Question

Identifying individuals with a high risk of Alzheimer’s disease usually involves a long series of cognitive tests. Researchers have developed a shorter test called the 7-Minute Screen. A study using the same participants evaluated whether scores from the 7-Minute Screen could predict scores from a series of cognitive tests for Alzheimer’s disease.

Participant 7-minute Screen Cognitive Series

1 3 11

2 8 19

3 10 22

4 8 20

5 4 14

6 7 13

7 4 9

8 5 20

9 14 25

a.Sketch a scatterplot of the test scores. Make sure to label both axes.

b. Calculate the Pearson correlation to measure the linear relationship between the two test scores.

c. What percentage of variance in cognitive test scores is predicted from the 7-Minute Screen scores?

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

e. Evaluate the significance of the regression equation at alpha 0.05. State the conclusion in the words of the problem.

f. Can the regression equation found in (d) be used to predict cognitive test scores if the 7-Minute Screen scores are 6 and 25? Either predict the cognitive test score or explain why the regression equation cannot be used.

7-Minute Screen score = 6, Cognitive test score =

7-Minute Screen score = 25, Cognitive test score =

Answer 1

Computational Table:

a)

b)

Sample correlation coefficient (r):

r = 0.835

C)

Coefficient of Determination (R2):

r2 = 0.8352 = 0.697 = 69.7%

69.7% of variance in cognitive test scores is predicted from the 7-Minute Screen scores.

d)

Calculation:

For Slope:

b = 1.30

For Intercept:

a = 17 - 1.30*7

a = 7.93

Therefore, the least square regression line would be,

= 7.93 + 1.30 (X)