How willing are you to donate your organs upon death? This was the question of interest in research published in Death Studies (Vol. 38, 2014). A sample of n = 307 Australians participated in the study. Willingness to donate organs upon death was measured for each participant on a 7-point scale (1 = very unlikely, 7 = very likely). Multiple regression was used to model willingness (y) as a function of general attitude (x1) toward donating organs (28-point scale), subjective norm (x2)-assessment of whether others would approve of organ donation (14-point scale), prototype favorability (x3)-opinion of those who do donate organs (14-point scale), prototype similarity (x4)-similarity to organ donors (14-point scale), age (x5) in years, and gender (x6).
a. Write a first-order, main-effects model for E(y) as a function of the six independent variables.
b. The model, part a, resulted in R2 = .39 and global F p-value 6 .001. Interpret these results.
c. What term would you add to the model, part a, to allow for the effect of prototype favorability on willingness to depend on prototype similarity?
d. The model, part c, resulted in R2 = .41 and global F p-value 6 .001. Interpret these results.
e. Are the models, parts a and c, nested models?
f. A nested model F-test comparing the models resulted in a test statistic of F = 10.94 with a p-value of .001. Interpret these results.