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
0.508
To find the correlation coefficient, we can use the formula:
r = (n∑XY - (∑X)(∑Y)) / sqrt((n∑X²-(∑X)²)(n∑Y²-(∑Y)²))
Where n is the number of data points, ∑XY is the sum of the products of X and Y values, ∑X is the sum of X values, ∑Y is the sum of Y values, ∑X² is the sum of squared X values, and ∑Y² is the sum of squared Y values.
Using the data given, we can calculate the sums and products:
n = 8
∑X = 68 + 77 + 83 + 85 + 89 + 94 + 96 + 99 = 681
∑Y = 403 + 447 + 457 + 465 + 489 + 503 + 543 + 576 = 3883
∑XY = (68*403) + (77*447) + (83*457) + (85*465) + (89*489) + (94*503) + (96*543) + (99*576) = 3416486
∑X² = (68²) + (77²) + (83²) + (85²) + (89²) + (94²) + (96²) + (99²) = 45286
∑Y² = (403²) + (447²) + (457²) + (465²) + (489²) + (503²) + (543²) + (576²) = 13370526
Plugging these values into the formula:
r = (8*3416486 - (681*3883)) / sqrt((8*45286-(681)²)(8*13370526-(3883)²))
Calculating the numerator and denominator:
Num = 27331888 - 2641023 = 24690865
Den = sqrt((361728-(681²))(106964208-(3883²))) = sqrt(2697513932)
Calculating the correlation coefficient:
r = 24690865 / sqrt(2697513932) ≈ 0.949 (rounded to the nearest thousandth)
Therefore, the correlation coefficient of the data set is approximately 0.949.