MVE190/MSG500 Linear statistical models

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Course PM

This page contains the program of the course: lectures, exercise sessions and computer labs. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

Midcourse meeting

A midcourse meeting has been held on 22 November between the examiner and the students' representatives. Here are the meeting minutes.

Program

2019-20_Topics and hence potential exam questions.pdf

Here is an updated Syllabus.

The schedule of the course is in TimeEdit.

Notice, there are some activities for which attendance is mandatory. These are the Fridays "mini-analyses". See the course PM for details and what to do in case you are unable to attend.

Here follows a rough list of topics covered in the course: linear models and underlying assumptions; the bias/variance trade-off; properties of least squares estimators. Outliers, residuals and other diagnostics. Using categorical covariates in regression. Model comparison and goodness of fit. Hypothesis testing; confidence and prediction intervals. Multivariate regression. Multicollinearity. Model selection via backward/forward/stepwise procedures. Prediction error and cross validation. Interactions between covariates. Generalised linear models, especially Poisson and negative-binomial regression. (If time) hints at Bayesian regression.

 

Lectures

week Material Topics MiniAnalysis
45

 

Nov 5: General intro to the course and mention of several topics: bias in linear regression, lest squares; parameters interpretation in simple linear regression; the 5 basic assumptions.

Nov 7: derivation of least squares estimates. Proof of the unbiasedness; variance of the estimators; began residuals-based diagnostics

 

46

 

Nov 12: leverage values; deletion-based diagnostics; MSE; unbiasedness of yhat and var of yhat; 

Nov 14: expectation and variance of residuals; standardised residuals; unbiasedness of MSE; proof variability decomposition (SSEr, SStor, SSRegr); Rsquared; t-test construction

Friday 15*: present minianalysis1 assigned in week 45

*maybe first hour only
47

 

Nov 19: (from slides_4) problems with p-values and large datasets; confidence intervals for parameters and for E(Y0). Prediction intervals for Ypred0. The Simpson's paradox and notation for multiple lin. regression

Nov 21: properties of the estimators in multiple regression and sampling distributions. Confidene intervals, t-test and categorical covariates (not everything). Topics  also found in chapter 9 ("Class variables") in Rawlings et al up to sect. 9.3. 

 no minianalysis this week
48

 

Nov 26: models with categorical and numerical covariates (from slides_6). Multicollinearity and VIF. Partial F test.

 

Nov 28: greedy variables selection: backward search. Global F test. Bias/variance tradoff and the pMSE. Training and testing but only up to slide 33.

Friday 29*: present minianalysis2 assigned in week 47.

*maybe first hour only
49

 

Dec 3: (from slides_8.pdf) PMSE with regsubsets. Then (slides_9.pdf) interactions, adj-Rsquared

 

Dec 5: AIC/BIC; K-fold CV; LOOCV; hat-matrix; standardised residuals

Friday 6*: present minianalysis3 assigned in week 48.

*maybe first hour only
50

 

Dec 10: studentised residuals; Cook's distance, DFBETAs; intro GLMs and the exponential family; Newton-Raphson; Poisson regression;

Dec 12: more on Poisson regression; confidence intervals for GLMs;  asymptotic properties of the MLE; CI for predictions; Wald test; deviance; likelihood ratio test; started talking of Poisson + offset term

Project:

Friday 13: practice exam exercises.*

*maybe first hour only
51

 

 

 Completed Poisson + offset. Negative binomial regression. Quick tour through GLM diagnostics

 

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Computer labs and software

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 encouraged to attend the lab on Thursday 7 November. No further supervised computer lab will be given. Attending the lab will give you a useful opportunity to group for the MiniAnalyses.

If you already have a copy of R installed on your computer, please check that its version is >= 3.6.0. If it is older install a more recent one.

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Course summary:

Date Details Due