Chapter 16, Problem 13P

Problem 14 in Chapter 15 described a study examining the effectiveness of a 7-Minute Screen test for Alzheimer’s disease. The study evaluated the relationship between scores from the 7-Minute Screen and scores for the same patients from a set of cognitive exams that are typically used to test for Alzheimer’s disease. For a sample of $n=\text{9}$ patients, the scores for the 7-Minute Screen averaged $M=\text{7}$ with $SS=\text{92}$ . The cognitive lest scores averaged $M=\text{l7}$ with $SS=\text{236}$ . For these data, $SP=\text{127}$ .

a. Find the regression equation for predicting the cognitive scores from the 7-Minute Screen score.

b. What percentage of variance in the cognitive scores is accounted for by the regression equation?

c. Does the regression equation account for a significant portion of the variance in the cognitive scores? Use $\alpha =.05$ to evaluate the F-ratio.

Identifying individuals with a high risk of Alzheimer’s disease usually involves a long series of cognitive tests. However, researchers have developed a 7-Minute Screen, which is a quick and easy way to accomplish the same goal. The question is whether the 7-Minute Screen is as effective as the complete series of tests. To address this question. Ijuin et al. (2008) administered both tests to a group of patients and compared the results. The following data represent results similar to those obtained in the study.

Patient

7-Minutes

Screen
Cognitive

Series
A
3
1
B
8
19
C
10
22
D
8
20
E
4
14
F
7
13
G
4
9
H
5
20
I
14
25

a. Compute the Pearson correlation to measure the degree of relationship between the two test scores.

b. Is the correlation statistically significant? Use a two-tailed test with $\alpha =.01$ .

c. What percentage of variance for the cognitive scores is predicted from the 7-Minute Screen scores? (Compute the value of $r^2$ .)