A researcher wishes to predict the graduation rates in a sample of 240 colleges and universities based on the percentage of freshmen who were in the top tier (10%) of their high school class and the percentage of classes that have fewer than 20 students. The correlation matrix of graduation rate (GRADRATE), percentage of freshmen in the top tier of their high school graduating class (TOPFRESH), and the percentage of classes at the college with fewer than 20 students (SMALLCLS) is shown as follows:

a. What percentage of the variance in GRADRATE does each of the predictor variables explain individually?
b. What percentage of the variance in GRADRATE do the two predictors explain in combination?
c. Why doesn’t the answer in (b) equal the sum of the two answers in (a)?

Transcribed Image Text:

GRADRATE TOPFRESH SMALLCLS GRADRATE TOPFRESH SMALLCLS 1.000 .613 .544 .613 1.000 404 544 404 1.000