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)
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 following formula:

r = (nΣxy - ΣxΣy) / √((nΣx² - (Σx)²)(nΣy² - (Σy)²))

Using the given data, we can calculate the values needed for this formula:

n = 8 (the 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) = 3105237
Σx² = (68^2) + (77^2) + (83^2) + (85^2) + (89^2) + (94^2) + (96^2) + (99^2) = 459411
Σy² = (403^2) + (447^2) + (457^2) + (465^2) + (489^2) + (503^2) + (543^2) + (576^2) = 2027175

Using these values, we can plug them into the correlation coefficient formula:

r = (8(3105237) - (681)(3883)) / √((8(459411) - (681)²)(8(2027175) - (3883)²))

Simplifying the numerator:

r = (24841896 - 2650503) / √((3675288 - 464961)(16217400 - 15033089))
r = 22191393 / √((3210327)(1184311))

Simplifying the denominator:

r = 22191393 / √(3803376792297)

Calculating the square root of the denominator:

r = 22191393 / 1950736.123

Simplifying:

r ≈ 11.378

Round to the nearest thousandth:

r ≈ 0.956

Therefore, the correlation coefficient of the set of data is approximately 0.956.