41301 - Statistical Inference

Learning outcomes

By the end of the course, the candidate has a solid knowledge of basic statistical inference and has some foundational knowledge about some of the main statistical techniques of data analysis, even when the number of variables is large. In particular, he/she is able to perform many parametric statistical tests, as well as the most used nonparametric tests, is able to get an estimator and to check its properties. He/she is familiar with the fundamental concepts of linear regression model.

Course contents

Introduction to statistical inference: population and sample spaces; statistics and sampling distributions.

Point estimation: the maximum likelihood method; properties of estimators. Applications and simulations in R.

Hypothesis testing: parametric statistical tests (hypotheses concerning means, proportions, and variances); non-parametric tests (tests of independence). Properties of statistical tests. Applications and simulations in R.

Interval estimation. Applications and simulations in R.

Simple linear regression: least-squares estimators and maximum likelihood estimators; coefficient of determination. Applications in R.

Multiple linear regression: estimation and interpretation of parameters; properties of least-squares estimators; residual analysis; hypothesis testing for the model and its coefficients; variable selection. Applications in R.

Readings/Bibliography

D. Piccolo, Statistica per le decisoni, Il Mulino, Bologna, 2010, PARTE III e IV.

Further teaching materials will be made available on https://virtuale.unibo.it/

Teaching methods

The theoretical introduction to the basic concepts will be complemented by practical exercises, also carried out with the aid of the statistical software R.

Assessment methods

The examination is designed to assess whether students have achieved the following learning outcomes:

• A thorough understanding of the foundations of statistical inference and the linear regression model.
• The ability to critically analyse univariate and multivariate datasets.

MIDTERM EXAMINATIONS. Students may take two midterm examinations. Those who complete both midterms may accept the final grade obtained by averaging the grades awarded in the two examinations. They may also choose to take an optional oral examination.

FINAL EXAMINATION. Assessment consists of a written examination and an optional oral examination.

The written examinations, whether midterm or final, last two hours. They are held in a computer laboratory and require the use of R software.

During the written examinations, students may consult a formula sheet prepared individually by each candidate. The formula sheet must not exceed four A4 pages. In addition to the formula sheet, students may consult the R scripts provided during the course. The formula sheet must be submitted together with the examination paper.

Grades will be awarded according to the following scale:

Below 18: fail

18–23: satisfactory

24–26: fair

27–28: good

29–30: excellent

30 with honours: outstanding

Students with specific learning disorders (SLD) or temporary or permanent disabilities are encouraged to contact the University's dedicated support office in good time (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will propose any appropriate accommodations for eligible students. These accommodations must be submitted to the course instructor for approval at least 15 days in advance. The instructor will assess their appropriateness, taking into account the intended learning outcomes of the course.

The use of AI tools is prohibited in all assessments. Any use of AI tools constitutes a breach of academic integrity.

 

Teaching tools

Slides and R scripts available on Virtuale.

Office hours

See the website of Fedele Pasquale Greco