The following data pairs represent the average temperature x (in degrees Fahrenheit) and electricity

costs y (in dollars) for different homes

(65, 147), (59, 141), (71, 176), (78, 189), (82, 183), (85, 211),

(88,231), (91, 227), (84, 198) (79, 188), (63, 152), (59, 126)

Which of the following values is most likely the closest to the correlation coefficient of the data?

r=-1

r=-0.5

=0

r=0.5

The correct answer is C. r = 0 because is most likely the closest to the correlation coefficient of the data.

Step-by-step explanation:

Using Excel, we captured the data provided for the 12 different homes for calculating the correlation coefficient manually, this way:

n = 12

∑x = 904

∑y = 2,169

∑xy = 167,532

∑x² = 69,552

∑y² = 404,615

r = [n * ∑xy - (∑x * ∑y) ]/[√ (n * ∑x² - (∑x) ²) * (n * ∑y² - (∑y) ²) ]

Replacing with the real values, we have:

r = [12 * 167,532 - (904 * 2,169) ]/[√ (12 * 69,552 - 904²) * (12 * 404,615 - 2,169²) ]

r = [2'010,384 - 1'960,776]/[√ (834,624 - 817,216) * (4'855,380 - 4'704,561]

r = 49,608/√17,408 * 150,819

r = 49,608 / 51'239.215

r = 0.00097

The correct answer is C. r = 0 because is most likely the closest to the correlation coefficient of the data.