripley, B.D. (2002). Modern applied statistics with S. Springer.Competence
- Capacity for identifying and solving problems.
- Independent working capacity.
- Writing statistical reports.
- Team working habilities.
- Model the dependence between a (dependent) random variable and several (independent) explanatory variables.
- Do inference on the model parameters.
- Know how to choose a suitable model for the data under analysis.
- Know how to use a statistical package, according to the contents of the course. Specifically, R software will be used.Teaching methodology
Teaching methodology will include lectures and practical sessions, as well as supervised learning and assignments. Handouts of the course will be provided, jointly with other materials for software usage.
The practical sessions will take place in computer room. During these sessions, some practical examples will be solved using the software R. Individual and group assignments will be proposed. These tasks will consist of solving a practical problem of regression modeling and writing the corresponding statistical report.
The USC virtual platform will be used.Assessment system
The assessment will be the maximum of the final exam and the weighted average of the final exam (with a weight of 60%) and the continuous assessment (with a weight of 40%).
The final exam will contain both theoretical and practical questions, and it will be made by the students partly in written and partly in the computer room.
The continuous assessment will be based on assignments.
The extraordinary assessment (September), will consists of an exam and the mark will be the maximum of this exam and the weighted average of the exam and the continuous assessment during the course.Study time and individual work
Individual work is about one hour and a half for each hour of teaching, including the preparation of the assignments.Recommendations for the study of the subject
Basic knowledge on probability and statistics is required. It is also recommended to have some experience as statistical software user. For a better understanding of the subject, it is advisable to keep in mind the practical meaning of the methods introduced in this course.