Applied Linear Statistical Models
Test 2
Fall 2003
Instructions: After completing the exam, please submit it via email to
dhjones@rci.rutgers.edu. The revised deadline is Midnight Sunday December 14, 2003.
Partial credit will apply to submissions after this date until 6 am Monday December 15,
2003.
In the subject line of your email, please put “Final Test” (without the quotes) followed by
your name.
In your answer sheet, begin each question on a new page. Number all pages.
A regional delivery service company recently conducted a study to investigate the
relationship between the cost of shipping a package (Y), the package weight (X1), and the
distance shipped (X2). Twenty packages were randomly selected from among the large
number received for shipment and a detailed analysis of the shipping cost was conducted
for each package. The data are displayed below.
Cost_of_Shipment
$3.30
$2.00
$11.00
$2.60
$1.90
$8.00
$15.50
$5.00
$1.00
$4.40
$6.00
$1.70
$14.50
$14.00
$9.20
$1.10
$12.10
$1.50
$8.00
$3.90
Dr. Douglas H. Jones
Package_Weight
4.10
0.30
5.10
5.90
4.50
3.50
7.00
2.40
0.60
0.75
6.20
1.10
6.50
7.50
6.60
2.70
8.10
0.70
4.40
3.20
Page 1
Distance_Shipped
95
160
240
47
53
250
260
209
100
280
115
90
240
190
160
45
160
80
202
145
Rutgers Business School
Question 1
Estimate a multiple regression model involving the two given explanatory variables.
Using the ANOVA table, perform and interpret the result of an F test. Use 5%
significance level in making the statistical decision in this case. Perform the preliminary
exploratory analysis first.
Step a) Copy and past the data to the statistical package. Create the proper names and
labels Variables View window. Press the Print Screen key, paste in your test answer
sheet.
Step b) Create the proper Summary Statistics and box-plots using Explore. Copy and
paste into your answer sheet. Are there any features that need discussing? What are they?
Step c) Create the Correlation Matrix, copy and paste into your answer sheet, discuss.
Step d) Fit the following model:
Copy and paste the coefficient table, discuss.
Step e) Test the hypotheses:
Copy and paste the ANOVA table, discuss.
Step f) Copy and paste the Model Summary table, compare the standard error of the
estimate with the appropriate statistic of y in step b.
Dr. Douglas H. Jones
Page 2
Rutgers Business School
Question 2
Is it worthwhile to add the terms X12 and X22 to the regression equation of Question 1?
Base your decision here on a partial F test. Once again, employ a 5% significance level in
performing this test.
Step a) What are the appropriate full (model 2) and reduced models (model 1)?
Step a) What are the Hypotheses for testing the Reduced Model vs. the Full Model?
Step b) Create the variables X1X2, X1X1, and X2X2. Open the Data View window;
press the print screen key, paste into your answer sheet.
Step c) Fit the Reduced Model 1, followed by the Full Model 2. Copy and paste the
appropriate ANOVA tables.
Step d) What is the computed partial F-statistic and it p-value?
Dr. Douglas H. Jones
Page 3
Rutgers Business School
Question 3
Is it worthwhile to explore other models versus the full model of Question 2? Once again,
employ a 5% significance level in performing this analysis.
Step a) Use the Block option with Stepwise Regression. Copy and paste the Stepwise
results. Compute the requires partial F-statistics.
Dr. Douglas H. Jones
Page 4
Rutgers Business School
Question 4
Based on the previous findings, what regression equation should this company use in
predicting the cost of shipping a package? Defend your recommendation.
Step a) What is the final regression equation is
Step b) At the 5% significance value, what are the results of using the partial F-test for
testing the reduced model (Y = X1 X2 X1X2) in favor of the full model (Y = X1 X2
X1X2 X1X1).
Step c) How much is the standard error of estimate less for model (Y = X1 X2 X1X2
X1X1) compared to model (Y = X1 X2 X1X2). What is the final standard error of
estimate?
Step d) Examine the residual plot and normal probability plot of residuals for the final
model. Copy and paste the plots. Discuss.
Dr. Douglas H. Jones
Page 5
Rutgers Business School