Applied Statistics

Code:

M3035

Acronym:

M3035

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 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	35	Official Study Plan	3	-	6	48	162
L:MA	23	Official Study Plan	3	-	6	48	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, 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 simple linear regression analysis

(d) be able to choose statistical methods appropriate to specific problems

(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.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.

4. Joint Distributions: bivariate normal and multinomial distributions.

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 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	114,00
Frequência das aulas	48,00
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

1. In the first call the final mark will be the sum of the scores obtained in two assessments: 

Assessment 1: with a total of 10 points, will take place in a date to be settled with students. 

Assessment 2: with a total of 10 points, will take place during the period settled for conclusion of distributed evaluation. 


2. In the second call, the final mark will be obtained in an exam with a total of 20 points. 
This exam will be divided in two parts, allowing the students which have not yet been aproved in the course (and only these students) to substitute the score in any of the two parts by the score obtained in the corresponding assessment.

Classification improvement

Improvement in the classification can be obtained in the second call only. In this case, both parts of the exam will have to be taken.