Question

Exhibit 14 -3 A sample of data The marketing manager of a large supermarket chain believes the sales volume, in dollars, of pet food depends on the amount of shelf space (measured in feet of shelf space) devoted to pet food. Shelf Space Sales 5 160 5 220 5 140 10 190 10 240 10 260 15 230 15 270 15 280 20 260 20 290 20 310

The proportion of the variation in sales that is explained by shelf space is

a. .8270064

b. .65232306

c. .6839006

d. 12

Answer 1

The correct option is,

The proportion of the variation in sales that is explained by shelf space is,

C) 0.6839 (68.39%).

The coefficient of determination will tells us how much the variablity in y Variable explained by x independent variable.

The coefficient of determination R^2 is calculated using following steps,

First we need to compute the correlation coefficient,

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	5	160	800	25	25600
	5	220	1100	25	48400
	5	140	700	25	19600
	10	190	1900	100	36100
	10	240	2400	100	57600
	10	260	2600	100	67600
	15	230	3450	225	52900
	15	270	4050	225	72900
	15	280	4200	225	78400
	20	260	5200	400	67600
	20	290	5800	400	84100
	20	310	6200	400	96100
Sum =	150	2850	38400	2250	706900

The correlation coefficient rr is computed using the following expression:

The value of correlation coefficient R = 0.827.

The coefficient of determination R^2 = (0.827)^2

= 0.6839.  

Thank you.