The district manager of Jasons, a large discount electronics chain, is investiga

Question

The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are related to total sales: the number of competitors in the region, the population in the surrounding area, and the amount spent on advertising. From her district, consisting of several hundred stores, she selects a random sample of 30 stores. For each store she gathered the following information.

What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4, and advertising expense of 30? (Omit the "$" sign in your response.)

Compute the multiple standard error of estimate. (Round your answer to 3 decimal places.)

State the decision rule. H0: 1 = 2 = 3 = 0; H1: Not all 's are 0. Use the .05 level of significance. (Round your answer to 2 decimal places.)

State the decision rule. Use the .05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are related to total sales: the number of competitors in the region, the population in the surrounding area, and the amount spent on advertising. From her district, consisting of several hundred stores, she selects a random sample of 30 stores. For each store she gathered the following information.

Explanation / Answer

a. What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4, and advertising expense of 30?

Answer : Y = 14.00 - X1 + 30 X2 + 0.20 X3

X1 = Number of competitiors = 4

X2 = Population in regions = 0.4 million

X3 = advertising expense = 30 thousand dollars

Y^= 14.00 - 4 + 30 * 0.4 + 0.20 * 30 = 28 thousand dollar

(b)  Coefficient of determination R2 = 3050/ 5250 = 0.581

(c) multiple standard error of estimate = sqrt(SSresidual /dF) = sqrt (2200/ 26) = 9.1987

(d) State the decision rule. H0: 1 = 2 = 3 = 0; H1: Not all 's are 0. Use the .05 level of significance.

H0 is rejected if F > 3.49 [ Fcr for dF1 = 3, dF2 =26]

Computed F = 1016.67/ 84.62 = 12.0145

We shall reject the null hypothesis. F > Fcr  At least one regression coefficient is not zero.

E(1) For dF = 26 , critical value tcr = 2.0555

so for variable x1 , l t l < tcr  so we say that it cannot reject the nul hypothesis.

so for variable x2 , t > tcr so we can reject the null hypothesis.

For variable x3 ,t > tcr so we can reject the null hypothesis.

(b) so we can drop the variable X1  number of competitors in the region

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