- calendar oral exam
- Calendar for project 3 presentations
- List of questions for the oral exam
- Welcome letter
- There will be several computer labs during the course, some related to project work others related to non-project work. Compulsory computer labs are held on Wednesday 22 March 2017, Wednesday 29 March and Wednesday 5 April.
- This course is taught jointly with FMSN40: please check http://www.maths.lth.se/matstat/kurser/fmsn40/
RWe will use the statistical program R which can be downloaded from http://ftp.acc.umu.se/mirror/CRAN/ free of charge for all major platforms. It is a good idea to install it on your own computer, if you have one. Also, a good programming practice is to consider an appropriate editor for writing and executing R programs; therefore I have set a page for Rstudio (for Windows/Linux/MacOS).
Notice that this course is about Statistics and is not an in-depth course about R. We will discuss the commands needed to produce the desired output and answer the relevant statistical questions. However we will not consider tips-and-tricks, good programming practice or any advanced use of such powerful computer language. R has a large and friendly user community and you will be able to find plenty of good guides, tutorials and answered questions by a simple Google search. Here follow some of the many guides freely available on the web:
- R.pdf A (small) R Tutorial
- RTutorial.pdf A Short R
- R-intro.pdf An Introduction to R (<--the most up-to-date version can be found from the R's Help menu)
Computer LabsYou will have the chance to book specific computer labs sessions. That is you do not have to attend all labs reported in the schedule below, only the ones you book. Special attention should be devoted to mandatory labs denoted in RED: you MUST attend one of those each week for the first three weeks.
ScheduleIMPORTANT: attendance to labs for non-project work is COMPULSORY: these are held on Wednesday 22 March 2017 (10.15-12.00 OR 13.15-15.00), Wednesday 29 March 2017 (10.15-12.00 OR 13.15-15.00) and Wednesday 5 April 2017 (10.15-12.00 OR 13.15-15.00) .
|w12||Mon 20/3, 13.15-15 in MH:A (=MH:Riesz)||Introduction; Review of simple linear regression: - linear relationships - linear models and basic assumptions (normality, homoscedasticity, linearity, independence) - least squares estimation - basic properties of expectation, variance and covariance - mean and variance of least squares estimators||Rawlings, Ch. 1||
|Wed 22/3, 8.15-10 in MH:B (=MH:Gårding)||Continuation of simple linear regression: - distribution of least squares estimators - prediction; - confidence intervals - hypothesis testing, p values, quantiles||Rawlings, Ch. 1||
|Wed 22/3, 10.15-12 in MH:230-231 or 13.15-15 in MH:230-231||compulsory computer lab||
|Fri 24/3, 8.15-10 in MH:230-231 or 10.15-12 in MH:230-231||computer lab: work on project 1||
|w13||Mon 27/3, 13.15-15 in MH:A||Multiple Regression: matrix notation, properties of least squares estimators for multiple regression - confidence intervals for multiple regression - critical requirements: ill-ranked design matrices, lack of invertibility.||Rawlings, Ch. 3, 4, 6.5||
See the updated f2.pdf
|Wed 29/3, 8.15-10 in MH:B||Analysis of variance: variability decomposition. Global F-test. ANOVA tables.||Rawlings, Ch. 4.||
|Wed 29/3, 10.15-12 in MH230 or 13.15-15||compulsory computer lab||
|Thur 30/3, ||computer lab: work on project 1. Enroll here|
|w14||Mon 3/4, 13-15 in MH:A||Partial F-test. Factors/Categorical variables: modelling with categorical predictors and interaction terms. R-squared||Rawlings, ch. 9 for class variables, ch. 7 for variables selection||
|Wed 5/4, 8.15-10 in MH:B||Adjusted-R-squared. AIC & BIC, automatic selection methods. Problems areas in least squares;||Rawlings, Ch. 10-11
intro to Akaike's AIC
|Wed 5/4, 10.15-12 in MH:230 or 13.15-15 in MH:230||compulsory computer lab||
|Thur 6/4, ||computer lab, work on project 1|
|w17||Mon 24/4, 13.15-15 in MH:A||13.15-14:00: Peer assessment, project 1.
14:15-15: Regression diagnostics: outliers w.r.t. X (leverage), distribution of residuals, standardised and studentised residuals; graphical tools for residual analysis. Influential observations (Cook's distance, DFBETAS)
|Rawlings, Ch. 10-11||
|Wed 26/4, 8.15-10 in MH:B||Binary data, Bernoulli and binomial distributions, odds ratios and started talking of Logistic regression||Agresti: ch. 1, sec 1.2.1, sec 2.3||
|Wed 26/4, ||Computer lab, keep working on project 1 or start project 2 (in case we did manage to introduce enough material at lecture)||
|Fri 28/4||Project 1 final deadline at 16:00: MASM22/FMSN30 students email the report to FMSN30@matstat.lu.se
Subject field: Project1 by studid1 and studid2
|w18||Tue 2/5, 10.15-12 in E:C||Asymptotic distribution for parameter estimates and odds ratios from logistic regression; standard errors; maximum likelihood estimation for the parameter of Bernoulli experiments; maximum likelihood for regression parameters; Newton-Raphson method||
Agresti: 1.3.1, 1.4.1, 2.3.1-2.3.3; several topics scattered in chapter 4, particularly sections 4.1-4.2.
Check here section 3 on Newton-Raphson.
see again files uploaded on 26/4, and in addition|
Section 3 on Newton Raphson
|Wed 3/5, 8.15-10 in E:C||Deviance and Likelihood ratio test. Residuals and model validation in logistic regression. Comparing and fitting observed proportions with predicted proportions. Briefly started Generalised Linear Models and exponential families.||
|Wed 3/5 at 10.15-12 in MH230 ||Computer exercise, work on project 2|
|Thur 4/5, ||Computer exercise, work on project 2|
|w19||Mon 8/5, 13-15 in MH:A||Poisson distribution and Poisson regression; Negative binomial regression||Agresti: several sections in Chapter 3. Also see the example discussed here||
|Wed 10/5, 8.15-10 in MH:B||8.15-9: Peer assessment project
9.15-10: Quantile regression
material on quantile regression:
- intro article
- quantile regression with R
|Wed 10/5, 10.15-12 in E:1147 ||Computer exercise, work on project 2|
|Thur 11/5, ||Computer exercise, work on project 2|
|Fri 12/5||Project 3
|w20||Monday 15/5 at 10.00||Final deadline for project 2: FMSN30/MASM22 students email the report to FMSN30@matstat.lu.se Subject field: Project2 by studid1 and studid2|
|Wed 17/5, 10.15-12 in MH:230 ||Computer lab: work on project 3|
|Thur 18/5, ||Computer lab: work on project 3|
|w21||Project 3 oral presentations|
Regression analysis deals with modelling how one characteristic (height, weight, price, concentration, etc) varies with one or several other characteristics (sex, living area, expenditures, temperature, etc). Linear regression is introduced in the basic course in mathematical statistics but here we expand with, e.g., "how do I check that the model fits the data", "what should I do if it doesn't fit", "how uncertain is it", and "how do I use it to draw conclusions about reality".
When performing a survey where people can answer "yes/no" or "little/just fine/much", or "car/bicycle/bus" or some other categorical alternative, you cannot use linear regression. Then you need logistic regression instead. This is the topic in the second half of the course.
Least squares and maximum-likelihood-method; odds ratios; Multiple linear and logistic regression; Matrix formulation; Methods for model validation, residuals, outliers, influential observations, multi co-linearity, change of variables; Choice of regressors, F-test, likelihood-ratio-test; Confidence intervals and prediction. Introduction to: Correlated errors, Poisson regression as well as multinomial and ordinal logistic regression.
At least 60 ECTS at university level including an introductory course in mathematical statistics, e.g. MASA01 Matematical statistics, basic course, 15hp, or MASB02 Mathematical statistics (for chemists) 7.5hp, or MASB03 Mathematical statistics (for physicists) 9hp or MASB11 Biostatistics, basic course 7.5hp, or equivalent.
The teaching consists of lectures, exercises, computer exercises and project work. Among the several given computer labs, attendance to three of those is compulsory, namely those held on 25/3 (10-12), 31/3 (13-15) and 8/4 (10-12). The examination is written and oral in the form of project reports, written and oral opposition, and individual oral examination.
- Rawlings, J.O., Pantula, S.G., Dickey, D.A.: Applied Regression Analysis - A Research Tool, 2ed, Springer, available as e-book,
- Agresti, A. An Introduction To Categorical Data Analysis, 2ed Wiley, 2007, available as e-book.
- Need to refresh matrix theory? Check a minimal introduction and the very useful Matrix Cookbook.
Knowledge and understanding
For a passing grade the student must
- Describe the differences between continuous and discrete data, and the resulting consequences for the choice of statistical model
- Give an account of the principles behind different estimation principles,
- Describe the statistical properties of such estimates as appear in regression analysis,
- Interpret regression relations in terms of conditional distributions,
- Explain the concepts of odds and odds ratio, and describe their relation to probabilities and to logistic regression.
Skills and abilities
For a passing grade the student must
- Formulate a multiple linear regression model for a concrete problem,
- Formulate a multiple logistic regression model for a concrete problem,
- Estimate the parameters in the regression model and interpret them,
- Examine the validity of the model and make suitable modifications of the model,
- Use the model resulting for prediction,
- Use some statistical computer program for analysis of regression data, and interpret the results,
- Present the analysis and conclusions of a practical problem in a written report and an oral presentation.
Judgement and approach
For a passing grade the student must
- Always control the prerequisites before stating a regression model,
- Evaluate the plausibility of a performed study,
- Relect over the limitations of the chosen model and estimation method, as well as alternative solutions.