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
0.956

negative 0 point 972
Image with alt text: negative 0 point 972

0.019
0.019

0.508

Answer 1

To find the correlation coefficient, we can use the formula:

r = (nΣxy - ΣxΣy) / √[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

where n is the number of data points, Σ represents summation (addition), x represents the temperature values, y represents the number of cones sold, Σxy represents the sum of all the products of x and y, Σx represents the sum of all the x values, and Σy represents the sum of all the y values.

Using the given data, we can calculate the necessary values:

n = 8
Σxy = (68*403) + (77*447) + (83*457) + (85*465) + (89*489) + (94*503) + (96*543) + (99*576) = 3,996 + 34,719 + 37,431 + 39,525 + 43,521 + 47,582 + 52,128 + 57,024 = 355,926
Σx = 68 + 77 + 83 + 85 + 89 + 94 + 96 + 99 = 691
Σy = 403 + 447 + 457 + 465 + 489 + 503 + 543 + 576 = 3,423
Σx^2 = (68^2) + (77^2) + (83^2) + (85^2) + (89^2) + (94^2) + (96^2) + (99^2) = 4,624 + 5,929 + 6,889 + 7,225 + 7,921 + 8,836 + 9,216 + 9,801 = 60,041
Σy^2 = (403^2) + (447^2) + (457^2) + (465^2) + (489^2) + (503^2) + (543^2) + (576^2) = 162,409 + 200,209 + 208,849 + 216,225 + 239,121 + 253,009 + 294,849 + 331,776 = 1,706,447

Plugging these values into the formula, we get:

r = (8*355,926 - (691*3,423)) / √((8*60,041 - (691)^2)(8*1,706,447 - (3,423)^2))
= (2,847,408 - 2,366,893) / √((480,328 - 476,281)(13,651,712 - 11,730,729))
= 480,515 / √((4,047)(1,920,983))
= 480,515 / √(7,782,744,201)
≈ 480,515 / 88,224.227
≈ 5.449

Rounding to the nearest thousandth, the correlation coefficient is approximately 0.005.