Degree | Type | Year | Semester |
---|---|---|---|
2500149 Mathematics | OT | 4 | 0 |
The students will learn to formalize, analyze and validate models that attempt to assess the relationships between different variables under uncertainty conditions whithin the mathematical statistics setting, in order to provide confidence intervals for the parameters'model and perform statistical hypotheses tests.
The goal of a regression model is to explain the mean behaviour of a response variable in terms of other variables related to it. Given a model, predictions and residuals can be obtained and analyzed, analysis that will be translated into decisions at an experimental level. The students must be conscious of the constraints in each mathematical model and select which model behaves better. Thus, they must know how to adjust, validate and compare various linear models and select the best set of regressors in each case.
Some extensions of the linear model are also introduced, such as generalized linear models, polynomial or nonlinear models, for example, as they extend the scope of modeling and allow constraints to be lowered. The general linear model is a theoretical framework that allows to formulate the techniques of analysis of the variance and the design of experiments within the linear model.
With this course, students will be able to explore and validate the theoretical properties of the general linear model, learn some extensions, and be trained to model data with free software. They will needto understand in depth the importance of the most important theorems in this area, as well as their proof.
Preliminaries
• The simple linear model: least squrares, maximum likelihood and other estimation methods.
• Multivariate Gaussian distributions and related laws.
The multiple linear model
• The linear model. Normal equations. Properties of the coefficients’ and variance estimators. BLUE. Goodness of fit indicators.
• Sum of squares decompositions and distributions. Hypothesis tests and confidence regions. The Cochran theorem.
• Model diagnostics. Transformations.
• Outliers and influential observations.
Design of experiments, anova and the general linear model
• One-way analysis of variance. Multiple comparisons.
• Analysis of the variance with several factors. Interactions.
• The design of experiments setting.
• The response surface models.
Certain extensions of the linear model
• Random effects models. Repeated measures models.
• Generalized linear models: binomial, Poisson, etc.
• Nonlinear regression.
The statistical models and their corresponding assumptions and properties are introduced in the theoretical sessions. Emphasis will be placed on rigor in the proofs as well as on the applicability and interpretation of the methods.
The discussion will be encouraged in the classroom and theoretical problems will be proposed to deepen the topics. Problems, and practical exercises to be performed with free software R will be proposed, with the aim that students will be able to model data. Some sections of the course will be developed by students in the form of work and will be a written as a short report and presented to the classroom.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Computer work | 24 | 0.96 | 1, 3, 4, 2 |
Problems sessions | 6 | 0.24 | 7, 4, 2 |
Theoretical classes | 30 | 1.2 | 7, 2 |
Type: Autonomous | |||
Personal work | 80 | 3.2 | 3, 4, 2 |
The evaluation scheme is as follows:
NC = 0.3 * P1 + 0.4 * P2 + 0.15 * Tb + 0.15 * Lli
P1: First partial exams (30%) = theory and problems (15% ) + computer test (15%).
P2: Second partial exams (40%) = theory and problems (20% ) + computer test (20%).
Tb: Personal project (15%).
Lli: Delivery of solved problems and practical exercices (15%).
Besides that, the students will have the option of taking an additional recovery exam (RE) with the same format, to recover only the P1+P2 amount.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
First partial exam | 0,2 | 4 | 0.16 | 7, 4, 2 |
Oral exposition of a report | 0,3 | 1 | 0.04 | 1, 3, 6, 5, 4, 2 |
Second partial exam | 0,3 | 4 | 0.16 | 1, 4, 2 |
Tasks delivery | 0,2 | 1 | 0.04 | 3, 4, 2 |
Complementary references