Joe uses age, family size, and income to predict scores on a survey of happiness. The results were statistically significant with a coefficient of determination of 64%. He collects a new sample and examines the regression equation. In Joe's second sample, the common variance will likely __________ due to __________.
A) decrease, attenuation
B) increase, replication
C) decrease, shrinkage
D) increase, regression.

Question

Quizplus · Accepted Answer

The correct answer is C because the common variance, which is represented by the coefficient of determination, is likely to decrease due to shrinkage in the second sample. Shrinkage occurs when the regression equation is tested on a new sample with a different distribution than the original sample, which leads to a decrease in the coefficient of determination. This means that the prediction accuracy of Joe's regression equation will likely be lower in the second sample, as the relationship between the predictor variables and happiness may not be as strong or significant in the new population.

Joe Uses Age, Family Size, and Income to Predict Scores