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 4 6 5 8 5 4 5 8 6 98 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 = 0.71 + 1.12 x c) The estimate for guitar sales if Maroon 5 performed on TV 10 times = 11.88 sales (round your response to two decimal places). d) The correlation coefficient (r) for this model = 0.8557 (round your response to four decimal places). The coefficient of determination (r) for this model = 0.7323 (round your response to four decimal places). The percentage of variation in sales that can be explained by TV appearances = % (round your response to two decimal places).

Answer 1

b) Let y=demand for guitars be the dependent variable

x=Maroon 5 TV appearances be the independent variable

N=6 (number of data points)

In Least squares regression method ,

slope=m=N* (xy) - x * y /N* (x^2) -( x)^2

=6*226-32*40/6*182-32^2

=1.1176

Intercept=b= y -m * x /N

=40-(1.1176*32)/6

=0.7059

The regression equation is ,

Demand for guitars =0.7059+1.1176 *Maroon 5 TV appearances

or y=0.7059+1.1176 *x

c.If x=10 ,

y=0.7059+1.1176 *10 =11.88

d.Coefficient of correlation =r=CORREL(B3:B8,C3:C8)=0.8557

Coefficient of determination =r^2 =0.8557^2 =0.7323

The percentage of variation in sales that can be explained by TV appearances is r^2=0.7323 =73.23 %

So,73.23 % is explained by the regression line.