The table below shows the temperature (in degrees) for eight consecutive days as well as the respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature
68
77
83
85
89
94
96
99
Number of Cones
403
447
457
465
489
503
543
576
What is the correlation coefficient of the set of data? Round your answer to the nearest thousandth.
(1 point)
Responses
0.956
negative 0 point 972
0.019
0.508
To calculate the correlation coefficient of the set of data, we can use the formula:
r = [n∑xy - (∑x)(∑y)] / √[(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)]
Where:
n = number of data points (in this case, 8)
∑ = sum of the values
First, let's calculate the necessary sums:
∑x = 68 + 77 + 83 + 85 + 89 + 94 + 96 + 99 = 691
∑y = 403 + 447 + 457 + 465 + 489 + 503 + 543 + 576 = 3923
∑xy = (68 * 403) + (77 * 447) + (83 * 457) + (85 * 465) + (89 * 489) + (94 * 503) + (96 * 543) + (99 * 576) = 372311
∑x^2 = (68^2) + (77^2) + (83^2) + (85^2) + (89^2) + (94^2) + (96^2) + (99^2) = 49231
∑y^2 = (403^2) + (447^2) + (457^2) + (465^2) + (489^2) + (503^2) + (543^2) + (576^2) = 1609359
Using the formula, we have:
r = [8(372311) - (691)(3923)] / √[(8 * 49231 - (691)^2)(8 * 1609359 - (3923)^2)]
r = [2978488 - (2708933)] / √[(393848 - 474481)(12874872 - 15356529)]
r = [268555] / √[(-80633)(-247164)]
r = 268555 / √[19925507812]
r = 268555 / 141097.707
r ≈ 1.903083357
Rounded to the nearest thousandth, the correlation coefficient of the set of data is 1.903.