Chapter 13, Problem 79PS

An accountant for a large department store has the business objective of developing a model to predict the amount of time it takes to process invoices. Data are collected from the past 32 working days, and the number of invoices processed and completion time (in hours) are stored in invoice. (Hint: First determine which are the independent and department variables.)

a. Assuming a linear relationship, use the least-square method to compute the regression coefficients $b_0$ and $b_1.$

b. interpret the meaning of the $Y$ intercept, $b_0,$ and the slope, $b_1,$ in this problem.

c. Use the prediction line developed in (a) to predict the mean amount of time it would take to process 150 invoices.

d. Determine the coefficient of determination $r^2,$ and interpret its meaning.

e. plot the residuals against the number of invoices processed and also against time.

f. Based on the plots in (e), does the model seem appropriate?

g. Based on the results in (e), and (f), what conclusions can you reach about the validity of the prediction made in (c)?

h. What conclusions can you reach about the relationship between the number of invoices and the completion time?