13.3 A small business analyst seeks to determine which variables should be used to predict small-business mean annual revenue for U.S. metropolitan areas. The analyst decides to consider the independent variables age, the mean age (in months) of small businesses in the metropolitan area; and BizAnalyzer, the mean BizAnalyzer score of small businesses in the metropolitan area. (The BizAnalyzer score measures on a scale of 1 to100 the level of risk that the small businesses in the metropolitan area present to potential lenders.) The dependent variable, revenue, is mean annual revenue. Using data collected from a sample of 25 metropolitan areas, the regression results are:

a) State the multiple regression equation.

b) Interpret the meaning of the slopes, b1 and b2, in this problem.

c) What conclusions can you reach concerning mean annual revenue?

13.50 The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach had proved useful in the past, but he would like to be able to develop a more accurate method of predicting the labor hours by using the amount of cubic feet moved. In a preliminary effort to provide a more accurate method, he has collected data for 36 moves, in which the travel time was an insignificant portion of the labor hours worked.

The data are in the Excel file, MOVING.xls

a) Set up a scatter diagram.

b) Assuming a linear relationship, find the regression coefficients, b0, b1, and its regression equation.

c) Interpret the meaning of the slope b1 in this problem.

d) Predict the labor hours for moving 500 cubic feet.

e) What factors besides the cubic feet moved might affect labor hours?

f) Determine the coefficient of determination r2, and interpret its meaning.

g) Find the standard error of the estimate.

h) How useful do you think this regression model is for labor hours?

i) Determine if the assumption of normality is violated by using the normal probability plot for residuals.

j) At the 0.05 level of significance, is there evidence of a linear relationship between the numbers of cubic feet moved and labor hours?

k) Set up a 95% confidence interval estimate of the population slope, β1.

l) Set up a 95% confidence interval estimate of the average labor hours for all moves of 500 cubic feet.

m) Set up a 95% confidence interval of the labor hours of an individual move that has 500 cubic feet.

n) Explain the difference in the results obtained in (l) and (m).