Laboratory of Mathematical Statistics
A.Y. 2024/2025
Learning objectives
The course aims to aware students to the theoretical and computational aspects of first statistical tools, by analyzing simulated and real data sets. We introduce and use R software, which is the state-of-art in scientific community and widely used in many industrial and commercial environments. Students will link mathematical theory and its application in modelling instances. Thy will improve their computing and computer science abilities as well as his probem solviving attitudes.
Expected learning outcomes
The student shall be able to perform a statistical analysis of data from different working contexts using the R package. He shall have acquired the ability to use basic R tools and to resume relevant information from the available data. Students become conscious of the role of mathematical theory in algorithms development.
Lesson period: Second semester
Assessment methods: Giudizio di approvazione
Assessment result: superato/non superato
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1. Introduction to the software R
2. Linear regression model
2.1. Parameters estimate
2.2. Hypothesis tests and confidence intervals for the parameters
2.3. Methods for variables selection
2.4. Analysis of residuals and regression diagnostics.
2.5. Case of dummy regressors
3. One way and two way ANOVA
4. Introduction to GLM and logistics regression
5. Introduction to classification problems: classification trees
2. Linear regression model
2.1. Parameters estimate
2.2. Hypothesis tests and confidence intervals for the parameters
2.3. Methods for variables selection
2.4. Analysis of residuals and regression diagnostics.
2.5. Case of dummy regressors
3. One way and two way ANOVA
4. Introduction to GLM and logistics regression
5. Introduction to classification problems: classification trees
Prerequisites for admission
An introductory course in Probability, and one in Mathematical Statistics.
The contents of the course Mathematical Statistics for 9 credits are strongly recommended for an in-depth understanding
The contents of the course Mathematical Statistics for 9 credits are strongly recommended for an in-depth understanding
Teaching methods
Frontal and computer lab lectures
Teaching Resources
· P.K.Dunn, G.K.Smyth, Generalized linear models with examples in R, Springer, 2018 (disponibile nella biblioteca digitale di UniMI)
· G.G. Roussas, A Course in Mathematical Statistics, Academic Press, 1997 (o edizioni più recenti)
· A.Agresti, Categorical data analysis, Wiley, 2nd edition (2002)
· N. Draper, H. Smith, Applied Regression Analysis, Ultima Edizione
· A.J.Izenman, Modern multivariate statistical techniques.. Regression, classification, and manifold learning, Springer, 2008
· S.Weisberg Applied linear regression. Fourth edition. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken, NJ, 2014.
· F.Ieva, C.Masci, A.M.Paganoni, Laboratorio di statistica con R, Pearson, 2016 (o edizioni successive)
· Notes and material from the teachers
· G.G. Roussas, A Course in Mathematical Statistics, Academic Press, 1997 (o edizioni più recenti)
· A.Agresti, Categorical data analysis, Wiley, 2nd edition (2002)
· N. Draper, H. Smith, Applied Regression Analysis, Ultima Edizione
· A.J.Izenman, Modern multivariate statistical techniques.. Regression, classification, and manifold learning, Springer, 2008
· S.Weisberg Applied linear regression. Fourth edition. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken, NJ, 2014.
· F.Ieva, C.Masci, A.M.Paganoni, Laboratorio di statistica con R, Pearson, 2016 (o edizioni successive)
· Notes and material from the teachers
Assessment methods and Criteria
Test with exercises in a computer lab
MAT/06 - PROBABILITY AND STATISTICS - University credits: 3
Laboratories: 36 hours
Professor:
Micheletti Alessandra
Professor(s)