The Data of Mail.XLS
The operations manager of 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. She 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 25 mail shipments is selected within a range of 200 to 700 pounds. The data are in MAIL.xls.
a) Set up a scatter diagram.
b) Assuming a linear relationship, find the regression coefficients, b0, b1, and its regression equation.
c) Interpret the meaning of the slope b1 in this problem.
d) Predict the average number of orders when the weight of the mail is 500 pounds.
e) Determine the coefficient of determination, r2, and interpret its meaning.
f) Find the standard error of the estimate.
g) Evaluate whether the assumptions of regression (LINE) have been seriously violated.
h) How useful do you think this regression model is for predicting predict the number of orders?
i) At the 0.05 level of significance, is there evidence of a linear relationship between the weight of mail and the number of orders received?
j) Set up a 95% confidence interval estimate of the population slope, 1.
k) Set up a 95% confidence interval estimate of the population average number of orders received for a weight of 500 pounds.
l) Set up a 95% confidence interval of the number of orders received for an individual package with a weight of 500 pounds.
m) Explain the difference in the results in k) and l).
The solution predicts the number of orders based on the weight of the mail.