Question
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)
To calculate the correlation coefficient of the set of data, we can use the formula:
r = (nΣxy - ΣxΣy) / √(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)
First, let's calculate the necessary sums:
n = 8 (number of data points)
Σx = 68 + 77 + 83 + 85 + 89 + 94 + 96 + 99 = 681
Σy = 403 + 447 + 457 + 465 + 489 + 503 + 543 + 576 = 3883
Σxy = (68)(403) + (77)(447) + (83)(457) + (85)(465) + (89)(489) + (94)(503) + (96)(543) + (99)(576) = 339716
Now let's calculate the sums of squares:
Σx^2 = (68^2) + (77^2) + (83^2) + (85^2) + (89^2) + (94^2) + (96^2) + (99^2) = 468861
Σy^2 = (403^2) + (447^2) + (457^2) + (465^2) + (489^2) + (503^2) + (543^2) + (576^2) = 16099269
Substitute these values into the correlation coefficient formula:
r = (8(339716) - (681)(3883)) / √((8(468861) - (681)^2)(8(16099269) - (3883)^2))
r = (2717728 - 2640423) / √((3750888 - 464161)(128794152 - 15068749))
r = 87305 / √((3286727)(113725403))
r ≈ 0.951
Therefore, the correlation coefficient of the set of data is approximately 0.951.