Question

Mark​ Gershon, owner of a musical instrument​ distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Gershon has collected the data shown in the following​ table:

                                                                                                          

Maroon 5 TV Appearances	33	33	66	66	88	55
Demand for Guitars	22	66	66	66	99	77

This exercise contains only parts​ b, c, and d.

​b) Using the​ least-squares regression​ method, the equation for forecasting is ​(round your responses to four decimal ​places)​:

Y​ =__​+___x

C) What is your estimate for guitar sales if Maroon 5 performed on TV nine times last month?

D) What are the correlation coefficient (r) and the coefficient of determination (r^2) for this model, and what do they mean?

Answer 1

TV Appearance (x)	Demand (y)	x*y	x*x	y*y
33	22	726	1,089	484
33	66	2,178	1,089	4,356
66	66	4,356	4,356	4,356
66	66	4,356	4,356	4,356
88	99	8,712	7,744	9,801
55	77	4,235	3,025	5,929
341	396	24,563	21,659	29,282
n	6
n*Sum(xy)	147,378
Sumx*Sumy	135,036
n*sumx2	129,954
(Sumx)2	116,281

b = (147378-135036)/(129954-116281) = 0.90

a = (396-341*0.90)/6 = 14.70

B) y = 14.70 + 0.90*x

C) For x = 9, y = 14.70 + 0.9*9 = 22.82

D)

n*sum(xy)	147378
Sumx*Sumy	135036
Root(nSumx2-(sumx)2)*Root(n*Sumy2)-(Sumy)2 16065.23

r = (147378-135036)/16065.23 = 0.77

r^2 = (0.77)^2 = 0.59

The r^2 value is less than 0.8, so it means that TV appearance is the moderate predictor for demand