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# Chair of Mathematical Statistics (SMAT)

# Linear Models - MATH 341

#### Instructor: Prof. Victor Panaretos

#### Assistants: Pavol Guričan, Valentina Masarotto

#### News:

- Exercise to hand in after Week 1: Exercise No.
**2** - Exercise to hand in after Week 2: Exercise No.
**2** - Exercise to hand in after Week 3: Exercise No.
**1** - Exercise to hand in after Week 4: Exercise No.
**4** - Exercise to hand in after Week 5: Exercise No.
**1** - First practical is online, the deadline for submission is
**Monday November 21** - Exercise to hand in after Week 6: Exercise No.
**2** - Exercise to hand in after Week 7: Exercise No.
**2** - Exercise to hand in after Week 8: Exercise No.
**4** - Exercise to hand in after Week 9: Exercise No.
**3** - Exercise to hand in after Week 10: Exercise No.
**2** - Second practical is online, the deadline for submission is
**Wednesday December 21** - 05/12: There was a small typo in exercise 1, the first line of code should have "PO56.txt" instead of "PO60.txt".
- Exercise to hand in after Week 11: Exercise No.
**3** - Exercise to hand in after Week 12: Exercise No.
**1**

#### Description

Regression modelling is a basic tool of statistics, because it describes how one variable may depend on another. The aim of this course is to familiarise students with the basics of regression modelling, and some related topics.

#### Topics covered include:

- Properties of the Multivariate Gaussian distribution and related quadratic forms.
- Gaussian linear regression: likelihood, least squares, variable manipulation and transformation, interactions.
- Geometrical interpretation, weighted least squares; distribution theory, Gauss-Markov theorem.
- Analysis of variance: F-statistics; sums of squares; orthogonality; experimental design.
- Linear statistical inference: general linear tests and confidence regions, simultaneous inference
- Model checking and validation: residual diagnostics, outliers and leverage points.
- Model selection: the bias variance effect, stepwise procedures. Information-based criteria.
- Multicollinearity and penalised estimation: ridge regression, the LASSO, relation to model selection, bias and variance revisited.
- Departures from standard assumptions: non-linear least Gaussian regression, robust regression and M-estimation.
- Nonparametric regression: kernel smoothing, roughness penalties, effective degrees of freedom, projection pursuit and additive models.

#### Required prior knowledge

The second-year course in statistics; first-year course in linear algebra

#### Useful Documents

- Structuring a report (V.M. Panaretos)
- Advice on writing a report (A.C. Davison)
- Advice on writing a report (D.R. Brillinger)
- Writing technical papers or reports (A.S.C. Ehrenberg)
- Some useful notes on matrix calculus (from C.A. Felippa's online book)
- How to cite other people's work: citation.epfl.ch

#### Recommended Texts

Draper, N.R. & Smith, H.S. (1998). Applied regression analysis. Wiley

Hocking, R.R. (1996). Methods and applications of linear models : regression and the analysis of variance. Wiley.

Davison, A.C. (2009).Statistical models. Cambridge.

#### Exam Information

There will be a mock midterm exam (test blanc) and a written final exam.

__No notes, books or any other material will be allowed in the exams.__

#### Midterm

The midterm will take place on **Wednesday November 23rd, 16:15-18:00** in **CM 3**.

#### Exercises/Solutions

Each week one or two exercises will be graded to provide feedback. Deadline to hand these in is either at the beginning of the exercise session (following the week when they are set), or until 16:00 on the same Monday in the box outside of office MA B1 493.

#### Practicals

Practicals aim at developing the practical skills required when applying regression methodology. Practicals are assigned on certain weeks and are due three weeks later.

#### Winter 2016 Schedule

Lectures: | CM3 | Wednesdays, 16:15-18:00 |
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Exercises: | CH B3 31 | Mondays, 16:15-18:00 |