Question

Bi-lo Appliance Stores has outlets in several large metropolitan areas in New England. The general sales manager plans to air a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She plans to get the information for Saturday-Sunday digital camera sales at the various outlets and pair them with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The pairings are as follows:

Location of
TV Station Number of Airings ($ thousands)
Providence 4 22
Springfield 2 24
New Haven 3 15
Boston 3 12
Hartford 6 10


a. Determine the correlation coefficient. (Round the final answer to 4 decimal places.)



Coefficient of correlation




b. Determine the coefficient of determination. (Round the final answer to 3 decimal places.)



Coefficient of determination



c. Interpret these statistical measures. (Round the final answer to 1 decimal place.)




(Click to select)



The coefficient of determination indicates x accounts for about
percent of the variation in y.

Answer 1

a. The Coefficient of correlation is r = -0.5845

b. The Coefficient of determination is 0.3416.

c. This is a moderate negative correlation, which means there is a tendency for high X variable scores to go with low Y variable scores (and vice versa).

How to get the correlation of coefficient

X Values

∑ = 18

Mean = 3.6

∑(X - Mx)2 = SSx = 9.2

Y Values

∑ = 83

Mean = 16.6

∑(Y - My)² = SSy = 151.2

X and Y Combined

N = 5

∑(X - Mx)(Y - My) = -21.8

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -21.8 / √((9.2)(151.2)) = -0.5845

Meta Numerics (cross-check)

r = -0.5845

The coefficient of determination shows a quite strong influence with the data.