ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable
To introduce the main principles of Statistical Inference, and the basic techniques related to the Linear Model.
Chapter 1. Introduction to Statistical Inference. (2 hours)
Chapter 2. Point estimation. (5 hours)
Parametric methods of estimation: method of moments and maximum likelihood. Bounds for the variance: Frechet-Cramer-Rao inequality.
Chapter 3. Parametric confidence regions. (3 hours)
Confidence intervals methods: pivotal method, Neyman’s method, Bayesian confidence intervals and asymptotic intervals.
Chapter 4. Parametric hypothesis testing. (6 hours)
Optimality criteria between hypothesis tests. Neyman-Pearson test. Likelihood ratio test.
Chapter 5. Nonparametric methods (3 hours)
Nonparametric methods of estimation. Goodness-of-fit testing.
Chapter 6. The simple linear model. (4 hours)
Elements of a linear model. Least squares estimation. Properties of the estimators. Inference on parameters. Variance decomposition. Prediction.
Chapter 7. Validation of a regression model. (2 hours)
The coefficient of determination. Model diagnosis. Transformations.
Chapter 8. Multiple linear regression model. (4 hours)
Formulation of the multiple linear regression model. Solution in the context of the general linear model: matrix notation, estimation for least squares, estimator properties, parameter inference , prediction. Interpretation of the coefficients in multiple regression. Simple, multiple and partial correlation. Variable selection methods.
Basic and complementary bibliography
Casella, G. and Berger, R.L. (1990). Statistical Inference. Wadsworth & Brooks/Cole.
Chihara, L. and Hesterberg, T. (2011). Mathematical Statistics with Resampling and R. Wiley.
Cristóbal Cristóbal, J.A. (1995). Inferencia Estadística. Universidad de Zaragoza.
Faraway, J.J. (2004). Linear models with R. Chapman and Hall.
García Pérez, A. (2010). Estadística básica con R. UNED.
Rohatgi, V.K. (1976). An introduction to Probability Theory and Mathematical Statistics. Wiley.
Shao, J. (2003). Mathematical Statistics. Springer.
Shao, J. (2005). Mathematical Statistics: Exercises and Solutions. Springer.
Sheather, S.J. (2009). A modern approach to regression with R. Springer.
Peña, D. (2002). Regresión y diseño de experimentos. Alianza Editorial.
Vélez Ibarrola, R. and García Pérez, A. (1997). Principios de Inferencia Estadística. UNED.
In this course, according to the proposal for the Degree in Mathematics, the following competences will be enhanced: basic competence with the code CB2, general competence with the code CG3, cross-area competence with the code CT3, and specific competences with the codes CE1, CE7 and CE9.
SCENARIO 1 (adapted normality). Lectures and interactive teaching will be given in classrooms, according to the plans of Facultad de Matemáticas, and will be supplemented with virtual campus (moodle), where students will find bibliographic materials, exercises, teaching videos, etc. Through the virtual campus, students will be able to make tests and to put their assignments for continuous assessment. Tutorial guidance will be in classrooms, by electronic mail or by MS Teams.
SCENARIO 2 (social distance). Partially virtual teaching, according to the plans of Facultad de Matemáticas. Virtual campus (moodle) will be used, with teaching videos and bibliographic materials provided by professors, together with MS Teams platform. Tutorial guidance will be given by electronic mail or MS Teams.
SCENARIO 3 (closing). Completely virtual teaching through the virtual campus (moodle), with some activities given by asynchronous materials. Tutorial guidance will be given by electronic mail or MS Teams.
Assessment will be based on continuous assessment and a final exam, where continuous assessment will contribute one half of the total assessment and the final exam will contribute the other half.
Continuous assessment will help to check competences CG3, CE1, CE7 and CE9 of the Degree in Mathematics.
Final exam will consist of a theoretical part and a practical part. The theoretical part will be based on concepts and short questions to assess whether some crucial knowledge is being acquired. Competences CG3 and CE1 will be assessed in this part. The practical part will be focused on solving exercises and problems similar to those proposed and solved in seminars and labs, assessing in this way competences CE7 and CE9.
Evaluation attendance: a student will be considered as attending the evaluation when he/she has participated in any evaluation activity, either in continuous assessment or in the final exam.
In the second opportunity of assessment, an exam will be done and the grade in this second opportunity will be a weighted average of the continuous assessment during the semester and the second opportunity exam, with weights 30% and 70%, respectively.
Continuous assessment will be adapted to the situation regarding COVID-19 as described below:
SCENARIO 1 (adapted normality). Continuous assessment will consist of problems individually solved by students and presented in seminars or through specific assignments in the virtual campus. Practical assignments will also be proposed, that can be done individually or in groups, in classrooms or by internet, using R software.
SCENARIO 2 (social distance). Continuous assessment will consist of problems, individually solved by students, and practical assignments using R, that can be in classrooms or by internet.
SCENARIO 3 (closing). Continuous assessment will consist of problems solved individually by students, and practical assignments using R. Activities that were expected to be in classrooms under scenarios 1 and 2 will be done by internet using MS Teams.
Individual work is about one hour and a half for each hour of teaching, including preparation of the assignments.
Attending lectures, seminars, computer labs and tutorial guidance is strongly recommended as fundamental tools to follow the course. Solving proposed exercises, studying the topics in a timely manner and practising R software are useful habits to get a fruitful outcome from the course.
R software, which will be the basic tool in computer labs, can be freely downloaded from http://www.r-project.org/
Online moodle-based platform “Campus Virtual” will be used.
Contingency plans for COVID-19:
SCENARIO 1 (adapted normality).
Teaching methodology: Lectures and interactive teaching will be given in classrooms, according to the plans of Facultad de Matemáticas, and will be supplemented with virtual campus (moodle), where students will find bibliographic materials, exercises, teaching videos, etc. Through the virtual campus, students will be able to make tests and to put their assignments for continuous assessment. Tutorial guidance will be in classrooms, by electronic mail or by MS Teams.
Continuous assessment: Continuous assessment will consist of problems individually solved by students and presented in seminars or through specific assignments in the virtual campus. Practical assignments will also be proposed, that can be done individually or in groups, in classrooms or by internet, using R software.
SCENARIO 2 (social distance).
Teaching methodology: Partially virtual teaching, according to the plans of Facultad de Matemáticas. Virtual campus (moodle) will be used, with teaching videos and bibliographic materials provided by professors, together with MS Teams platform. Tutorial guidance will be given by electronic mail or MS Teams.
Continuous assessment: Continuous assessment will consist of problems, individually solved by students, and practical assignments using R, that can be in classrooms or by internet.
SCENARIO 3 (closing).
Teaching methodology: Completely virtual teaching through the virtual campus (moodle), with some activities given by asynchronous materials. Tutorial guidance will be given by electronic mail or MS Teams.
Continuous assessment: Continuous assessment will consist of problems solved individually by students, and practical assignments using R. Activities that were expected to be in classrooms under scenarios 1 and 2 will be done by internet using MS Teams.
Wenceslao Gonzalez Manteiga
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813204
- wenceslao.gonzalez [at] usc.es
- Category
- Professor: University Professor
Cesar Andres Sanchez Sellero
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813208
- cesar.sanchez [at] usc.es
- Category
- Professor: University Lecturer
Rosa María Crujeiras Casais
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813212
- rosa.crujeiras [at] usc.es
- Category
- Professor: University Lecturer
Alberto Rodriguez Casal
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- alberto.rodriguez.casal [at] usc.es
- Category
- Professor: University Lecturer
Mercedes Conde Amboage
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mercedes.amboage [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
Fernando Castro Prado
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- f.castro.prado [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLIS_01 | Spanish, Galician | Classroom 02 |
| 11:00-12:00 | Grupo /CLIS_02 | Galician, Spanish | Classroom 06 |
| 11:00-12:00 | Grupo /CLE_02 | Spanish, Galician | Classroom 09 |
| Tuesday | |||
| 10:00-11:00 | Grupo /CLE_02 | Galician, Spanish | Classroom 09 |
| 11:00-12:00 | Grupo /CLIS_04 | Galician, Spanish | Classroom 06 |
| 12:00-13:00 | Grupo /CLIS_03 | Galician, Spanish | Classroom 02 |
| 12:00-13:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 07 |
| Wednesday | |||
| 10:00-11:00 | Grupo /CLIL_01 | Galician, Spanish | Computer room 3 |
| 12:00-13:00 | Grupo /CLIL_03 | Galician, Spanish | Computer room 3 |
| 13:00-14:00 | Grupo /CLIL_02 | Spanish, Galician | Computer room 2 |
| Thursday | |||
| 09:00-10:00 | Grupo /CLIL_04 | Spanish, Galician | Computer room 3 |
| 10:00-11:00 | Grupo /CLIL_06 | Galician, Spanish | Computer room 2 |
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 07 |
| 11:00-12:00 | Grupo /CLIL_05 | Galician, Spanish | Computer room 4 |
| 05.31.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 02 |
| 05.31.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 03 |
| 05.31.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 05.31.2021 10:00-14:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 07.06.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |