Applied Statistics in Science and Engineering

Code:

M4083

Acronym:

M4083

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ENM	13	Official Study Plan since 2013-2014	1	-	6	56	162
M:FM	5	Study plan since 2013/2014	1	-	6	56	162

Teaching language

Portuguese

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) 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 software
d) know how to identify the statistical model that is most adequate to a given contexto
e) have perceived 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 1. 1. Pearson and Spearman correlation.
2. Simple linear regression. Parameter estimation by the least square method and the maximum likelihood method
3. Multiple linear regression. Model and underlying assumptions, parameter estimation, hypothesis tests on the model parameters, confidence intervals, prediction intervals, coefficient of determination, multicollinearity, explanative categorical variables, variable selection algorithms, model selection and comparison, diagnosis. Interactions.
4. Analysis of variance (ANOVA) models
5. Generalized linear models. Logistic regression.

Mandatory literature

Docentes da UC ; Apontamentos escritos

Complementary Bibliography

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
M. Kutner, C. Nachtsheim, J. Neter, W. Li; Applied Linear Statistical Models, McGraw-Hill, 2005. ISBN: 0-07-238688-6
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 Project

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Teste	75,00
Trabalho escrito	25,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	100,00
Frequência das aulas	42,00
Trabalho escrito	20,00
Total:	162,00

Eligibility for exams

No requisites.

Calculation formula of final grade

Evaluation by  two assessments and optional project.

1. Assessment 1 will take place in a date to be settled with students and Assessment 2 will take place during the period settled for conclusion of the distributed evaluation.

2. The project consists of a written report and an oral presentation. 

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

4. Evaluation formula: 

(a) for students who complete the project:

max{0.75(T1+T2)+0.25TE, 0.65(T1+T2)+0.35TE}

T1:  grade in the first assessment
T2:  grade in the second assessment
TE:  grade in the project.

(a) for students who have not complete the project:

T1+T2 but will never exceed 16

5. The exam in the appeal season (época de recurso) must be fully solved.

Classification improvement

The grade improvement can only be done in the exam of the second period and not in the project.

Observations

The way the course will be provided is conditioned to the limitations imposed by FCUP according to the evolution of the pandemic COVID19. It is not expected a 100% face-to-face scheme.