Applied Statistics

Code:

M4158

Acronym:

M4158

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Medical Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:FM	15	Study plan since academic year 2023/2024	1	-	6	42	162

Teaching language

English

Objectives

1. Train the student for regression analysis involving responses following a distribution belonging to the exponential family (generalized linear models)
2. Implement statistical analyses in suitable software
3. Promote critical thinking in a data analysis process (data collection, modeling, interpretation of results, ...)

Learning outcomes and competences

At the end of the curricular unit, students are expected to:
a) acquire knowledge about the organized collection of information
b) learn techniques and statistical models commonly used in data processing
c) know how to apply and implement the models studied in R
d) know how to correctly choose the learned statistical models for concrete problems
e) acquire a critical spirit and the ability to interpret the results obtained.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Previous knowledge on random variables, probability distribution, sample statistics, confidence intervals and hypothesis tests is required. Those are usual contents of an introductory course on Probability and Statistics for undergrduate students. A brief review of these topics will be given. 

Program

1     0. Brief review of basic statistical inference techniques - confidence intervals and hypothesis tests.
1- Introduction to the programming language in R software environment.
2. Pearson and Spearman correlation.
3. Simple linear regression.
4. Multiple linear regression. Model, parameter estimation, hypothesis tests on model parameters, confidence intervals, prediction intervals, coefficient of determination, multicollinearity, model selection methods, model comparison, diagnosis and residual analysis.
5*. Analysis of variance: 1 and 2 factors.
6*. Generalized linear models. Logistic regression.
*Only one subject, from 5* or 6*, will be studied. 

Mandatory literature

Rita Gaio; Apontamentos

Complementary Bibliography

000083800. ISBN: 1-58488-029-5
000040469. ISBN: 0-387-95475-9
000098707. ISBN: 978-0-521-86116-8
000074783. ISBN: 0-387-95187-3
000040365. ISBN: 0-387-95284-5
000102543. ISBN: 1-58488-325-1
000040221. ISBN: 0-387-98218-3
Julian Faraway; Linear Models with R, Taylor and Francis, 2009. ISBN: 1584884258
Julian Faraway; Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Chapman & Hall/CRC Texts in Statistical Science, 2006. ISBN: 158488424X

Teaching methods and learning activities

Classes will be simultaneously theoretical and practical, with several examples of application and always making use of statistical programming. The used software will be the free programming language R.

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	75,00
Trabalho prático ou de projeto	25,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

No requirements.

Calculation formula of final grade

Evaluation by final examination and optional project.

1. There will be an exam in both evaluation periods, split into two equally valued parts.

2. There will be a midterm exam that may replace the second part of the final exam (concerning the first part of the course material);

3. The grade obtained in the project cannot be improved;

4. Evaluation formula: There are two evaluation formulas:

F1: 
Examination [12,15]; project [5,8]
From these 2 components, the one where the student had the highest score is worth the maximum of the respective interval. The worst component is worth the minimum of the respective interval.

F2: The student does not turn in the project and in this case only the examination result counts, but the final mark for the course will never exceed 16, even if the examination grade is higher. 

The final classification of the student is MAX(F1, F2).

Classification improvement

Improvement of the final mark: final examination and the possibility of attending the midterm exam. The possibility of turning in the project. The evaluation formula is the same (see above).