Becky is an experienced swimmer. The table contains data on her times in the 100-meter freestyle event for each year over the past six years.

Year Time

(seconds)

1 98

2 101

3 109

4 117

5 119

6 127

Sketch a scatter plot for this data, and then determine which of these numbers is the closest to the correlation coefficient for the data set.

a. 0.20

b. 0.99

c.-0.20

d.-0.83

e.-1.01

Correlation coefficient (r) = [nΣxy - (Σx) (Σy) ] / [sqrt (nΣx^2 - (Σx) ^2) sqrt (nΣy^2 - (Σy) ^2) ]

Σx = 21 = > (Σx) ^2 = 21^2 = 441

Σy = 671 = > (Σy) ^2 = 671^2 = 450,241

Σx^2 = 1 + 4 + 9 + 16 + 25 + 36 = 91

Σy^2 = 98^2 + 101^2 + 109^2 + 117^2 + 119^2 + 127^2 = 75,665

Σxy = 1 (98) + 2 (101) + 3 (109) + 4 (117) + 5 (119) + 6 (127) = 2,452

r = [6 (2,452) - 21 (671) ] / [sqrt (6 (91) - 441) sqrt (6 (75,665) - 450,241) ] = 621/sqrt (105) sqrt (3749) = 0.99

option b is the correct answer.