MATH-408 / 5 credits

Teacher: Davison Anthony Christopher

Language: English

## Summary

General graduate course on regression methods

## Content

Linear regression and analysis of variance. Geometric interpretation.  Properties of estimators.  Orthogonality and balance.  Diagnostics.  Transformations.  Variable selection and post-selection inference.  Robustness and estimating equations.  Quantile regression.

PIWLS algorithm and general regression models.  Generalized linear models: variance and link functions; proportion and binary responses; logistic regession; count data and Poisson responses; log-linear models; overdispersion.

Penalised regression: ridge, lasso, thresholding.

Components of variance: nested and crossed effects, mixed models.  REML.

## Keywords

Binary response. Count data.  Deviance. Least squares. Likelihood.  Mixed model. Overdispersion. Penalised regression model. Random effects.  Ridge regression.

## Required courses

Courses on basic probability and statistics (e.g., MATH-240, MATH-230) and a first course on the linear model (e.g., MATH-341).

## Important concepts to start the course

Linear regession.  Likelihood inference.  Use of computer package R.

## Learning Outcomes

By the end of the course, the student must be able to:

• Develop elements needed in a regression analysis
• Apply the statistical package R for the analysis of data
• Assess / Evaluate the quality of a model
• Formulate a suitable regression model and assess its validity

## Transversal skills

• Demonstrate the capacity for critical thinking
• Demonstrate a capacity for creativity.
• Write a scientific or technical report.

## Teaching methods

Ex cathedra lectures; homework both theoretical and applied; mini-project

## Expected student activities

Attending lectures; solving theoretical problems; solving applied problems using suitable software

## Assessment methods

Written final exam.  Mini-project.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

## Supervision

 Office hours No Assistants Yes Forum Yes

No

## Bibliography

Davison, A. C. (2003) Statistical Models.

See moodle page

## In the programs

• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Regression methods
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory

## Reference week

Tuesday, 8h - 10h: Lecture CM1221

Tuesday, 10h - 12h: Exercise, TP CM1221

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