Course Syllabus for

# Linear and Logistic Regression Linjär och logistisk regression

## FMSN30F, 7.5 credits

Valid from: Autumn 2020
Decided by: Professor Thomas Johansson
Date of establishment: 2020-08-26

## General Information

Division: Mathematical Statistics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMSN30
Teaching language: English

## 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. If you have a data material suitable for analysis using linear or logistic regression, you may analyse it as part of the project.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to describe the differences between continuous and discrete data, and the resulting consequences for the choice of statistical model
• be able to give an account of the principles behind different estimation principles,
• describe the statistical properties of such estimates as appear in regression analysis,
• be able to interpret regression relations in terms of conditional distributions,
• be able to 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 doctoral student must

• be able to formulate a multiple linear regression model for a concrete problem,
• be able to formulate a multiple logistic regression model for a concrete problem,
• be able to estimate the parameters in the regression model and interpret them,
• be able to examine the validity of the model and make suitable modifications of the model,
• be able to use the model resulting for prediction,
• be able to use some statistical computer program for analysis of regression data, and interpret the results,
• be able to 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 doctoral 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.

## Course 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.

## Course Literature

• Rawlings, John O., Pantula, Sastry G. & Dickey, David A.: Applied Regression Analysis: A Research Tool. Springer Science & Business Media, 2001. ISBN 9780387984544.
• Agresti, A.: An Introduction to Categorical Data Analysis. Wiley-Interscience, 2007. ISBN 9780471226185.

## Instruction Details

Types of instruction: Lectures, laboratory exercises, project

## Examination Details

Examination formats: Oral exam, written report, seminars given by participants