Chapter 14, Problem 43PS

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 objective 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 whether there is an elevator in the apartment building as the independent variables and has collected data for 36 movers 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. For (a) through (k), do not include an interaction term.

a. State the multiple regression equation for predicting labor hours, using the number of cubic feet moved and whether there is an elevator.

b. Interpret the regression coefficients in (a).

c. Predict the mean labor hours for movie 500 cubic feet in an apartment building that has an elevator and construct a $95\%$ confidence interval estimate and a $95\%$ prediction interval.

d. Perform a residual analysis on the model and determine whether the regression assumptions are valid.

e. Is there a significant relationship between labor hours and the two independent variables (cubic feet moved and whether there is an elevator in the apartment building) at the 0.05 level of significance?

f. At the 0.05 level of significance, determine whether each inde- pendent variable makes a contribution to the regression model. Indicate the most appropriate regression model for this set of data.

g. Construct a $95\%$ confidence interval estimate of the population slope for the relationship labor hours and cubic feet moved.

h. Construct a $95\%$ confidence interval estimate for the relationship between labor hours and the presence of an elevator.

i. Compute and internet the adjusted $r^2.$

j. Compute and coefficients of partial determination and interpret their meaning.

k. What assumption do you need to make about the slope of labor hours with cubic feet moved?

l. Add an interaction term to the model, and at the 0.05 level of significance, determine whether it makes a significant contribution to the model.

m. On the basis of the result of (f) and (l), which is most appropriate? Explain.

n. What conclusions can you reach concerning the effect on the number of cubic feet moved and whether there is an elevator on labour hours?