Applied Statistics

Code:

M4154

Acronym:

M4154

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Computational Statistics and Data Analysis

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ECAD	17	Study plan since 2021/2022.	1	-	6	42	162

Teaching language

Suitable for English-speaking students

Objectives

To train the student for:
1. regression models, involving  responses (condicioned on explanatory variables) following a distribution from the exponencial family (generalized linear models)
2. implementing the corresponding statistical analyses in a suitable language/software
3. critical thinking in a data analysis process (data collection, modeling, interpretation of results, model diagnostics,...)

Learning outcomes and competences

At the end of the curricular unit, students are expected to:

a) have acquired knowledge about the organized collection of information
b) have learned techniques and statistical models commonly used in statistical data analyses
c) be able to perform regression analyses involving continuous or discrete responses (generalized linear models), in a context of cross-sectional data, using appropriate statistical analysis language/software
d) know how to identify the statistical model that is most adequate to a given contexto
e) know the mechanisms of estimation and inference underlying the studied models
f) have acquired a critical spirit and the ability to interpret the obtained results.

Working method

Presencial

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

Previous knowledge on random variables, probability distributions, sample statistics, confidence intervals and hypothesis tests is required. Those are usual contents of an introductory course on Probability and Statistics for undergrduate students.

Program

1. Simple linear regression. Parameter estimation by the least square method and the maximum likelihood method (includes revision of Pearson correlation coefficient, if necessary)


2. Multiple linear regression. Model and underlying assumptions, parameter estimation, hypothesis tests on the model parameters, confidence intervals, prediction intervals, coefficient of determination, multicollinearity, categorical explanatory variables, variable selection algorithms, model selection and comparison, diagnosis.


3. Analysis of variance (ANOVA) models


4. Generalized linear models. Logistic regression and Poisson regression.

Mandatory literature

Docentes da UC ; Apontamentos escritos

Complementary Bibliography

Julian Faraway; Linear Models with R, Taylor and Francis, 2009. ISBN: 1584884258
P. McCullagh; Generalized linear models. ISBN: 0-412-31760-5
David Hosmer, Stanley Lemeshow , Rodney Sturdivant; Applied Logistic Regression, John Wiley & Sons, Inc., 2013. ISBN: 9780470582473
S Weisberg; Applied Linear Regression, John Wiley & Sons, 2014. ISBN: 9781118386088
John Fox, Sanford Weisberg; An R Companion to Applied Regression, 3rd Edition, SAGE Publications, Inc., 2019. ISBN: 978-1-5443-3647-3

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 language/software will be the free programming language R.

Software

R Project

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
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

According to FCUP rules.

Calculation formula of final grade

Evaluation by 2 tests. The last test will be performed in the normal season (1st evaluation season).

For each student, the test with the best mark has a weight of 60% while the other test has a weight of 40%, in the computation of the final mark. 
The mark of each test will only be taken into account for the final assessment if it is equal to or greater than 6 (on a scale of 0 to 20).
The second test can only be taken by students who have obtained a mark of 6 or more in the first test, in the scale 0-20.

The exam in the appeal season must be solved completely - the marks from the tests will not be considered.  

Classification improvement

The grade improvement can only be done in the exam of the second period (appeal season).