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	4	4	6	5	9	7
Demand for Guitars	4	6	6	4	11	8

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) The estimate for guitar sales if Maroon 5 performed on TV 10 times = ? sales (Round to two decimal places)

d) The correlation coefficient (r) for this model = ? (Round to 4 decimal places)

The coefficient of determination (r^2) for this model = ? (Round to 4 decimal places)

The percentage of variation in sales that can be explained by TV appearances = ?% (round to two decimal places)

Answer 1

	Maroon ( TV ) X	Demand for Guitars (Y)	X * Y	X2	Y2
	4	4	16	16	16
	4	6	24	16	36
	6	6	36	36	36
	5	4	20	25	16
	9	11	99	81	121
	7	8	56	49	64
Total	35	39	251	223	289

Part b)
Equation of regression line is Ŷ = a + bX


b = 1.2478
a =( Σ Y - ( b * Σ X) ) / n
a =( 39 - ( 1.2478 * 35 ) ) / 6
a = -0.7788
Equation of regression line becomes Ŷ = -0.7788 + 1.2478 X

Part c)
When X = 10
Ŷ = -0.779 + 1.248 X
Ŷ = -0.779 + ( 1.248 * 10 )
Ŷ = 11.70

Part d)


r = 0.9088

Coefficient of Determination
R² = r² = 0.8260

Explained variation = 0.826* 100 = 82.60%