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
0.956
negative 0 point 972
Image with alt text: negative 0 point 972
0.019
0.019
0.508
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.