A large mailorder house believes that there is an associatio

A large mail-order house believes that there is an association 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 be able 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 25 mail shipments is selected within a range of 200 to 700 pounds. The results were as follows:

Weight of Mail

Orders

Weight of Mail

Orders

(pounds)

(thousands)

(pounds)

(thousands)

216

6.1

432

13.6

283

9.1

409

12.8

237

7.2

553

16.5

203

7.5

572

17.1

259

6.9

506

15

374

11.5

528

16.2

342

10.3

501

15.8

301

9.5

628

19

365

9.2

677

19.4

384

10.6

602

19.1

404

12.5

630

18

426

12.9

652

20.2

482

14.5

A) Calculate the value of Pearson’s correlation coefficient and interpret your value. (show all your work for full marks!)

B) Calculate the least squares regression line. (show all your work for full marks!)

C) Predict the number of orders to be filled when the weight of the mail is 315 pounds. Predict the number of orders to be filled when the weight of the mail is 680 pounds.

D) What proportion of observed variation in the number of orders to be filled can be explained by the approximate linear relationship between the two variables? (show all your work and explain your answer.)

E) Predict the average number of orders when the weight of the mail is 500 pounds.  

Weight of Mail	Orders		Weight of Mail	Orders
(pounds)	(thousands)		(pounds)	(thousands)
216	6.1		432	13.6
283	9.1		409	12.8
237	7.2		553	16.5
203	7.5		572	17.1
259	6.9		506	15
374	11.5		528	16.2
342	10.3		501	15.8
301	9.5		628	19
365	9.2		677	19.4
384	10.6		602	19.1
404	12.5		630	18
426	12.9		652	20.2
482	14.5

Solution