Applied Statistics

Code:

M3035

Acronym:

M3035

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	21	Official Study Plan	3	-	6	56	162
L:MA	1	Official Study Plan	3	-	6	56	162

Teaching language

Portuguese

Objectives

To consolidate and complement concepts and principles of Statistics, both in a general theoretical perspective and in terms of their application to concrete problems.

Learning outcomes and competences

Upon completing this course, the student should:

(a) master the fundamental concepts and principles of Statistics, and in particular of basic Statistical Inference

(b) know the most common hypothesis tests, how to apply them to concrete problems and correctly interpret the results

(c) be able to perform correlation analysis and understand the geometric significance of Pearson's correlation coefficient

(d) be able to perform simple linear regression analysis

(e) have developped critical thinking skills, capacity to understand results and be comfortable using the R programming languange

Working method

Presencial

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

introductory course on Probability and Statistics

Program

1. Statistics: bias and consistency of estimators; most common statistics, with a special emphasis on the sample mean and sample variance.

2. Point Estimation: the method of moments; maximum likelihood estimation; properties of the maximum likelihood estimator.

3. Joint Distributions: bivariate normal and multinomial distributions.

4.Hypothesis testing: type I and type II errors; test statistic, power; one- and two-sample parametric tests; relation between hypothesis tests and confidence intervals; non-parametric hypothesis tests: goodness-of-fit, central tendency, independence and homogeneity.

5. Correlation Analysis: Pearson and Spearman correlation coefficients; hypothesis tests on correlation coefficients.

6. Simple Linear Regression:model and parameter interpretation; parameter estimation; properties of estimators; confidence intervals and hypothesis testing; prediction; analysis of variance and determination coefficient.

Mandatory literature

Helena Mena Matos; Notas de aulas

Complementary Bibliography

George Casella; Statistical inference. ISBN: 978-0-534-24312-8
Jay L. Devore, Kenneth N. Berk; Modern Mathematical Statistics with Applications, Springer, 2018. ISBN: 978-1-4614-0390-6
Peter Dalgaard; Introductory statistics with R. ISBN: 0-387-95475-9

Teaching methods and learning activities

Classes are of theoretical-practical type. They include theoretical exposition of the subjects and solving exercises to apply the techniques and statistical models studied, with special attention devoted to the interpretation and discussion of the results obtained.  The software used will be the R programming language in a software environment.

Software

R

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

To be eligible, students must meet the two following criteria:

1. not to exceed 25% of the planned TP classes in absences;
2. take a test approximately halfway through the semester.

Calculation formula of final grade

The final classification will be the one obtained in the exam. The exam will be divided into two parts and the classification in the 1st part can be replaced by the classification obtained in the intermediate examination if the student has not been excluded.

Examinations or Special Assignments

Students who are legally exempt from attending classes, must do additional work that will be specified at a timely date.