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# Correlation & Regression Analysis

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2. What information is provided by the numerical value of the Pearson correlation?

12a. For the following sets of scores.

X Y
0 5
1 1
2 5
3 9
4 7
a. Compare the Pearson correlation.
b. Multiply each X value by 2 and compute the Pearson correlation for the modified scores.
c. Compare the values obtained in parts a and b, how does multiplying each score by a constant affect the value of the correlation?

14. It is well known that similarity in attitude, beliefs and interests plays an important role in interpersonal attraction (see - Byrne, 1971, for example). Thus correlations for attitudes between married couples should be strong. Suppose a researcher developed a questionnaire that measures how liberal or conservative ones attitudes are. Low scores indicate that the person has liberal attitudes, whereas high scores indicate conservatism. The following hypothetical data are scores for married couples.

Couple White Husband

A 11 14
B 6 7
C 16 15
D 4 7
E 1 3
F 10 9
G 5 9
H 3 8

15. Compare the Pearson correlation for these data and determine whether there is a significant correlation between attitude for husbands and wives.

Set alpha at .05, two tails.

A professor obtains SAT scores and freshman grade point averages (GPAs) for group of n= 15 college students. The SAT scores have a mean of M= 580 with SS = 22, 400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84.

a. Find the regression equation for predicting GPA from SAT scores.
b. What percentage of the variance in GPA's is accounted for by the regression equation ? (Compute the correlation, r, then find r2.)

c. Does the regression equation account for a significant portion of the variance in GPA? Use a = .05 to evaluate the F - ratio.