A firm is experiencing theft problems at its warehouse. A consultant to the firm

Question

A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = alpha + bG + cU and obtained the following results: a. Based on the above information, hiring one more guard per week will decrease the losses due to theft at the warehouse by _____ per week. a. $5, 150 b. $211 c. $130 d. $480.92 b. Based on the above information, if the firm hires 6 guards and the unemployment rate the in county is 10% (U = 10), what is the predicted dollar loss to theft per week? a. $4, 375 per week b. $5, 150 per week c. $8, 300 per week d. $9, 955 per week c. Which of the parameter estimates are significant at the 5% level? Which of the parameter estimates are significant at the 1% level?

Explanation / Answer

a)

480.92

from value of slope, (coefficient of G)

b)

regresison equation:

T = 5150.43-480.92*G+211.0*U

When G = 6 and U = 10; predicted T = 5150.43-480.92*6+211.0*10

=4374.91

c)

Ho: beta1 is not significant

H1: beta1 is significant

If p-value < alpha%, I reject ho at alpha%. If p-value > alpha%, I fail to reject ho at alpha %

With p-value = .0012, I can say that G is significant at 1% as well as 5% level of significance.

Ho: beta2 is not significant

H1: beta2 is significant

If p-value < alpha%, I reject ho at alpha%. If p-value > alpha%, I fail to reject ho at alpha %

With p-value = .0296, I can say that U is significant at 5% level of significance. But U is in-significant at 1% level of significance.

Hence at 1% G is significant and U is not significant. At 5% both U and G are significant predictors.

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