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 this relationship in order to predict the number of orders to be filled based on the weight of the mail. From an operational perspective, knowledge of the number of orders to be filled will help in the planning of the order-fulfillment process. A sample of 15 mail shipments is selected within a range of 200 to 700 pounds. The results are as follows.

Weight of Mail (Pounds) Orders to be Filled (In Thousands)

240 6.5

290 9.0

237 7.2

380 11.5

342 10.3

384 10.6

482 14.5

430 13.6

409 12.8

553 16.5

572 17.1

501 15.8

628 19.0

670 19.6

620 19.2

1. Assuming a linear relationship, determine the regression results by using Excel. What are the values for the regression coefficients b₀ and b₁ for this problem?
2. Interpret the meaning of the slope, b₁, in this problem
3. Predict the mean number of orders to be filled when the weight of the mail is 500 pounds
4. Determine the coefficient of determination r² and interpret its meaning.

5. Find the standard error of the estimate.

6. At the 0.05 level of significance, is there evidence of a linear relationship between the weight of the mail and the number of orders to be filled?