Statistics

The objective of this course is for students to learn the basics of probability, statistical inference and regression models that will serve as a basis for building advanced statistical models for data analysis.

UNIT 1. DESCRIPTIVE STATISTICS
1.1 General concepts.
1.2 Frequency distributions.
1.3 Graphic representations.
1.4 Characteristic measurements: position, dispersion and shape.
1.5 Two-dimensional descriptive statistics. Contingency tables.

UNIT 2. FUNDAMENTALS OF PROBABILITY
2.1 Random experiment. Events and sample space.
2.2 Assignment and definition of probability. Operations with events.
2.3 Conditional probability. Independence of events. Remarkable results.

UNIT 3. RANDOM VARIABLES
3.1 Discrete variable. Support, probability mass function and distribution function.
3.2 Continuous variable. Probability density function and distribution function.
3.2 Characteristic measures.
3.3 Main models of discrete and continuous distributions.
3.4 Central Limit Theorem.
3.5 Approximation of distributions.

UNIT 4. INTRODUCTION TO STATISTICAL INFERENCE AND PARAMETER ESTIMATION
4.1 Introduction to Statistical Inference.
4.2 Estimation for a population.
4.3 Estimation for two populations.
4.4 Estimation by confidence intervals.

UNIT 5. HYPOTHESIS TESTING
5.1 Introduction to hypothesis testing.
5.2 Testing procedure.
5.3 Tests for one population.
5.4 Tests for two populations.

UNIT 6. INTRODUCTION TO LINEAR REGRESSION
6.1 Two-dimensional descriptive statistics for continuous variables. Dispersion diagram.
6.2 Linear regression model.

BASIC BIBLIOGRAPHY
Borrajo, M. I., Conde, M. and Crujeiras, R. (2020). Estatística Descritiva. Esenciais USC Collection. Online: https://www.usc.gal/libros/es/categorias/948-estatistica-descritiva-334…
Borrajo, M. I., Conde, M. and Crujeiras, R. (2021). Fundamentos da Teoría da Probabilidade. Esenciais USC Collection. Online: https://www.usc.gal/libros/es/categorias/1025-fundamentos-da-teoria-da-…
Borrajo, M. I., Conde, M. and Crujeiras, R. (2021). O programa estatístico R. Esenciais USC Collection. Online: https://www.usc.gal/libros/es/categorias/1024-o-programa-estatistico-r-…
Borrajo, M. I., Conde, M. and Crujeiras, R. (2023). Inferencia Estatística Paramétrica I. Esenciais USC Collection.
Borrajo, M. I., Conde, M. and Crujeiras, R. (2023). Inferencia Estatística Paramétrica II. Esenciais USC Collection.
Febrero Bande, M., Galeano San Miguel, P., González Díaz, J. and Pateiro López, B. (2008). Estadística: Ingeniería Técnica en Informática de Sistemas. Universidade de Santiago de Compostela, Santiago de Compostela. Online: http://eio.usc.es/pub/julio/papers/PubDocenteTeoriaEstadistica.pdf
Fernández-Viagas, Escudero, V., Framiñán Torres, J. M., Pérez González, P. and Villa Caro, G. (2016) Problemas Resueltos de Probabilidad y Estadística en la Ingeniería. Universidad de Sevilla, Sevilla.
COMPLEMENTARY BIBLIOGRAPHY
Agresti, A., and Kateri, M. (2021). Foundations of Statistics for Data Scientists: With R and Python. CRC Press, Boca Raton. Online: http://sage.unex.es/502243/4-Stats4DS-RPy_2022-Agresti-Kateri.pdf
Cao, R., Francisco, M., Naya, S., Presedo, M. A., Vázquez, M., Vilar, J. A. and Vilar, J. M. (1998). Estadística Básica Aplicada. Tórculo Edicións, Santiago de Compostela.
Cao, R., Francisco, M., Naya, S., Presedo, M. A., Vázquez, M., Vilar, J. A. and Vilar, J. M. (2001). Introducción a la Estadística y sus Aplicaciones. Ediciones Pirámide, Madrid.
Devore, J. L. (2001). Probabilidad y Estadística para Ingeniería y Ciencias. Thomson Learnin, México. Online: https://elibro-net.ezbusc.usc.gal/es/lc/busc/titulos/93280
Guisande-González, C., Vaamonde-Liste, A. and Barreiro-Felpeto, A. (2011). Tratamiento de Datos con R, Statistica y SPSS. Díaz de Santos, Madrid. Online: https://www-ebooks7-24-com.ezbusc.usc.gal/stage.aspx?il=4021&pg=&ed=
Mendenhall, W. M. and Sincich, T. L. (2016). Statistics for Engineering and the Sciences. CRC Press, Boca Raton.
Montgomery, D. C., Runger, G. C. and Medal, E. G. U. (2007). Probabilidad y Estadística Aplicadas a la Ingeniería. Limusa-Wiley, México.
Peña, D. (1991). Fundamentos de Estadística. Alianza Editorial, Madrid.
Peña, D. (1993). Estadística: Modelos y Métodos. Alianza Editorial, Madrid.
Quesada Paloma, V. e García Pérez, A. (1988). Lecciones de Cálculo de Probabilidades. Ediciones Díaz de Santos, Madrid.
Ross, S. M. (2014). Introduction to Probability and Statistics for Engineers and Scientists. Elsevier, Burlington. Online: https://www-sciencedirect-com.ezbusc.usc.gal/book/9780128243466/introdu…

The recommended bibliography is available in the librarys of the USC.

After completing this course, students are expected to work on the skills listed in the memory of the Degree in Artificial Intelligence of the Universities of A Coruña, Santiago de Compostela and Vigo. Thus, students must acquire the following basic, general, transversal and specific skills: CG2, CG4, CB2, CB3, CB5, TR3, CE1, CE2 and CE3.
As learning outcomes, students should know the basic probabilistic fundamentals, the fundamentals of statistical inference and the fundamentals of regression models. Students are expected to be able to describe a random event in one or/and two statistical variables, choosing appropriate graphs for their representation and using appropriate statistics for each case, and to be able to justify the relevance of a statistical procedure or hypothesis test in a specific application. Furthermore, they should be able to design the eligibility criteria of a sample and they should be able to validate the statistical models appropriately and correct them accordingly. Taking all this into account, once the subject is finished, students should have the basis to build advanced statistical models for data analysis.

Expository teaching (30 hours). For the transmission of knowledge, slides and blackboard will be used and type problems will be solved, so that students can work on the provided exercise bulletins. Regarding the material for monitoring the subject, apart from the recommended bibliography, students will have the help of additional material on the USC Virtual Campus. In the expository teaching sessions the following skills will be worked on: general skills (CG4), basic skills (CB2, CB3 and CB5) and specific skills (CE1 and CE2).
Practical sessions in the computer room and/or laboratory (20 hours). In this type of teaching, the involvement of the students in solving the practical exercises will be guided by the teacher during the hours taught in the classroom. These problems will be solved with the help of software that allows solving the practical problems that arise throughout the subject. Outside the classroom, students must solve exercises autonomously to consolidate concepts and face the problems of analyzing databases and programming functions in the statistical software on their own. Objectives developed: general skills (CG2, CG4), basic skills (CB2 and CB3), transversal skills (TR3) and specific skills (CE1, CE2 and CE3).

Tutorials (1 hour): the tutorials are aimed at monitoring student learning. In the tutoring sessions, different activities will be carried out that allow students to achieve an overview of the subject and, at the same time, identify in which aspects they need to improve. Objectives developed: general skills (CG4), basic skills (CB2, CB3 and CB5) and specific skills (CE1, CE2 and CE3).

The distribution of lecture hours (30 hours) and seminars (20 hours), by topic, is as follows, in one-hour sessions:
Unit 1. Descriptive statistics: 5 lectures, 4 seminars.
Unit 2. Foundations of probability: 4 lectures, 2 seminars.
Unit 3. Random variables: 8 lectures, 4 seminars.
Unit 4. Introduction to inference and parameter estimation: 5 lectures, 4 seminars.
Unit 5. Hypotheses testing: 4 lectures, 4 seminars.
Unit 6. Introduction to linear regression: 4 lectures, 2 seminars.

During the course, the degree to which students have achieved the objectives proposed for this subject will be evaluated continuously. The qualification will be done through continuous evaluation and a final exam. The weight of each part of the evaluation is detailed below.
Continuous evaluation (30%): continuous evaluation will be carried out based on participation in different types of tasks. The continuous evaluation activities will include the resolution of practical cases (individual or in group), which may include the use of statistical software. Individual resolution exercises will also be proposed to be carried out in person and/or remotely. The grade obtained will be kept between opportunities of the same academic year (ordinary and extraordinary). During this part, the participation and involvement of the students in the classroom will also be evaluated. Competences evaluated: CG2, CG4, CB2, CB3, TR3, CE1, CE2 and CE3.

Final exam (70%): the final exam will consist of several questions and theoretical-practical exercises on the contents of the subject, which may include the interpretation of results obtained with the statistical software used during the interactive teaching. Competences evaluated: CG2, CG4, CB2, CB3, CB5, TR3, CE1, CE2 and CE3.

Note that, in cases of fraudulent completion of exercises or tests, the provisions of the "Regulations for the evaluation of the academic performance of students and the review of grades" will apply.

Finally, it is considered that the evaluation is attended when the interested person participates in activities that allow them to obtain at least 50% of the final evaluation. The weight of the continuous evaluation in the second opportunity will be the same as in the ordinary call of the semester. For repeating students, the evaluation will be carried out in the same manner, and no grades obtained in the previous course will be retained (including the continuous assessment grade).

In this subject, the students have the following teaching given by the professors: 30 hours of expository teaching, 20 hours of practical sessions in the computer room and/or laboratory and 1 hour of tutorials. The students must dedicate, in addition, 60 hours to deepen the knowledge of the expository classes and 39 to the resolution of practical problems. During these hours, the acquired knowledge must be deepened, through the review of concepts, practice of problem solving and the consultation of the recommended bibliography.

The follow-up to the expository and interactive sessions is essential to pass the course. Students must carry out all the activities recommended by the professors (problem solving, literature review and practical exercises) to successfully pass the subject. In addition, it is recommended to make use of the tutorial hours to resolve any questions that may arise.

Recommended prerequisites: Algebra.