 # FMSN30/MASM22: Linear and Logistic Regression, 7.5 ECTS credits

## News

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, computer exercises and project work. Attendance to the three exercises is compulsory. The examination is written and oral in the form of written reports for project 1 and 2, oral presentation of project 3 and individual oral examination.

### Lecturer

Anna Lindgren, tel 046-2224276, office MH:136, Matematikcentrum anna@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.