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 county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T= a + bG + cU and obtained the following results: a. Write out the estimated regression equation for loss from thefts each week: b. Interpret the numerical value of the estimated slope parameters on G and H in the context of this regression case. For each additional _____ hired, holding ______ constant, on average, weekly loss from theft ______ by _____ dollars. For each ______ percent ______ in the _______, holding _____ constant, weekly loss from theft ______ by _____ dollars c. Evaluate the overall goodness of fit of the sample regression by interpreting the coefficient of determination (R^2) in the context of this regression. R^2 = ______ Interpretation:______ d. Complete each of the following statements assuming 1% significance level for any tests: The critical t value to test for significance of the individual slope parameters is t_er = t_-0.1, 24 = 2, 797. The estimates of the parameters a, b, and are all statistically significant because the absolute values of their t-ratios_ _____ 2.797. The estimates of the parameters a, b, and are all statistically significant because each of their p-values is _____ 001. The regression equation (overall sample regression) is statistically _____ because the p-value of F is ____ 0.01. e. If the firm lures 6 guards and the unemployment rate in the county is 10%(U = 10), what is the predicted dollar loss to theft per week? (You should obtain an expected theft loss of $4, 375 per week)

Explanation / Answer

Result:

a). T= 5150.43 -480.92*G+211.0*U

b).

For each additional Guards hired, holding U constant, on average weekly loss from theft decreases by 480.92 dollars.

For each one percent increase in the U, holding Number of Guards constant, on average weekly loss from theft increases by 211.0 dollars.

R2 = 0.7793

77.93% of variation in loss from theft is explained by the model.

d).

absolutes values of t ratios greater than 2.797.

each p values is less than 0.01.

regression equation is statistically significant because the p value of F is less than 0.01.

e).

expected loss = 5150.43 -480.92*6+211.0*10

=4374.91

=$4375 ( rounded).

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