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News

• [7 March] The exam calendar
• [5 March] UPDATED: Calendar for the project 3 presentations
• [28/2-13] Questions for the oral exam. Linear regression + logistic regression + further methods.
• Download links for the course literature have been updated! See below. You can now download the pdf of each book chapter!
• Welcome letter (updated version, 11th October 2013)
• First meeting Monday January 21, 2013, 13.15-15.00 in E:3308.
• Lectures Mondays 13.15-15.00 in E:3308 and Wednesdays 10.15-12.00 in E:C (except where noted in red).
  Exercises Wednesdays 15.15-17.00 in E:1145.
  Computer exercises Fridays 10.15-12.00 in the rooms indicated in the schedule below.
• Do you wish to follow the course? If you are an LTH student please send an email to anna@maths.lth.se, otherwise you should make a late application at http://www.lu.se/lubas/info-uh-lu-MASM22 .

R

We will use the statistical program R which can be downloaded from http://ftp.sunet.se/pub/lang/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 R programs; therefore I have set a page for the Tinn-R editor (Tinn is for Windows only, but the page contains alternative suggestions for other operative systems) and one for Rstudio (for Windows/Linux/MacOS).

Notice that this course is about statistics and 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 Tutorial
  
• R-intro.pdf An Introduction to R (<--it can also be found from the R's Help menu)

Schedule

Preliminary plan.

Week		Contents	Chapter	Notes
v3	Mon 21/1 in E:3308	Introduction; Review of simple linear regression	Rawlings, Ch. 1	lecture_1.pdf (updated! only third last slide has been changed)
	Wed 23/1 in E:C	Multiple regression	Rawlings, Ch. 2-3	lecture_2.pdf (updated! only slides 8 and 11 have been modified) The Matrix Cookbook (<-- might be useful) R code for lectures 1-2 (can be opened with R or any text editor).
	Wed 23/1 in E:1145	Exercises: 1.4, 1.9 (*), 1.14, 1.15, 1.16, 1.19, 1.21 (*); 3.5, 3.6, 3.9, 3.10, 3.12, 3.14 (*): skip the "analysis of variance" part.	Exercises 1.x, Exercises 3.x	Answers to exercises 1.x and 3.x R code for exercise 1.9
	Fri 25/1 in E:Hacke and E:Panter	Computer exercise, work on project 1		project 1 manual project1_data.Rdata (R data-file) project1_data.csv (semicolon-separated ascii data-file)
v4	Mon 28/1 in E:3308	Analysis of variance	Rawlings, Ch. 1.4, 1.6, 4.1-5	lecture_3.pdf some R code for multiple regression some R code for t and F tests
	Wed 30/1 in E:C	Class variables and variable selection	Rawlings, Ch. 9 and 7 respectively	lecture_4.pdf R code for lecture 4 data for lecture 4 (<--right mouse click + save-link-as)
	Wed 30/1 in E:1145	Exercises: older ones + 4.6(a)(i)+(b)(ii)+(c)(i), 4.10(a)+(b)+(c)+(e)	Exercises 4.x	Answers to exercises 4.x
	Fri 1/2 in E:Falk and E:Val	Computer exercise, work on project 1
v5	Mon 4/2 in E:3308	Problems areas in least squares.	Rawlings, Ch. 10	lecture_5.pdf
	Wed 6/2 in E1406	Regression diagnostics	Rawlings, Ch. 11	lecture_6.pdf R code for lecture 6 data for lecture 6
	Wed 6/2 in E:1145	Exercises: old ones + 10.1-10.2, 11.1-11.2		answers Ch. 10-11
	Fri 8/2 in E:Falk and E:Val	Computer exercise, work on project 1
v6	Mon 11/2 in E:3308	Peer assessment, project 1. Summary of linear regression. If time allows I will start talking about binary data and odds ratios.
	Wed 13/2 in E:C	Binary data and odds ratios. Logistic regression	Christensen, Ch. 1, 2.1-3, 2.6; also check sec. 1.4.1-1.4.2 in Agresti	lecture_7.pdf R code for lecture 7 (as shown at lecture) R code for lecture 7 (richer version)
	Wed 13/2 in E:1145	Exercise: ex. on binary data (but skip (d))		Solution for excercise on binary data
	Fri 15/2 in E:Falk and E:Val	Computer exercise, final deadline project 1, work on project 2		project2.pdf (manual)
v7	Mon 18/2 in E:3308	Maximum Likelihood and likelihood ratio tests	Agresti:, sec. 3.4.4; check here section 3 on Newton-Raphson	lecture 8 R code for lecture 8
	Wed 20/2 in E:C	Residuals and model validation in logistic regression		lecture_9.pdf R code for lecture 9 made up data more made up data
	Wed 20/2 in E: Falk, E:Val	Computer exercise, work on project 2
	Fri 22/2 in E:Falk and E:Val	Computer exercise, work on project 2
v8	Mon 25/2 in E:3308	Poisson, Negative binomial	Christensen, Ch. 1.5, 9	lecture_10.pdf R code Poisson regr data Neg bin regr data
	Wed 27/2 in E1406	10-11: Peer assessment, project 2; 11-12: Quantile regression	Quantile Regression An R "vignette"	lecture_11.pdf f11a.R (simple version, as shown at lecture) f11.R (applies QR to several situations)
	Wed 27/2 in E: Falk, E:Val	(Computer) exercise
	Fri 1/3 in E:Falk and E:Val	Computer exercise, Final deadline project 2, work on project 3		project3.pdf
v9	Mon 4/3 in E: Varg, E:Val	Work on project 3
	Wed 6/3 in E:C	CANCELLED Lecture: Summary
	Wed 6/3 in E: Falk, E:Val	Work on project 3
	Fri 8/3 in E:Falk and E:Val	Work on project 3
v10-11		Presentation of project 3. See the calendar for the project 3 presentations (updated)
v12--...		Individual oral exams. See the exam calendar

Level

Advanced level.

Aim

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.

Contents

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.

Prerequisites

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.

Teaching and examination

The teaching consists of lectures, exercises, computer exercises and project work. The examination is written and oral in the form of project reports, written and oral opposition, and individual oral examination.

Literature (NEWS of 10th January: download links have been fixed and you can now download the pdf for each chapter!)

• Rawlings, J.O., Pantula, S.G., Dickey, D.A.: Applied Regression Analysis - A Research Tool, 2ed, Springer, available as e-book,
• Christensen, R.: Log-Linear Models and Logistic Regression, 2ed, Springer, available as e-book.

Lecturer

Umberto Picchini, tel 046 222 9270, office MH:125a, email address.

Teaching Assistants

Behnaz Pirzamanbin, tel 046 222 4623, office MH:326, behnaz@maths.lth.se
Elham Pirnia, elham@maths.lth.se

Learning outcomes

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.