Exercise on Simple/Multiple Regression

The data are available at http://www.uv.es/mperea (“traer datos”)

(Remove all participants whose “sincerity” score is 3 or more.)

1. How is the relationship between “social support” and “well-being before surgery”? (you may need to draw the scattergram and then compute Pearson’s coefficient)

2. Can we predict the values of “well-being before surgery” on the basis of “social support”? If so, write down the equation of the regression line of well-being before surgery” when using “social support” as a predictor

3. What value of “well-being before surgery” would you predict for someone with a “social support” of 4?

4. Do you see any similarities between the slope of the regression line in standardized values and Pearson’s coefficient?

5. Compute the predicted values of “well-being before surgery”

6. Idem for the residuals (i.e., observed-predicted)

7. Compute the means and variances for the OBSERVED values of “well-being before surgery”, the PREDICTED values of “well-being before surgery”, and the residuals.

8. Can you see any relationship between the values of point 7?

9. What is the proportion of variance of “well-being before surgery” which can be explained by the regression line?

10. Let’s assume that we have two predictors (instead of one) when trying to predict “well-being before surgery”: “social support” and “age”. Write down the regression equation.

11. Which one of the predictors is more strongly associated to “well-being before surgery”? Why?

12. Are there any problems of collinearity between the predictors? (Check the Variance Inflation Factor; in “Statistics” button)

13. What is the proportion of variance of “well-being before surgery” which can be explained by this regression equation with two predictors? Do you think it was worth including the new predictor?

14. What would happen if you employ the “stepwise” procedure when introducing the predictors? Would the two predictors be added to the equation? Or just one?