Question: A large mail-order house believes that there is a linear relationship between the weight of the mail it receives and the number of orders to be filled. It would like to investigate the relationship in order to predict the number of orders based on the weight of the mail. From an operational perspective, knowledge of the number of orders will help in the planning of the order-fulfillment process. A sample of 12 mail shipments is selected within a range of 200 to 500 pounds. The results are as follows.

Weight of Mail (Pounds) Orders (In Thousands)

216 6.1

283 9.1

237 7.2

203 7.5

259 6.9

374 11.5

342 10.3

301 9.5

365 9.2

384 10.6

404 12.5

426 12.9

a. Construct a scatter diagram.

b. Assuming a linear relationship, use the least-squares method to find the regression coefficients b₀ and b₁.

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

d. Predict the mean number of orders when the weight of the mail is 500 pounds.