Course syllabus

# Linjär och logistisk regression med datainsamling Linear and Logistic Regression with Data Gathering

## FMSN40, 9 credits, A (Second Cycle)

Valid for: 2014/15
Decided by: Education Board B
Date of Decision: 2014-04-08

## General Information

Main field: Technology.
Elective Compulsory for: I3
Language of instruction: The course will be given in English on demand

## 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 i it doesn't fit", "how uncertain is it", and "how do I use it to draw conclusions about reality".

When perfoming a survey where people can awnser 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.

As part of the course you should construct a questionaire or experimental plan for a problem of your choice, collect the data and analyse it using an suitable regression model.

## 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 odds and odds ratio, and describe their relation to probabilities and to logistic regression.

Competences and skills
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.
• Construct a form for data collection that can be used to answer a particular practical problem.

Judgement and approach
For a passing grade the student must

• Always check the prerequisites before stating a regression model,
• Evaluate the plausibility of a performed study,
• Reflect over the limitations of the chosen model and estimation method, as well as alternative solutions.

## Contents

Least squares and maximum-likelihood-method; odds ratios; Multiple and linear 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. Questionaire construction and design of experiments.

## Examination details

Assessment: The examination is written and oral in the form of project reports, written and oral opposition, and individual oral examination.

Parts
Code: 0114. Name: Examination.
Credits: 5,5. Grading scale: TH. Assessment: Oral examination
Code: 0214. Name: Project.
Credits: 3,5. Grading scale: UG. Assessment: Collection of, or description of existing, own data material, written project report with oral presentation and opposition of another report.

• FMS012 Mathematical Statistics, Basic Course or FMS032 Mathematical Statistics, Basic Course or FMS035 Mathematical Statistics, Basic Course or FMS086 Mathematical Statistics or FMS140 Mathematical Statistics, Basic Course

The number of participants is limited to: No
The course overlaps following course/s: FMSN30, MASM22

• Rawlings, J.O., Pantula, S.G., Dickey, D.A.: Applied Regression Analysis - A Research Tool, 2ed. Springer, 1998, ISBN: 0-387-98454-2. Available as e-book.
• Alan Agresti: An introduction to categorical data analysis, 2nd ed. Wiley, 2007. Available as e-book.

## Contact and other information

Director of studies: Anna Lindgren, studierektor@matstat.lu.se
Course homepage: http://www.maths.lth.se/matstat/kurser/fmsn30/