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: ,Observation 1,Observation 2,Observation 3,Observation 4,Observation 5,Observation 6 Maroon 5 TV Appearances,3,5,8,5,9,6 Demand for Guitars,4,5,6,5,9,6

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 11 times = ...... sales (round your response to two decimal places).

d) The correlation coefficient (r) for this model =.... (round your response to four decimal places).

e)The coefficient of determination (r squared ) for this model = ...... (round your response to four decimal places).

f) The percentage of variation in sales that can be explained by TV appearances =....... (round your response to two decimal places).

Explanation / Answer

The least-squares regression method Calculation

Equation is y = a + bx

Where a is intercept and b is slop

Therefore y = 1.58 +0.71 *x

b) Using the least-squares regression method, the equation for forecasting is (round your responses to four decimal places): Y = 1.58+ 0.71x

c) The estimate for guitar sales if Maroon 5 performed on TV 11 times = 9.39 sales (round your response to two decimal places).

Y = 1.58+ 0.71x

Here we have x = 11

Therefore y = 1.58 +0.71 *11 = 9.39

d) The correlation coefficient (r) for this model = 0.9010 (round your response to four decimal places).

r = (xy) / sqrt [ ( x2 ) * ( y2 ) ]

where is the summation symbol, x = xi - x, xi is the x value for observation i, x is the mean x value, y = yi - y, yi is the y value for observation i, and y is the mean y value.

And r = 0.9010

e)The coefficient of determination (r squared ) for this model = 0.8118 (round your response to four decimal places).

The coefficient of determination (r squared) = r^2 = 0.9010^2 = 0.8118

Observation Maroon 5 TV Appearances (x) Demand for Guitars (y) x - x bar y - y bar (x-xbar)*(y-ybar) (x-xbar)^2 (y-ybar)^2 1 3 4 -3 -1.83 5.50 9.0 3.3611 2 5 5 -1 -0.83 0.83 1.0 0.6944 3 8 6 2 0.17 0.33 4.0 0.0278 4 5 5 -1 -0.83 0.83 1.0 0.6944 5 9 9 3 3.17 9.50 9.0 10.0278 6 6 6 0 0.17 0.00 0.0 0.0278 Mean 6 5.83 x bar ybar Sum 17.00 24.00 14.8333 slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2} 0.71 Intercept a = ybar - b * x bar 1.58 correlation coefficient (r) 0.9010

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