Question: 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 predict the number of orders based on the weight of the mail. A sample of 25 mail shipments is selected, and the data (weight of mail in pounds, orders in thousands) were studied.

A Minitab scatter plot and a Minitab simple linear regression printout are shown below.

Regression Analysis: Orders versus Weight

The regression equation is

Orders = 0.191 + 0.0297 Weight

Predictor Coef SE Coef T P

Constant 0.1912 0.4747 0.40 0.691

Weight 0.029703 0.001030 28.82 0.000

S = 0.725784 R-Sq = 97.3% R-Sq(adj) = 97.2%

Analysis of Variance

Source DF SS MS F P

Regression 1 437.64 437.64 830.82 0.000

Residual Error 23 12.12 0.53

Total 24 449.76

Please answer the following questions, and explain your reasons.

a. What is the proposed straight-line model to relate the number of orders to the weight of the mail?

b. From the scatter-plot of the data, does it appear that a straight-line model will be an appropriate fit?

c. From the Minitab printout, is the proposed model appropriate? Use ?= 0.05.

d. Interpret the y-intercept of the least squares line. Does it have a practical meaning?

e. Interpret the slope of the least squares line. Over what range of weight is the interpretation is meaningful?

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