Question 1:
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.
| Weight |
Orders |
| 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 |
| 482 |
14.5 |
| 432 |
13.6 |
| 409 |
12.8 |
| 553 |
16.5 |
| 572 |
17.1 |
| 506 |
15 |
| 528 |
16.2 |
| 501 |
15.8 |
| 628 |
19 |
| 677 |
19.4 |
| 602 |
19.1 |
| 630 |
18 |
| 652 |
20.2 |
a) Set up a scatter diagram.
b) Assuming a linear relationship, use the least square method to determine the regression coefficients b0, b1, and its regression equation.
c) Interpret the meaning of the slope b1 in this problem.
d) Determine the coefficient of determination, r2, and interpret its meaning.
e) Find the standard error of the estimate.
f) Evaluate whether the assumptions of regression (LINE) have been seriously violated.
g) How useful do you think this regression model is for predicting predict the number of orders?
h) Predict the average number of orders when the weight of the mail is 500 pounds.
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, β1.
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).
Question 2:
An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars.
|
Age (x)
|
8
|
3
|
6
|
9
|
2
|
5
|
6
|
3
|
|
Price (y)
|
25
|
144
|
40
|
19
|
234
|
56
|
33
|
189
|
a) Find the value of the linear correlation coefficient r.
b) Find the value of the coefficient of determination r2, and interpret the meaning for this problem.
c) At the 0.05 level of significance, is there a significant linear relationship between two variables?
d) If there is a linear correlation, what is the regression equation?
e) Interpret the meaning of the slope b1 in this problem.
f) Interpret the meaning of the Y-intercept b0 in this problem. Will it make sense to you as far as this model is concerned? Explain why.
g) Evaluate whether the assumptions of regression (LINE) have been seriously violated.
h) Determine the adequacy of the fit of the model.
i) Set up a 95% confidence interval estimate of the population slope.
j) Set up a 95% confidence interval estimate of the average price for all cars of this model after 7 years.
k) Set up a 95% confidence interval of the average price of a car of this model after 7 years.
l) Explain the difference in the results obtained in (j) and (k).