2. The numerical value of the Pearson correlation indicates how well the data points fit a straight line. A value of 1.00 indicates a perfect linear fit and a value of zero indicates no linear trend.
4. a. SS-X = 5, SS-Y = 5, SP = -1, and r = -.20 b. SS-X = 50, SS-Y = 50, SP = 44, and r = .88 6. a. The graph shows a strong, positive correlation. b. r = .75
c. Although the points in the graph are displaced, the graph shows exactly the same relation as in the original data. Adding a constant does not affect the Pearson correlation.
d. r = .75
8. a. SS-exercise = 64, ss-health = 36, SP = 34, and r = .708
b. You cannot conclude that regular exercise causes better health. The two variables are positively related, but it is not necesarily a causal relationship.
10. With a sample of n = 2, the two data points always will fit perfectly on a straight line. Therefore, the correlation will be +1.00 or -1.00. With a sammple of only n = 2 the corrlation is meaningless.
12. For a correlation of .25 to be significant at the .05 level, the sample size must be n = 62 or greater (df = 60 or greater).
14. a. SS-IQ = 647.34, SS-RT = 968.84, SP = -264.33, and the correlation is r = -.334.
b. The sample correlatin is not significant. With n = 6, the critical value is .811 at the .05 level.
16. a. X Y
1 9
1 7
1 6
1 10
0 4
0 7
0 3
0 6
b. r = .668
18. a. The converted data show five individuals with scores of X = 1 and Y = 1, three individuals with X = 1 and Y = 0, one individual with X = 0 and Y = 1, and three individuals with X = 0 and Y = 0.
b. r = .354 (the sign is meaningless)
20. a. For company A, Y = 6X + 10. For company B, Y = 5X + 20.
b. For company A the cost is $70, and for company B the cost is $70.
c. An order of 20 rats should be less money from company B ($120 versus $130).
22. a. The standard error of estimate is 4.00
b. The standard error of estimate is .80
c. The standard error of estimate is 3.00
24. a. SS-X = 1385.67, SS-Y = 1586, SP = 920, and R = .621 which is smaller than the critical value of .658.
b. The standard error of estimate is 9.87