Question

 

Part 1. Provide an example regression equation from your notes and based on that, provide which is/are the explanatory variable(s) and which is the response variable.

Part 2 Contrast confounding and effect modification.

Part 3. Explain what you are looking for in a residual plot?

Part 4 What is R squared? Provide an example interpretation from a multivariate regression model.

Answer 1

Part 1.

The regression equation is:

y = 17.418 + 0.713*x

where y = GPA

x = Time spent studying

The explanatory variable is time spent studying and the response variable is GPA.

Part 2.

Confounding factors are a “nuisance” and can account for all or part of an apparent association between an exposure and a disease. Effect Modification is not a “nuisance”, it in fact provides important information. The magnitude of the effect of an exposure on an outcome will vary according to the presence of a third factor.

Part 3.

The residual plots show the typical patterns. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a nonlinear model is more appropriate.

Part 4.

R-squared is a statistical measure of how close the data are to the fitted regression line.

For example, 94.5% of the variation in GPA is explained by time spent studying.