MSG500, Linear Statistical Models, Autumn 18

Latest news

Teachers

Course coordinator: Umberto Picchini

Office hours: on Tuesdays at 15.00-16.00 you can either visit Umberto Picchini (in H3030) or Juan Inda Diaz (in L3062). If you see a queue outside one of the offices try the other one!

Teaching assistants: Juan Inda Diaz

Student representatives

Student representatives 2018-19 are (emails should be followed by @student.chalmers.se)

Anton Björk, email: anbjork
Stefan Kittler, email: kittler
Linus Lagergren, email: linlag

Course literature


a monography for linear models: J.O. Rawlings, S.G. Pantula, D.A. Dickey. Applied Regression Analysis. This is available as ebook. Notice we will not follow this book. It is only a suggested resource if there is need for further support.
a monography for generalised linear models: Alan Agresti. "Categorical Data Analysis", Wiley. This is available as ebook. Notice we will not follow this book. It is only a suggested resource if there is need for further support.

Lecture notes by Prof. Rebecka Jörnsten will be posted on this page.

Software: We will use the statistical package R to analyze data, powered via the Rstudio interface. You will need to install both on your computer, see the instructions.
NO previous knowledge of R is required. But you are enouraged to attend the lab on Thursday 8 November. No further supervised computer lab will be given. Attending the lab on Thursday 8 November it will give you a useful opportunity for you to form groups for the MiniAnalyses.

Program

Syllabus
(pdf file)

Here follows a rough list of topics covered in the course: linear models and underlying assumptions; the bias/variance tradeoff; properties of least squares estimators. Outliers and diagnostics. Residuals and leverage. Variance decomposition and the R-squared. Hypothesis testing, global F test; confidence and prediction intervals. Multivariate regression. Multicollinearity. The Hat matrix. Model selection via backward/forward/stepwise procedures. Prediction error, cross validation and Mallow's Cp. Categorical covariates. Interactions. Regression via regularization. Bayesian regression.


Lecture notes, codes and MiniAnalyses



Week Material
Topics covered
MiniAnalysis
45
 lecture 1: Notes1.pdf, Lecture1.R, slides_1.pdf (updated)
lecture 2: Demo1.R, sleeptab.dat
Notes2.pdf, Lecture2.R, slides_2.pdf

There will be a computer lab 8 Nov at 15.15! Lab material: lab0.pdf, lab1.pdf, repair1.txt 		See the notes and the slides Mini1.pdf due 16 November. kc_house_data.csv, TV.dat
46
lecture 3: Notes3.pdf, Lecture3.R, slides_3.pdf
lecture 4: Notes4.pdf, slides_4.pdf, Demo3.R, Lecture4.R 		lecture 3: we completed Notes2.pdf that is, besides what's in slides_3.pdf, we covered diagnostics and the leverage. Then started Notes3.pdf with expectation/variance of the predictions; expectation/variance of residuals; standardised residuals.
lecture 4: we completed Notes3.pdf and started Notes4.pdf without the F-test and up to section 3.2 included
 Mini2.pdf due 23 November.
47
 lecture 5: Notes5.pdf, slides_5.pdf, Demo4.R, multicollinear.R, multipleregression.R, Lecture5.R
lecture 6: Notes6.pdf, Notes7.pdf, slides_6.pdf, global+partial_Ftests.R, Lecture6.R, Lecture7.R SA.dat, cars.dat (previously missing) 		lecture 5: confidence and prediction intervals in smple linear regression; multivariate regression, matrix notation and model construction. Least squares estimation and properties of the parameter estimates. Sampling distributions. Confidence and prediction intervals. T-test. Global F test.
lecture 6: partial F test; greedy search via backward selection; back to the bias/variance tradeoff 		Mini3.pdf (updated) due 30 November.
48
 Lecture 7: Notes10.pdf, Notes11.pdf, slides_7.pdf, auction.R, auction.dat
Lecture 8: slides_8.pdf, Lecture7.R (new version), rsquaredAICstep.R, AkaikeEasyIntro.pdf 		Lecture 7: training and testing data; all-subsets regresion; estimation of pMSE; started talking of categorical covariates and their parametrization;
Lecture 8: more on categorical variables; models with categorical covariates and numerical ones; interactions; Kullback-Leibler discrepancy, likelihood function and information criteria (AIC, BIC); back to R-squared and adjusted R-squared 		no mini released for next week
49
 Lecture 9: Notes8.pdf, Lecture8.R, slides_9.pdf, f6.R, f6data.txt
Lecture 10: Notes17.pdf, Lecture17.R; slides_10.pdf, (optional) see the book by Agresti, chapters 4 and 14.4; poissregr-awards.R, poisson_sim.csv, poisson_nb.R, f10.txt, f10b.txt 		Lecture 9: K-fold cross-validation; leave-one-out cross validation; choosing K and consequences on prediction variance; brushing-up diagnostics (again leverage and residuals) and introducing new tools like studentised residuals, Cook's distance, DFBETAs
Lecture 10: introduced generalised linear models (GLMs) and the exponential family; maximum likelihood estimation; asymptotic properties of the MLE and hence asymptotic properties of estimators for GLMs; Poisson regression; 		mini4.pdf due Friday 14 december
50
 Lecture 11: slides_11.pdf, poissregr-awards.R (updated), poisson_nb.R (updated), shipdamage.R
Lecture 12: slides_12.pdf, poisson_nb.R (updated), shipdamage.R (updated)
 Lecture 11: testing over/under-dispersion for Poisson regression; standard erros and confidence intervals for GLMs; Wald test; deviance; likelihood-ratio test; Poisson regression with an offset term;
Lecture 12: negative binomial distribution and regression; using an offset term with negative binomial regression; diagnostics for GLMs and their limitations (leverage; sveral types of residuals; Cook's distance) 		project18.pdf, data18.txt, deadline 14 January at 16.00
2
 Lecture 13: slides_13.pdf, USpresidentsHeights_Stan.R, USheights_model.stan, carsdata_withpriors.R, carsdata_withpriors.stan Lecture 13: this is the last lecture and will consider Bayesian methods. The material covered is NOT part of the examination.

Course requirements

The learning goals of the course can be found in the course plan.

Assignments

MiniAnalyses are computer exercises where you will have a week to perform an analysis task and prepare slides to present in class on FRIDAYS. It is mandatory to present a few times (we'll decide on how many times depending on this year's number of students). You must work in teams. Teams will be selected at random on Friday Mini sessions. We discuss your findings in class. Slides should be emailed to Umberto Picchini ahead of class or brought on a USB stick or be made available online through Box/Dropbox etc. If you do not attend Friday sessions (I will take the presences) you will have to write a report, which is a lot more work!

Examination

The Minis contribute 10% to your final grade AND the minis will also be part of your final project exam. The project counts for 40% of your grade and a written final for 50%.

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Old exams


Old exams: April 2019, January 2019, Final Jan 2018 (includes solutions in italic), Final Jan 2017, Final Aug 2016, Final Jan 2016

Solutions: April 2019, January 2019, Final Jan 2017 (merged exam and solutions), Final Aug 2016, Final Jan 2016