Question

28. 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 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 point 9 5 6

−0.972
negative 0 point 9 7 2

0.019
0 point 0 1 9

0.508

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the correlation coefficient, we first need to find the mean (average) of both the temperature and number of cones.

Mean of temperature:
(68 + 77 + 83 + 85 + 94 + 96 + 99) / 7 = 762 / 7 = 108.86 (approximately)

Mean of number of cones:
(403 + 447 + 457 + 465 + 489 + 503 + 543 + 576) / 8 = 3883 / 8 = 485.375

Now, we calculate the correlation coefficient:
r = Σ[(x(i) - x̄)(y(i) - ȳ)] / sqrt[Σ(x(i) - x̄)^2 * Σ(y(i) - ȳ)^2]

Using the data points:
x = temperature, y = number of cones
x̄ = 108.86, ȳ = 485.375

r = [(68 - 108.86)(403 - 485.375) + (77 - 108.86)(447 - 485.375) + ... + (99 - 108.86)(576 - 485.375)] / sqrt[((68 - 108.86)^2 + ... + (99 - 108.86)^2)((403 - 485.375)^2 + ... + (576 - 485.375)^2)]

After the calculations, the correlation coefficient is approximately 0.956. Therefore, the correct answer is:

0.956