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Statistics Applied to Sciences and Engineering

Code: M4108     Acronym: M4108

Keywords
Classification Keyword
OFICIAL Mathematics

Instance: 2021/2022 - 1S Ícone do Moodle

Active? Yes
Responsible unit: Department of Mathematics
Course/CS Responsible: Master's degree in Remote Sensing

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
M:DR 7 The study plan from 2018 1 - 6 42 162

Teaching Staff - Responsibilities

Teacher Responsibility
Ana Rita Pires Gaio

Teaching - Hours

Theoretical and practical : 2,00
Other: 1,00
Type Teacher Classes Hour
Theoretical and practical Totals 1 2,00
Ana Rita Pires Gaio 0,00
Other Totals 1 1,00
Ana Rita Pires Gaio 0,00

Teaching language

English
Obs.: Notar que a língua de trabalho será o inglês, podendo sempre os alunos tirar dúvidas em português.

Objectives

1. Train the student for regression analysis involving continuous or discrete responses (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


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 for the coefficients, confidence intervals, prediction intervals, coefficient of determination, multicollinearity, model selection methods, model comparison, diagnosis.
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 escritos pela professora

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 Project

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation Weight (%)
Teste 37,50
Trabalho escrito 25,00
Exame 37,50
Total: 100,00

Amount of time allocated to each course unit

designation Time (hours)
Estudo autónomo 110,00
Frequência das aulas 42,00
Trabalho escrito 10,00
Total: 162,00

Eligibility for exams

Attendency is not mandatory.

Calculation formula of final grade

1. The assignment consists of a written report and an oral presentation, and it is optional. 

2. The grade obtained in the assignment cannot be improved.

3. The evaluation in "época normal" (1st evaluation period) will include the marks from two tests (T1 and T2), each rated 10 points. Test T2 will be performed on the day the examination in "época normal" would take place.

4. Evaluation in "época de recurso" (2nd evaluation period) will include a single exam, evaluating all subjects studied in the course. Marks from the tests (T1 and/or T2) will not be considered.

5. Evaluation formula in "época normal": There are two evaluation formulas depending on whether or not the student submits the assignment. 

a) For the students that submit the assignment:
a1) T1+T2: weight of 13 or 15 (out of 20); assignment: weight of 7 or 5 (out of 20)
From these 2 components, the one where the student obtained the highest score is worth the maximum of the respective weight. The worst component is worth the minimum of the respective weight.
a2) The student will only be approved if he/she marks at least 20% on each evaluation component.

b) For the students that do no submit the assignment:
In this case only the marks from the two tests are considered; however, the final mark for the course will never exceed 16, even if the grade from the tests is greater. 

6. Evaluation formula in "época de recurso": There are two evaluation formulas depending on whether or not the student submits the assignment. 

a) For the students that submit the assignment:
a1) exam in "época de recurso": weight of 13 or 15 (out of 20); assignment: weight of 7 or 5 (out of 20)
a1) From these 2 components, the one where the student obtained the highest score is worth the maximum of the respective weight. The worst component is worth the minimum of the respective weight.
a2) The student will only be approved if he/she marks at least 20% on each evaluation component (exam and assignment).

b) For the students that do no submit the assignment:
In this case only the mark from the exam is considered; however, the final mark for the course will never exceed 16, even if the grade from the exam is greater.


Classification improvement

Improvement of the final mark: final examination. The mark obtained in the project cannot be improved. The mark from tests T1 and T2 cannot be individually improved. The evaluation formula is the same (see above).

Observations

1) Jury: Rita Gaio and Óscar Felgueiras.

2) The way the course will be provided is conditioned to the limitations imposed by FCUP according to the evolution of the COVID19 pandemic.

3) Th evaluation method is conditioned by the evolution of the COVID19 pandemic.
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