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 has proved useful in the past, but the owner has the business ob-jective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved and the number of pieces of large furniture as the independent vari-ables and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving . a. State the multiple regression equation. b. Interpret the meaning of the slopes in this equation.
c. Predict the mean labor hours for moving 500 cubic feet with two large pieces of furniture. d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.
e. Determine whether there is a significant relationship between labor hours and the two independent variables (the number of cubic feet moved and the number of pieces of large furniture) at the 0.05 level of significance. f. Determine the p-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determina-tion in this problem. h. Determine the adjusted r2.
i. At the 0.05 level of significance, determine whether each inde-pendent variable makes a significant contribution to the regres-sion model. Indicate the most appropriate regression model for this set of data.
j. Determine the p-values in (i) and interpret their meaning.
k. Construct a 95% confidence interval estimate of the population slope between labor hours and the number of cubic feet moved. How does the interpretation of the slope here differ from that in Problem 12.44 on page 443? l. What conclusions can you reach concerning labor hours?
13.3 A small business analyst seeks to determine which vari-ables should be used to predict small-business mean annual rev-enue 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 an-nual revenue. Using data collected from a sample of 25 metropoli-tan areas, the regression results are:
a. State the multiple regression equation.
Variable Coefficients Standard Error t Statistic p – value
Intercept -680.2357 1,313.5154 -0.52 0.6097
Age 1.7454 7.8519 0.22 0.8261
BizAnalyzer 20.5265 29.1859 0.70 0.4885
b. Interpret the meaning of the slopes, b1 and b2, in this problem.
c. What conclusions can you reach concerning mean annual revenue?