Question

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)

Answer 1

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.