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.

Question

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

Answer 1

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.