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	3	8
Springfield	4	9
New Haven	7	16
Boston	2	11
Hartford	5	9

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 correlation coefficient indicates a very moderate positive correlation.  The correlation coefficient indicates a very strong negative correlation.  The correlation coefficient indicates no relationship between X and Y.  

The coefficient of determination indicates X accounts for about    percent of the variation in Y.

Answer 1

Y 64 3 The computation table for the data: x Y x 8 9 4 9 16 49 2 11 4 9 25 81 7 256 121 81 24 36 112 22 45 5 X; = 21 Y = 53 x = 103 27 = 603 x,y; = 239 i-1 ¿-1 1-1 The correlation coefficient is given by X- x = 5(239)-(21)(53) (5(103)- (21*)(5(603)– (53)") 1195–1113 (515-441)(3015–2809) 82 (74)(206) 82 15244 82 123.4666 = 0.664147 rs 0.6641 Therefore, the value of the coefficient of correlation between the two quantitative variables number of airings (x) and Tv sales (Y) is r* 0.6641 (b) The value of the coefficient of determination is obtained by squaring the correlation coefficient is of the part(a) R? =(r) =(0.664147) 0.441092 R2 -0.441 Therefore, the value of the coefficient of determination is R 0.441 (c) The interpretation of the correlation coefficient(r): The correlation coefficient(r = 0.6641) indicates a moderate positive linear relationship between the two quantitative variables (x) and (y). The interpretation of the coefficient of determination (RⓇ): The value of the coefficient of determination is R2 = 44.11 percent of the variation in the dependent variable (y) can be explained by the independent variable(x).