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Correlation questions

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1. For the following scores,

X Y
3 6
6 1
3 4
3 3
5 1

a) Find the regression equation for predicting Y from X
b) Calculate the predicted Y value for each X
2. For the following scores

X Y
1 6
4 1
1 4
1 3
3 1

a) Compute the Pearson correlation

3. Identifying individuals with a high risk of Alzheimer's disease usually involves a long series of cognitive tests. However, researcher have developed a 7-Minute Scree, 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-Minute Screen Cognitive Series
A 3 11
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 scores.
b) Is the correlation statistically significant? Use a two-tailed test with an alpha=.01
c) What percentage of variance for the cognitive scores is predicted from the 7-Minute Screen scores? (Compute the value of r2 )