Question

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

Answer 1

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.