1. Week 4: Multiple regression analysis Overview Questions from last week What is regression analysis? The mathematical model Interpreting the β coefficient Least squares model fitting R and R 2 An example using SPSS (ethnicity and LOS) Discussion of the 2 articles Data analysis discussion

2. What is regression analysis? Used to learn more about the relationship between several exposure variables and a continuous outcome variable Multiple regression is an extension of bivariate regression with several exposure variables instead of just one Used to predict the association

3. The mathematical model Y’ (known a Y prime) is the predicted value on the outcome variable A is the Y axis intercept β 1 is the coefficient assigned through regression X 1 is the unit of the exposure variable Thus the model is: Y’=A + β 1 X 1 + β 2 X 2 + β 3 X 3

4. Interpreting the β coefficient The β coefficient is of the most interest to us It tells us the predicted change in the association between the exposure variable and the outcome variable

5. Least squares model fitting Most regression models use the least squares method to fit regression models Tries to find the best fit for the regression line with the least variance

6. R and R 2 R is the regression coefficient R 2 is the square of the regression coefficient R 2 tells you the amount of variance in the outcome variable explained by the exposure variables The adjusted R 2 tells you how much of the population variation is likely to be explained by your sample

7. Sample size calculation Sample size calculation is done when planning a research study The size of the sample is determined by: –-variability in the data –-the size of difference to be detected -the smaller the difference to detect, the larger the sample size –Power and significance level –Practical issues (budget, participant availability)

8. A linear regression example Background Many parents new to Canada use the Emergency Department as the source of primary health care for their children Often the parents have limited understanding of English and have difficulty describing their child’s symptoms and understanding treatment modalities ED physicians are concerned that language barriers may lead to a longer LOS in the ED

9. Methods A survey was conducted in the ED at the Hospital for Sick Children in Toronto Parents whose mother tongue was not English were compared to parents with English as a primary language Outcome variable: LOS in the ED in minutes Exposure variables: Primary language (5 levels dichotomized into English and other), CTAS (1 to 5, 1= resuscitation, 5 = non-urgent), age in months,

10. Statistical analysis Univariate statistics (histograms for continuous variables, frequency distributions for categorical variables) Bivariate statistics (t-tests and chi square statistics) Multiple linear regression analysis Let’s try it in SPSS

11. For next week Read 2 articles Data analysis plan due: background and description of the variables, univariate stats, bivariate comparisons, multivariate analysis Start your own data analysis