ORMS 3310
Ch 12 Practice
NAME: _______________________
Show ALL of your work in a legible and organized fashion.
4 Questions and Problems
1.
At State University, a study was done to establish whether a relationship existed between a student’s GPA
when graduating and SAT score when entering the university. The sample data are reported as follows.
GPA 2.5 3.5 3.0 2.9
SAT 640 550 620 600
Compute the regression equation based on this sample data using the SAT scores to predict the GPA. In
addition, compute the coefficient of determination and interpret your results.
ANSWER:
yˆ  9  0.01x
r2 = 0.8818
A
1
2.
The following data show the case sales (millions) and the media expenditures (millions of dollars) for five
major brands of soft drinks. Plug these numbers in to Microsoft Excel and answer the following questions
based on the regression output tables from Excel.
Brand
Media Expenditure ($) Case Sales
Coca-Cola Classic 131.3
1929.2
Pepsi-Cola
92.4
1384.6
Diet Coke
60.4
811.4
Sprite
55.7
541.5
Dr Pepper
40.2
536.9
Identify the independent and dependent variables.
ANSWER:
x = media expenditure ($)
y = case sales
Compute the regression equation based on the sample data above. Compute the coefficient of
determination and interpret your results.
ANSWER:
yˆ  208.41  16.4359x
r2 = 0.9718
Enter the data in Excel and run the regression analysis. Use the Excel output to determine if the model is
significant at the 5% level of significance.
The model is significant at a 5% level of significance
Predict the case sales for a brand with a media expenditure of $70 million.
ANSWER:
942.023 (case sales in millions)
A
2
3.
You want to determine if wages rise with experience. The following data show the weekly wages of
employees and their respective length of service (LOS) in months.
Wages
389
295
315
312
516
LOS
94
20
45
10
24
Identify the independent and dependent variables.
ANSWER:
x = LOS
y = wages
Compute the regression equation based on the sample data above. Compute the coefficient of
determination and interpret your results.
ANSWER:
yˆ  351.44  0.3617 x
r2 = 0.0175
Enter the data in Excel and run the regression analysis. Use the Excel output to determine if the model is
significant at the 5% level of significance.
The model is not significant at a 5% level of significance
Predict the weekly wages for an employee with a LOS of 63 months.
ANSWER:
374.2271
Enter the data in Excel and run the regression analysis. Use the Excel output to determine if the model is
significant at the 1% level of significance.
ANSWER:
The model is not significant at a 1% level of significance
A
3
The following sample data contains the number of years of college and the current annual salary for a random
sample of knowledge workers
Years of College 5 2 3 4 3 1
Annual Income 45 23 25 26 28 24
Calculate the least squares estimated regression line.
ANSWER:
yˆ  15  4.5x
Calculate the coefficient of determination.
ANSWER:
r2 = 0.5930
Calculate the sample correlation coefficient between income and years of college. Interpret your results.
ANSWER:
r = 0.7700
Enter the data in Excel and run the regression analysis. Use the Excel output to determine if the model is
significant at the 10% level of significance.
ANSWER:
The model is significant at a 10% level of significance
A
4
5.
You are interested in determining if there is a relationship between age and liquid assets. The following sample
data contains the age of several participants in the study and the amount of liquid assets that they have available.
38 48 38 28 40 50
Age
Liquid Assets (in thousands) 16 18 10 7 19 22
Calculate the least squares estimated regression line.
ANSWER:
yˆ  9.9070  0.6258 x
Calculate the coefficient of determination.
ANSWER:
r2 = 0.7561
Enter the data in Excel and run the regression analysis. Use the Excel output to determine if the model is
significant at the 5% level of significance.
ANSWER:
The model is significant at a 5% level of significance
A
5