Mark Gershon, owner of a musical instrument distributorship, thinks that demand

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 Demand for Guitars 4 5 76 8 6 3 6 6 6 10 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) c) The estimate for guitar sales if Maroon 5 performed on TV 10 times : sales round your response to two de mal places d) The correlation coefficient (for this model(round your response to four decimal places) The coefficient of determination )for this model(round your response to four decimal places). The percentage of variation in sales that can be explained by TV appearances- 96 (round your response to two decimal places).

Explanation / Answer

PLEASE FIND ANSWERS TO FIRST 4 QUESTION :

Let the Linear Regression equation is:

Y = A + B.X

X ( independent variable ) = Number of TV appearances

Y ( Dependent variable ) = Demand for guitars

A, B = Constants

We place all the values of TV appearances and demand for Guitars in two different columns in excel and apply the formula LINEST () and we get following values of A and B :

A = - 1.9

B = 1.4

Thus,

Y = 1.4X – 1.9

THE EQUATION FOR FORECASTING IS     Y = 1.4X – 1.9

The estimate of Guitar sales if Maroon % performed on TV 10 times

= 1.4 x 10 – 1.9

= 14 – 1.9

= 12.1

THE ESTIMATE FOR GUITAR SALES IF MAROON 5 PERFORMED ON TV 10 TIMES = 12.1

The Correlation coefficient can be found by placing data on TV appearance and demand for guitars in two different columns and applying the formula CORREL ( )

Accordingly , Correlation coefficient is = 0.8442

Coefficient of determination for this model = 0.8442 x 0.8442 = 0.7126

CORRELATION COEFFICIENT FOR THIS MODEL = 0.8442

COEFFICIENT OF DETERMINATION = 0.7126

THE EQUATION FOR FORECASTING IS     Y = 1.4X – 1.9

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