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. y 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. y 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. The expository, interactive sessions and tutorials will be held completely in person according to scenario 1.
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.
According to scenario 1, at least two continuous assessment tests will be carried out in person (face-to-face), a final exam in the ordinary opportunity and another in the extraordinary opportunity (July).
Continuous evaluation (30 %): continuous evaluation will be carried out based on problem solving by students. In these problems, students will use the R program and write the obtained conclusions. With the different activities that will be proposed throughout the course, the level of acquisition of the basic skills CB7 and CB9 and general skills CG3, CG4 and CG5 will be assessed. The level achieved in the specific competences E2, E5 and E8 will also be evaluated. Likewise, the level reached in the transversal competence CT3 will be taken into account in the evaluation.
Final exam (70 %): the final exam of the ordinary and extraordinary opportunities will consist of several theoretical-practical questions about the contents of the subject, within which the interpretation of results obtained with the statistical language R used in the interactive teaching. In these exams, the specific competences will be evaluated: E1, E2, E4, E5, E6 and E8.
Presentation to the evaluation: it is considered that a student attends a call when she participates in activities that allow her to obtain at least 50 % of the final evaluation.
The weight of the continuous evaluation and its weight will be kept in the ordinary and extraordinary opportunities within the call for each course.
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 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. .
This guide and the criteria and methodologies described in it are subject to modifications derived from regulations and guidelines of the participating universities in the Master in Statistical Techniques.
Contingency plan
a) Teaching methodology
The details for Scenarios 2 and 3, alternatives to Scenario 1, are described below:
Scenario 2: Whenever the dimensions of the classroom allow it, the expository, interactive sessions, tutorials and evaluation tests will be face-to-face. Otherwise, they will be held electronically and, preferably, synchronously using Microsoft Teams or similar means provided by the participating universities. It will be guaranteed that the volume of information and time devoted to telematic tasks is proportionate to the credit load of the subject. The delivery of the proposed continuous evaluation activities will allow, for example, to carry out the follow-up of the subject. The course materials (which comply with the regulations regarding intellectual property and data protection) will be available through the website of the Master in Statistical Techniques.
Scenario 3: The expository, interactive sessions, tutorials and evaluation tests will be completely virtual and, preferably, synchronous using Microsoft Teams or similar means provided by the participating universities. It will be guaranteed that the volume of information and time devoted to telematic tasks is proportionate to the credit load of the subject. The delivery of the proposed continuous evaluation activities will allow, for example, to carry out the follow-up of the subject. The course materials (which comply with the regulations regarding intellectual property and data protection) will be available through the website of the Master in Statistical Techniques.
b) Evaluation criteria and methods
Scenario 2: The evaluation criteria coincide with those set out for scenario 1. Regarding the evaluation methods, whenever the dimensions of the classroom allow it, all the tests will be face-to-face. Otherwise, they will be held electronically and, preferably, synchronously using Microsoft Teams or similar means provided by the participating universities. The tests would be similar to those that would be carried out in person using the tools that the participating universities provide for their supervision. In addition, they would be held on a fixed schedule, the same for all students, and with limited time.
Scenario 3: The evaluation criteria coincide with those set out for scenario 1. Regarding the evaluation methods, all the evaluation tests will be non-face-to-face as described in scenario 2.
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.
Paula Saavedra Nieves
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- paula.saavedra [at] usc.es
- Category
- Professor: Temporary PhD professor
Maria Isabel Borrajo Garcia
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mariaisabel.borrajo [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor