# Regression Analysis and Applications

## Objectives

- A broad knowledge of linear regression analysis (simple and multiple) in the context of its application to health
- Interpretation and critical evaluation of empirical results
- Procedures and validation techniques of linear models
- Theoretical framework used in the empirical analysis of linear regression models, such as the properties of least squares estimators, maximum likelihood and hypothesis testing.
- Interpretation and evaluation of the survival curves
Skills
- Be a proficient user of the regression models applied to problems in health
- Perform statistical tests to ascertain the validity of the assumptions underlying the linear regression model.
- Build and interpret survival curves and respective hypothesis testing
- Being a critical reader of literature of linear regression models and survival analysis in health

## General characterization

12394

6.0

##### Responsible teacher

Isabel Cristina Maciel Natário, Sara Alexandra da Fonseca Marques Simões Dias

##### Hours

Weekly - Available soon

Total - 61

Português

### Prerequisites

Basic notions of Analysis and intermediate level notions of Probability and Statistics.

### Bibliography

Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach. 3rd ed. Mason, OH: Thomson/South-Western, 2006.

Carvalho, M. S., Andreozzi, V. L., Codeço, C, T., Barbosa, M. T. S. & Shimakura, S. E. Análise de Sobrevivência: teoria e aplicações em saúde, 2.ª edição, 2011.

Collet, D. Modelling Survival Data in Medical Research. 2nd edition. Chapman & Hall/CRC. 2003.

### Teaching method

Expository method by lectures, viewing the films, problem solving and practical exercises.

### Evaluation method

Two moments of evaluation: test and report.

## Subject matter

0. Introduction
1. Simple linear regression
1.1 Model assumptions
1.2 Model estimation – method of least square
1.3 Regression and correlation
2. Multiple linear regression
2.1 Model assumptions
2.2 Estimation and properties of estimators
2.3 Gauss Markov theorem
2.4 Interpretation of the dos coefficients estimated
2.5 Dummy variables
3. Inference
3.1 Hypothesis testing
3.2 Confidence intervals
4. Goodness of fit
5. Multicolinearity and Heterocedasticity
6. Chow test of structural stability
7. Prediction
8. Survival analysis
8.1 Introduction – measuring time
8.2 Kaplan meier
8.3 Nelson Aalen
8.4 Confidence interval
8.5 Median survival time
8.6 Kaplan meier stratified
8.7 Log-Rank and Peto tests

## Programs

Programs where the course is taught: