(1 point) A national sporting good store wishes to use demographic information t

Question

(1 point) A national sporting good store wishes to use demographic information to predict its monthly sales, in $1000s. Thrity-eight, n 38 stores of the chain are randomly chosen across the country. It is known that each store is approximately the same size and carries the same merchandise The geographic area from which a store draws its customers is known as the customer base. One of the variables is the percentage of the customer base who have graduated from high school. Monthly Sales Bo B1PercentHSGradsi ei where Monthly Sales is the total sales in month i, in $1000s s percentage of all customers in store i customer base that have graduated from high school Percent HAS Grads A least-squares regression was ran in Minitab producing the following output Scatter Plot: Salesto High Sdhool Graduates 4000 3500 3000 8 2500 2000 9 1500 1000 500 26612ceb. ffac071d-af51-3ab0

Explanation / Answer

Part a

Here, we have to write the regression equation for the prediction of monthly sales. We are given a regression output. From this output, the regression equation is given as below:

MonthlySalesi = -2970 + 59.66*PercentHSGradsi

Where Y-intercept = -2970 and slope = 59.70

Part b

Here, we have to find out the total percentage of the variation in a store monthly sales. Total variation in the dependent variable due to independent variable is explained by the coefficient of determination. The formula for coefficient of determination or R square is given as below:

Coefficient of determination = SSR/SST

We are given

SSR = 7333350

SSE = 23155564

SST = SSR + SSE = 7333350 + 23155564 = 30488914

Coefficient of determination = SSR/SST = 7333350 / 30488914 = 0.24052513

Required Answer: 24.05%

Part c

Correct statistically hypotheses are given as below:

B. H0: 1 = 0, Ha: 1 0

(This is a two tailed test)

Part d

Here, we have to find the F test statistic value.

F = MSR/MSE

df for regression = 2 – 1 = 1

df for error = 37 – 1 = 36

MSR = SSR/df = 7333350 / 1 = 7333350

MSE = SSE/df = 23155564 / 36 = 643210.111

F = MSR/MSE = 7333350 / 643210.111

Fcalc = 11.40

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