(Created 2011-09-01.)

LINEAR AND LOGISTIC REGRESSION | FMSN30 |

**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.

*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.

*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 checkthe 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.

**Literature**

Rawlings, J.O., Pantula, S.G., Dickey, D.A.: Applied Regression Analysis - A Research Tool, 2ed, Springer 1998. ISBN: 0-387-98454-2 (finns som e-bok).

Christensen, R.: Log-Linear Models and Logistic Regression, 2ed, Springer 1997. ISBN: 0-387-98247-7 (finns som e-bok).

**Code: **0112.
**Name: **Examination.

**Higher education credits: ** 5,5.
**Grading scale: **TH.
**Assessment:** Oral examination.

**Code: **0212.
**Name: **Project.

**Higher education credits: ** 2.
**Grading scale: **UG.
**Assessment:** Written project report with oral presentation and opposition of another report.