ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 20 Interactive Classroom: 15 Total: 125
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
In this subject, we try to familiarize the students with the regression models. The objectives to achieve are:
• In-depth knowledge of the theoretical aspects of linear regression analysis and, in particular, of the general linear model.
• To know how to apply linear regression methods in the analysis of real data of a complex nature.
• To know how to communicate the results obtained with linear regression techniques in multidisciplinary environments.
• To know the potentialities and limitations of linear regression analysis.
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. 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.
4. Diagnosis of outliers and influential observations.
Introduction to outliers and influential observations. Leverage in simple and multiple regression. Outliers detection:
residual standarization. Normality diagnosis. Influence detection: influence measurements. Outliers and leverage
treatment.
5.Construction of a regression model.
Polynomial regression. Interactions. Linearized models. Validation of a multiple regression model. Colinearity. Variable
selection methods
6. 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.
7. Analysis of covariance.
Model with a discrete and a continuous explanatory variables, with and without interactions. Testing principal effects
and testing interaction. Regression models with several discrete and continuous explanatory variables.
8. Logistic regression.
The logistic regression model: odds and odds ratio. Maximum likelihood parameter estimation. Estimation algorithms.
Estimation algorithms. Inference on the parameters. Model testing using the deviance.
BASIC
Faraway, J.J. (2015). Linear models with R (2nd edition). Chapman and Hall.
Faraway, J.J. (2006). Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Chapman and Hall.
Montgomery, D. C., Peck, E. A. and Vining, G. G. (2012). Introduction to linear regression analysis (5th ed). Wiley
Ritz, C. and Streibig, J.C. (2008). Nonlinear regression with R. Springer.
Sheather, S.J. (2009). A modern approach to regression with R. Springer.
COMPLEMENTARY
Agresti, A. (1996). An introduction to categorical data analysis. Wiley.
Fox, J. and Weisberg, S. (2011). An R companion to applied regression. SAGE Publications.
Greene, W.H. (1999). Análisis econométrico. Prentice Hall.
Hosmer, D. W., Lemeshow, S. and Sturdivant, R. X. (2013). Applied logistic regression (3rd edition). John Wiley & Sons.
Huet, S., Bouvier, A., Gruet, M.A. and Jolivet, E. (1996). Statistical tools for nonlinear regression (A practical guide with S-Plus examples). Springer.
Peña, D. (2010). Regresión y diseño de experimentos. Alianza Editorial.
Venables, W.N. and Ripley, B.D. (2010). Modern applied statistics with S (4th edition). Springer.
Below are the specific competences (E), which will be worked in this area:
E1 - To know, identify, model, study and solve complex problems of statistics and operational research, in a scientific, technological or professional context, arising in real applications.
E2 - To develop autonomy for the practical resolution of complex problems arising in real applications and for the interpretation of the results in order to help in making decisions.
E4 - To acquire the necessary skills in the theoretical-practical management of the theory of probability and random variables that allow their professional development in the scientific / academic, technological or professional specialized and multidisciplinary field.
E5 - To know in depth the theoretical-practical fundamentals of modeling and study of different types of dependency relationships between statistical variables.
E6 - To acquire advanced theoretical-practical knowledge of different mathematical techniques, specifically aimed at assisting in decision-making, and develop reflection skills to evaluate and decide between different perspectives in complex contexts.
E8 - To acquire advanced theoretical-practical knowledge of the techniques used to make inferences and contrasts regarding variables and parameters of a statistical model, and know how to apply them with sufficient autonomy in a scientific, technological or professional context.
In this subject, the basic (CB6-CB10), general (CG1-CG5) and transversal (CT1-CT5) competences collected in the title memory will be worked, focusing on the following:
CB7 - To know how to apply the acquired advanced knowledge, integrating them in solving problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study.
CB9 - To know how to communicate their conclusions and the knowledge and ultimate reasons that sustain them to specialized and non-specialized audiences in a clear and unambiguous way.
CG3 - To develop the capacity to carry out studies and research tasks and transmit the results to specialized, academic and generalist audiences.
CG4 - To integrate advanced knowledge and face decision making based on scientific and technical information.
CG5 - To develop the ability to apply algorithms and complex problem solving techniques in the field of statistics and operational research, managing the appropriate specialized software.
CT3 - To solve complex problems in new environments through the integrated application of knowledge.
The teaching will consist of expository and interactive classes, as well as the tutoring of learning and the tasks entrusted to the students.
In the expository and interactive classes, examples will be solved using the statistical software R. In addition, activities will be proposed for the students, which will consist of solving questions, exercises and examples related to the Regression Models.
Notes on the subject will be provided, as well as other guidance materials for learning the software. The notes and other teaching tools will be fully available through a web access tool.
The evaluation of this subject consists of two parts: a final exam with a weight of 70%, and a part of continuous evaluation with a weight of 30%. The qualification obtained in the continuous evaluation and its weight will be kept in the ordinary and extraordinary opportunities within the announcement of each course.
The final exam of the ordinary and extraordinary calls will consist of several theoretical-practical questions on the contents of the subject. In these exams, the specific skills will be evaluated: E1, E2, E4, E5, E6 and E8.
The continuous assessment of the subject is divided into two parts. The first part corresponds to Themes 1, 2 and 3, with a weight of 10% in the final grade. The second corresponds to Topics 4, 5, 6, 7 and 8, with a weight of 20% in the final grade. The continuous evaluation will be carried out based on the resolution of problems, face-to-face or remote, by the students. In these problems, the students will use the R program and write the conclusions drawn. With the different activities that will be proposed throughout the course, the level of acquisition of the basic competences CB7 and CB9, general CG3, CG4 and CG5 and transversal CT3 will be assessed. The level reached in the specific competences E2, E5 and E8 will also be evaluated.
Presentation to the evaluation: it is considered that a student attends a call when he participates in activities that allow him to obtain at least 50% of the final evaluation.
Each ECTS credit translates into 7.6 hours of face-to-face activities: 20 hours of expository sessions, 15 hours of interactive sessions (seminars, laboratories in computer classrooms and presentation of tasks) and 3 hours for exams.
It is estimated that the student must dedicate 87 hours to non-face-to-face activities, including the resolution of exercises, the resolution of practical cases, activities of data analysis and models, the task elaboration and personal study time.
In total, 25 hours per ECTS credit.
It is convenient that students have basic knowledge of probability and statistics. It is also advisable to have medium skills in the use of computers, and in particular statistical software. For a better learning of the subject, it is convenient to keep in mind the practical sense of the models that are introduced in this subject.
The material used in the teaching-learning process is both the recommended bibliography and material provided by the teaching staff. The website of the Master in Statistical Techniques is used as support for the subject material.
The development of the contents of the subject will be carried out taking into account that the competences to be acquired by the students must comply with the MECES3 level. In this sense, although the contents of the subject focus only on linear regression models (with continuous and binary response - logistic regression - and with continuous but also categorical explanatory variables), these will be studied in an exhaustive way, presenting all the phases of the modeling process in a rigorous way: formulation of the model, estimation, validation and diagnosis. In addition, the errors that can be made when making decisions based on models with specification problems (models that do not meet the hypotheses under which the inference is formulated, or models that do not directly fit the observations) will also be discussed.
In cases of fraudulent performance of exercises or tests, the provisions of the respective regulations of the participating universities in the Master in Statistical Techniques will apply.
This guide and the criteria and methodologies described in it are subject to modifications derived from regulations and guidelines of the universities participating in the Master in Statistical Techniques.
Maria Jose Ginzo Villamayor
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mariajose.ginzo [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
Paula Saavedra Nieves
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- paula.saavedra [at] usc.es
- Category
- Professor: University Lecturer
| 01.24.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 04 |
| 06.30.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 04 |