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BUSN 4000, section MORSE, Fall 2021
INSTRUCTOR
BUSN 4000: Homework 11 (Homework)
Jack Morse
University of Georgia
Current Score
QUESTION
1
2
3
4
5
6
7
8
9
10
POINTS
2/2
5/5
2.5/2.5
4.5/5
2.5/2.5
10/11
23/23
4/5
20.5/23
21/21
TOTAL SCORE
95/100 95.0%
Due Date
TUE, DEC 7, 2021
11:59 PM EST
Instructions
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Assignment Submission &
Scoring
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
- All of the data sets needed to complete this assignment
are either embedded in the question prompt or contained
as separate worksheets in the same file: HW 11 Data.xls.
You only need to download this file ONCE in order to
obtain ALL of the data sets for this assignment.
- Here is the link to one instructional video intended to
assist you in completing this assignment. We recommend
watching this video BEFORE attempting any items on this
assignment.
Assignment Submission
For this assignment, you submit
answers by question parts. The
number of submissions remaining for
each question part only changes if
you submit or change the answer.
Assignment Scoring
Your last submission is used for your
score.
BUSN 4000 HW11 Video
- Consult the instructions for each individual item for
information concerning the decimal precision of your
answer. The classwide expectation is that you will do
ALL calculations in EXCEL to avoid any intermediate
rounding. Only round your final answer. If you do not
round EXACTLY as described you may not receive
credit for your answer.
- Note that you will receive three attempts for full credit on
any question that requires submission of a numerical
answer. Multiple choice questions with 3-choices or less
will only give one attempt at full credit (50% credit on the
second attempt, 0% credit on the third), whereas multiple
choice questions with more than 3-choices will give two
attempts at full credit (50% credit on the third).
- Note that once the due date for the homework has
passed you will be able to re-enter the homework to view a
solution key.
Description
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1.
BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[2/2 Points]
DETAILS
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Data on 1,470 cars were obtained from the October 2002 issue of Road & Track: The New Cars. The following
variables were available in order to predict selling price (y): (Hint: Realize that the raw data are NOT necessary in
order to answer these questions and therefore are NOT provided in the HW11 Data file.)
weight, in pounds (WEIGHT)
mileage in city driving (CITYMPG)
mileage in highway driving (HWYMPG)
horsepower, @ 6300 rpm (HP)
number of cylinders (CYLIN)
displacement, in liters (LITER)
(a) If an all possible regressions analysis is performed, how many regression models are possible? (Enter a
whole number.)
64
(b) For the number of models you found above, which of the following statements are true? (Select all that
apply.)
This includes a model with no explanatory variables and only the intercept (i.e., the mean
model).
This does not include a model with no explanatory variables (i.e., the mean model).
This does not include 1 model with all explanatory variables.
This includes 1 model with all explanatory variables.
This includes 6 1-variable models.
This does not include 6 1-variable models.
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[5/5 Points]
DETAILS
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MY NOTES
Fibre-Optic Connector 1: Techcore is a high-tech company located in Fort Worth, Texas. The company produces a
part called a fibre-optic connector (FOC) and wants to generate forecasts of the sales of FOCs over time. The
company has weekly sales data for the past 265 weeks. The available variables are contained in the worksheet
"FOC8" and defined as follows.
SALES: Sales of FOC (y)
COMPOSITE: Friday close of the NYSE Composite Index
INDUSTRIAL: Friday close of the NYSE Industrial Stocks
TRANS: Friday close of the NYSE Transportation Stocks
UTILITY: Friday close of the NYSE Utility Stocks
FINANCE: Friday close of the NYSE Financials
Perform a stepwise regression with the criterion for adding a variable set to .05 and the criterion for removing a
variable set to .051. Use the resulting output to answer the following questions.
(a) In the 2nd step of the process, what happened?
The variable COMPOSITE was added to the model because it was found to be important.
The variable INDUSTRIAL was added to the model because it was found to be important.
The variable INDUSTRIAL was dropped from the model even though it was important.
The variable COMPOSITE was added to the model even though it was found to be unimportant.
The variable COMPOSITE was dropped from the model because it was unimportant.
The variable COMPOSITE was dropped from the model even though it was important.
(b) How many variables are in the model after step #5 of the process? (Enter a whole number.)
3
(c) In the 1st step of the process, what happened?
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INDUSTRIAL was added to the model.
UTILITY was added to the model.
UTILITY was removed from the model.
INDUSTRIAL was removed from the model.
COMPOSITE was removed from the model.
COMPOSITE was added to the model.
(d) In the last step of the process, what happened?
UTILITY was added to the model.
COMPOSITE was removed from the model.
INDUSTRIAL was removed from the model.
COMPOSITE was added to the model.
UTILITY was removed from the model.
INDUSTRIAL was added to the model.
(e) According to this analysis, which is the best model overall?
The model with INDUSTRIAL and COMPOSITE.
The model with COMPOSITE, TRANS, and UTILITY.
The model with INDUSTRIAL, COMPOSITE, TRANS, and UTILITY.
The model with INDUSTRIAL, FINANCE, TRANS, and UTILITY.
The model with all 5 variables.
(f) Explain what happened in the first and last steps of the process.
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In the first step, INDUSTRIAL was identified as the single most
important variable in predicting
SALES. However, the stepwise process identified that when the model already had
the
variables COMPOSITE, TRANS, and UTILITY, then INDUSTRIAL was no longer
needed. Hence, the
variable INDUSTRIAL was removed from
the model during the last step, even though, by itself, it
is the single most
important variable in predicting SALES.
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[2.5/2.5 Points]
DETAILS
PREVIOUS ANSWERS
MY NOTES
Fibre-Optic Connector 2: Techcore is a high-tech company located in Fort Worth, Texas. The company produces a
part called a fibre-optic connector (FOC) and wants to generate forecasts of the sales of FOCs over time. The
company has weekly sales data for the past 265 weeks. The available variables are contained in the worksheet
"FOC8" and defined as follows.
SALES: Sales of FOC (y)
COMPOSITE: Friday close of the NYSE Composite Index
INDUSTRIAL: Friday close of the NYSE Industrial Stocks
TRANS: Friday close of the NYSE Transportation Stocks
UTILITY: Friday close of the NYSE Utility Stocks
FINANCE: Friday close of the NYSE Financials
Use the computer output below to answer the following questions.
(a) Which variable selection technique has been used here?
All Possible Regressions
Backward Elimination
Stepwise Regression
Forward Selection
(b) In the 2nd step of the process, what happened? (Assume a 5% level of significance.)
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The variable COMPOSITE was added to the model even though it was found to be unimportant.
The variable COMPOSITE was dropped from the model even though it was important.
The variable COMPOSITE was dropped from the model because it was unimportant.
The variable COMPOSITE was added to the model because it was found to be important.
(c) How many variables are in the model at the end of step #3 of the process? (Enter a whole number).
3
(d) According to this analysis, if you were to use just one explanatory variable in a model to predict sales of FOCs,
which one should be chosen?
UTILITY
COMPOSITE
TRANS
FINANCE
INDUSTRIAL
(e) According to this analysis, which is the best model overall? (Use a 5% level of significance.)
The model with INDUSTRIAL and COMPOSITE.
The model with INDUSTRIAL, COMPOSITE, TRANS, and UTILITY.
The model with INDUSTRIAL, FINANCE, TRANS, and UTILITY.
The model with all 5 variables.
The model with INDUSTRIAL only.
The model with INDUSTRIAL, COMPOSITE, and TRANS.
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4.
BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[4.5/5 Points]
DETAILS
PREVIOUS ANSWERS
MY NOTES
Fibre-Optic Connector 3: Techcore is a high-tech company located in Fort Worth, Texas. The company produces a
part called a fibre-optic connector (FOC) and wants to generate forecasts (i.e., predictions) of the sales of FOCs
over time. The company has weekly sales data for the past 265 weeks. The available variables are contained in the
worksheet "FOC8" and defined as follows.
SALES: Sales of FOC (y)
COMPOSITE: Friday close of the NYSE Composite Index
INDUSTRIAL: Friday close of the NYSE Industrial Stocks
TRANS: Friday close of the NYSE Transportation Stocks
UTILITY: Friday close of the NYSE Utility Stocks
FINANCE: Friday close of the NYSE Financials
Perform a Backward Elimination variable selection analysis for these data. Use a 5% level of significance in your
analysis and to answer all questions below. Use the output to answer the following questions.
(a) In the 1st step of the process, what happened?
The variable INDUSTRIAL was dropped from the model because it was found to be unimportant in a
model that included the other four variables.
The variable INDUSTRIAL was dropped from the model because it was found to be important in a model
that included the other four variables.
The variable TRANS was dropped from the model because it was found to be important in a model that
included the other four variables.
The variable UTILITY was dropped from the model because it was found to be unimportant in a model
that included the other four variables.
The variable UTILITY was dropped from the model because it was found to be important in a model that
included the other four variables.
The variable TRANS was dropped from the model because it was found to be unimportant in a model
that included the other four variables.
(b) How many variables are in the model at the beginning of step #2 of the process? (Enter a whole number.)
4
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(c) According to this analysis, which is the least significant variable in this process?
TRANS
FINANCE
UTILITY
INDUSTRIAL
COMPOSITE
(d) How many variables are in the final model? (Enter a whole number.)
3
(e) According to this analysis, which is the best model overall?
The model with INDUSTRIAL, FINANCE, and TRANS.
The model with COMPOSITE, TRANS, and UTILITY.
The model with COMPOSITE and UTILITY.
The model with INDUSTRIAL, FINANCE, and UTILITY.
The model with INDUSTRIAL, FINANCE, TRANS, and UTILITY.
The model with TRANS and UTILITY.
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5.
BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[2.5/2.5 Points]
DETAILS
PREVIOUS ANSWERS
MY NOTES
Fibre-Optic Connector 4: Techcore is a high-tech company located in Fort Worth, Texas. The company produces a
part called a fibre-optic connector (FOC) and wants to generate forecasts of the sales of FOCs over time. The
company has weekly sales data for the past 265 weeks. The available variables are defined as follows.
SALES: Sales of FOC (y)
TRANS: Friday close of the NYSE Transportation Stocks
UTILITY: Friday close of the NYSE Utility Stocks
FINANCE: Friday close of the NYSE Financials
PROD: Industrial Production—computers, communications equipment, and semiconductors, not
seasonally adjusted
HOUSE: Monthly housing permits in thousands, seasonally adjusted rates
Use the computer output below to answer the following questions. (Note: You do NOT have the raw data and it is
NOT required to answer these questions.)
(a) Which variable selection technique has been used here?
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Forward Selection
Backward Elimination
All Possible Regressions
Stepwise Regression
(b) Which is the best fitting 4 variable model?
Model #27 is best because it has the highest R2 among the 4-variable models.
Model #28 is best because it has the lowest R2 among the 4-variable models.
Model #31 is best because it has the highest Cp among the 4-variable models.
Model #29 is best because it has the lowest Cp among the 4-variable models.
(c) Which is the best fitting model overall?
Model #25 is best because it has the highest Cp.
Model #17 is best because it has the highest adjusted R2.
Model #31 is best because it has the highest adjusted R2.
Model #15 is best because it has the lowest Cp.
(d) What value of p should be used when using Cp to evaluate Model #9? (Enter your answer as a whole number.)
3
(e) Which of the following statements are true? (Select all that apply.)
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Model #9 has a large bias component because of the large discrepancy between Cp and p.
Model #9 does not have a bias component because of the large discrepancy between Cp and p.
Model #9 is the best 2 variable model.
Model #9 is the worst 2 variable model.
Model #9 is neither the best nor the worst 2 variable model.
Model #9 has omitted an important variable.
Model #9 has not omitted an important variable.
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[10/11 Points]
DETAILS
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MY NOTES
Finance 1: The National Bank of Fort Worth, Texas, wants to examine methods for predicting sub-par payment
performance on loans. It has data on unsecured consumer loans made over a 3-day period in October 2016 with a
final maturity of 2 years. The data, which have been transformed to provide confidentiality, include the following.
PASTDUE: Coded as 1 if the loan payment is past due and 0 if the loan is settled (i.e., currently paid in full).
CBSCORE: Credit score generated by the CSC Credit Reporting Agency. Values range from 400 to 804, with
higher values indicating a better credit rating.
DEBT: This is a debt ratio calculated by taking required monthly payments on all debt and dividing it by
the gross monthly income of the applicant and co-applicant. This ratio represents the amount of the
applicant's income that will go toward repayment of debt. Values range between 0 and 99.
GROSSINC: Gross monthly income of the applicant and co-applicant (Measured in hundreds of U.S.
dollars).
LOANAMT: Loan amount in USD (Measured in thousands of U.S. dollars).
You have been asked to examine the feasibility of predicting past-due loan payment.
THE RAW DATA FOR THIS QUESTION ARE **NOT** AVAILABLE TO YOU. Use the output below to answer the
following questions.
(a) What is the response variable in this model?
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
DEBT
PASTDUE
CBSCORE
GROSSINC
LOANAMT
Out of a total of n = 348
your answers as whole numbers.)
loans in the sample, 150
were past due. (Enter
(b) Compute the odds ratio for the variable CBSCORE (Enter your answer rounded to three decimal
places).
OR =
.983
Choose the proper interpretation of the odds ratio you calculated immediately above.
For every additional point on the applicant's credit score, a loan is approximately _____ times as
likely to be settled.
For every additional point on the applicant's credit score, a loan is approximately _____ times as
likely to be past due.
An applicant without a credit score is _____ times as likely than one with a credit score to be
settled.
An applicant with a credit score is _____ times as likely than one without a credit score to be
settled.
An applicant with a credit score is _____ times as likely than one without a credit score to be past
due.
An applicant without a credit score is _____ times as likely than one with a credit score to be past
due.
(c) Compute the percent increase/decrease associated with the variable CBSCORE (Enter your answer
rounded to two decimal places).
-1.69
%
Choose the proper interpretation of the percent increase/decrease you calculated immediately above by
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mentally inserting the ABSOLUTE VALUE of that number in the blanks below.
The likelihood that a loan is past due is _____% times greater for those without a credit score.
The likelihood that a loan is settled decreases by _____% for every additional point on the
applicant's credit score.
The likelihood that a loan is past due decreases by _____% for every additional point on the
applicant's credit score.
The likelihood that a loan is past due is _____% times greater for those with a credit score.
The likelihood that a loan is past due is _____% times greater for every additional point on the
applicant's credit score.
The likelihood that a loan is past due increases by _____% for every additional point on the
applicant's credit score.
(d) Complete the following statement based on results from your previous work (Enter your answer
rounded to three decimal places):
For every additional point on the applicant's credit score, a loan is approximately 1.017
times more likely to be settled.
(e) What is the model predicted probability of a loan being past due when the applicant has a credit score
of 720, a debt ratio of 10, a gross monthly income of $2,000, and a loan amount of $60,000 (Enter your
answer rounded to four decimal places)?
P(The Loan is Past Due) =
0.9999
(f) What is the model predicted probability of a loan being past due when the applicant has a credit score
of 720, a debt ratio of 10, a gross monthly income of $7,000, and a loan amount of $40,000 (Enter your
answer rounded to four decimal places)?
P(The Loan is Past Due) =
0.34796417
What is the model predicted probability of a loan being settled when the applicant has a credit score of
720, a debt ratio of 10, a gross monthly income of $7,000, and a loan amount of $40,000 (Notice: This is
the EXACT same applicant in terms of the x variables as the previous item) (Enter your answer rounded to
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four decimal places)?
P(The Loan is Settled) =
0.65203583
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[23/23 Points]
DETAILS
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Graduate School Admission: UGA wishes to build a model to classify graduate school applicants into two groups:
Those who are qualified and should be admitted and those who are not qualified and should not be admitted. The
applicants in the sample data were reviewed using traditional means (i.e., application, statement of purpose, and
essays reviewed by an expert panel of admissions officers) and scored "Yes" to be admitted or "No" not to be
admitted. The available variables are contained in the worksheet "Admissions" and defined as follows.
Admit: Coded as "Yes" if the applicant is to be admitted and "No" otherwise.
GRE: The applicant's score of the Graduate Record Examination (GRE).
GPA: The applicant's undergraduate GPA.
Rank: The ranking (1-4) of the applicant's undergraduate institution.
Fit the proper regression model to predict the variable Admit. Fit the model so that the event being modeled is
"Yes" for the variable Admit. Furthermore, treat the variable Rank as a categorical predictor variable and code it so
that Rank #1 serves as the reference group.
(a) Complete the following statement (Enter your first answer as a whole number and the percent
rounded to two decimal places).
Out of a total of n = 400
applicants in the sample, 31.75
% were
admitted.
(b) State the model equation.
P(Y = Admitted) =
1
1+e−(𝛽0+𝛽1(GRE)+𝛽2(GPA)+𝛽3(Rank1)+𝛽4(Rank2)+𝛽5(Rank3))
ŷ = 𝛽0+𝛽1(GRE)+𝛽2(GPA)+𝛽3(Rank2)+𝛽4(Rank3)+𝛽5(Rank4)
P(Y = Admitted) =
1
1+e−(𝛽0+𝛽1(GRE)+𝛽2(GPA)+𝛽3(Rank2)+𝛽4(Rank3)+𝛽5(Rank4))
ŷ = 𝛽0+𝛽1(GRE)+𝛽2(GPA)+𝛽3(Rank1)+𝛽4(Rank2)+𝛽5(Rank3)
ŷ = 𝛽0+𝛽1(GRE)+𝛽2(GPA)+𝛽3(Rank)
P(Y = Admitted) =
1
1+e−(𝛽0+𝛽1(GRE)+𝛽2(GPA)+𝛽3(Rank))
(c) Test the fit of the overall model. Use a 5% significance level.
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State the hypotheses to be tested.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 0
Ha: At least one of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 0
Ha: All of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 = 0
Ha: All of the coefficients are equal to zero.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 = 0
Ha: At least one of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 0
Ha: At least one of the coefficients is not equal to 0.
State the decision rule.
Reject H0 if p < 0.05.
Do not reject H0 if p ≥ 0.05.
Reject H0 if p > 0.025.
Do not reject H0 if p ≤ 0.025.
Reject H0 if p < 0.025.
Do not reject H0 if p ≥ 0.025.
Reject H0 if p > 0.05.
Do not reject H0 if p ≤ 0.05.
State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated pvalue (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places,
and the p-value to four decimal places).
χ2
(5
) = 41.459
,p <
0.0001
State your decision.
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Reject the null hypothesis. At least one of the coefficients is not equal to 0. In other words, at
least one of the variables is helpful in predicting admission.
Do not reject the null hypothesis. At least one of the coefficients is not equal to 0. In other
words, at least one of the variables is helpful in predicting admission.
Do not reject the null hypothesis. All of the coefficients may be equal to 0. In other words, none
of the variables are helpful in predicting admission.
Reject the null hypothesis. All of the coefficients may be equal to 0. In other words, none of the
variables are helpful in predicting admission.
(d) Is GRE score important in predicting graduate school admissions? Use a 5% significance level.
State the hypotheses to be tested.
H0: 𝛽3 = 0
Ha: 𝛽3 ≠ 0
H0: 𝛽3 ≥ 0
Ha: 𝛽3 < 0
H0: 𝛽1 = 0
Ha: 𝛽1 ≠ 0
H0: 𝛽4 = 0
Ha: 𝛽4 ≠ 0
H0: 𝛽0 ≥ 0
Ha: 𝛽0 < 0
State the appropriate test statistic name, test statistic value, and the associated p-value (Enter the test
statistic value to three decimal places and the p-value to four decimal places).
χ2
= 4.284
,p =
0.0385
State your decision.
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Do not reject the null hypothesis. No, GRE score is not an important predictor of graduate school
admissions.
Reject the null hypothesis. No, GRE score is not an important predictor of graduate school
admissions.
Do not reject the null hypothesis. Yes, GRE score is an important predictor of graduate school
admissions.
Reject the null hypothesis. Yes, GRE score is an important predictor of graduate school
admissions.
(e) State the odds ratio for GRE score. (Round your answer to three decimal places.)
OR =
1.002
Choose the proper interpretation of the odds ratio you calculated immediately above.
For every additional point an applicant scores on the GRE, their application is approximately
_____ times more likely to be denied.
An applicant without a GRE score is _____ times as likely than one with a GRE score to be
accepted.
An applicant with a GRE score is _____ times as likely than one without a GRE score to be denied.
For every additional point an applicant scores on the GRE, their application is approximately
_____ times more likely to be accepted.
An applicant with a GRE score is _____ times as likely than one without a GRE score to be
accepted.
An applicant without a GRE score is _____ times as likely than one with a GRE score to be denied.
(f) Compute the percent increase/decrease associated with the variable GRE score (Enter your answer
rounded to two decimal places).
0.22
%
Choose the proper interpretation of the percent increase/decrease you calculated immediately above by
mentally inserting the ABSOLUTE VALUE of that number in the blanks below.
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The likelihood that an application is accepted is _____% times greater for those with a GRE score.
The likelihood that an application is accepted increases by _____% for every additional point the
applicant scores on the GRE.
The likelihood that an application is accepted decreases by _____% for every additional point the
applicant scores on the GRE.
The likelihood that an application is denied is _____% times greater for every additional point the
applicant scores on the GRE.
The likelihood that an application is denied increases by _____% for every additional point the
applicant scores on the GRE.
The likelihood that an application is denied is _____% times greater for those with a GRE score.
(g) What is the predicted probability of an application being accepted when the applicant has a GRE score
of 600, a GPA of 2.50, and graduated from a school ranked #2 (Enter your answer rounded to four
decimal places)?
P(The Applicant is Admitted) =
0.2147
What is the predicted probability of an application being accepted when the applicant has a GRE score of
600, a GPA of 2.50, and graduated from a school ranked #1 (Enter your answer rounded to four decimal
places)?
P(The Applicant is Admitted) =
0.3495
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8.
BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[4/5 Points]
DETAILS
PREVIOUS ANSWERS
MY NOTES
Marketing Campaign: A high-end automotive company is interested in launching a new marketing campaign for
their most recent luxury car model. They choose a direct mail style campaign which will cost the company
approximately $1 (USD) for each offer mailed. The company is interested in maximizing sales of the new car model
and is curious about the U.S. vs. European markets for this product. A pilot study from the market research
division of the company shows that 3.9% of the U.S. customers who receive an offer make an additional inquiry
about the car. The same research showed that the odds of a European customer who receives an offer making an
additional inquiry are 0.0165. Use this information to complete the following statements.
(a) The odds of a U.S. customer making an additional inquiry given that they receive an offer is
0.0406
. (Enter your answer to four decimal places.)
(b) The anticipated percent of European customers who will make an additional inquiry given that they
receive the offer is 1.62
(c) Then the OR is 2.4596
%. (Enter your answer to two decimal places.)
, indicating that U.S. customers are 2.4596
times more
likely to make an additional inquiry about the car than European customers. (Enter your answers to four
decimal places.)
(d) Therefore, the percent increase of customers making an additional inquiry when moving from the
European market to the U.S. market is 2.28
%. (Enter your answers to two decimal places.)
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9.
BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[20.5/23 Points]
DETAILS
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MY NOTES
Finance 2: A lending organization has acquired data on a sample of recent customers and is interested in building
a model to predict whether or not a given customer will default on a loan. The available data are contained in the
worksheet "Default" and the variables are defined as follows.
Default: Coded as "Yes" if the customer defaulted on the loan and "No" otherwise.
Student: Whether or not the customer is currently a student (coded Yes/No)
Balance: The average balance carried by the customer in hundreds of USD.
Income: The income of the customer in ten thousands of USD.
Fit the proper regression model to predict whether or not a customer will default on a loan. Fit the model so that
the event being modeled is "Yes". Furthermore, code the variable Student so that "No" serves as the reference
group. Finally, it is hypothesized that income has a curvilinear relationship with the likelihood of being in default.
Therefore, fit a second-order polynomial model in terms of the variable Income to test this theory.
(a) Complete the following statement (Enter your first answer as a whole number and the percent
rounded to two decimal places).
Out of a total of n = 500
customers in the sample, 11.80
% were in
default.
(b) State the model equation.
P(Y = Default) =
P(Y = Default) =
1
1+e−(𝛽0+𝛽1(Student)+𝛽2(Balance)+𝛽3(Income))
1
1+e−(𝛽0+𝛽1(Student)+𝛽2(Balance)+𝛽3(Income)+𝛽4LN(Income))
ŷ = 𝛽0+𝛽1(Student)+𝛽2(Balance)+𝛽3(Income)+𝛽4(Income2)
P(Y = Default) =
1
2
1+e−(𝛽0+𝛽1(Student)+𝛽2(Balance)+𝛽3(Income)+𝛽4(Income ))
ŷ = 𝛽0+𝛽1(Student)+𝛽2(Balance)+𝛽3(Income)+𝛽4LN(Income)
ŷ = 𝛽0+𝛽1(Student)+𝛽2(Balance)+𝛽3(Income)
(c) Test the fit of the overall model. Use a 1% significance level.
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
State the hypotheses to be tested.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 0
Ha: At least one of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 0
Ha: All of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 = 0
Ha: All of the coefficients are equal to zero.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 = 0
Ha: At least one of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 0
Ha: At least one of the coefficients is not equal to 0.
State the decision rule.
Reject H0 if p > 0.01.
Do not reject H0 if p ≤ 0.01.
Reject H0 if p < 0.01.
Do not reject H0 if p ≥ 0.01.
Reject H0 if p < 0.005.
Do not reject H0 if p ≥ 0.005.
Reject H0 if p > 0.005.
Do not reject H0 if p ≤ 0.005.
State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated pvalue (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places,
and the p-value to four decimal places).
χ2
(4
) = 202.785
,p <
0.0001
State your decision.
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
Reject the null hypothesis. At least one of the coefficients is not equal to 0. In other words, at
least one of the variables is helpful in predicting loan default.
Do not reject the null hypothesis. All of the coefficients may be equal to 0. In other words, none
of the variables are helpful in predicting loan default.
Reject the null hypothesis. All of the coefficients may be equal to 0. In other words, none of the
variables are helpful in predicting loan default.
Do not reject the null hypothesis. At least one of the coefficients is not equal to 0. In other
words, at least one of the variables is helpful in predicting loan default.
(d) Is there a statistically significant curvilinear relationship between income and the likelihood to default
on a loan? In other words, test whether or not the polynomial effect is needed in the model when the
other variables are present. Use a 1% significance level.
State the hypotheses to be tested.
H0: 𝛽4 = 0
Ha: 𝛽4 ≠ 0
H0: 𝛽1 = 0
Ha: 𝛽1 ≠ 0
H0: 𝛽0 ≥ 0
Ha: 𝛽0 < 0
H0: 𝛽3 ≥ 0
Ha: 𝛽3 < 0
H0: 𝛽3 = 0
Ha: 𝛽3 ≠ 0
State the appropriate test statistic name, test statistic value, and the associated p-value (Enter the test
statistic value to three decimal places and the p-value to four decimal places).
χ2
= 0.615
,p =
0.3742
State your decision.
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
Reject the null hypothesis. There is sufficient evidence to conclude there is a curvilinear
relationship between income and the likelihood of loan default.
Do not reject the null hypothesis. There is insufficient evidence to conclude there is a curvilinear
relationship between income and the likelihood of loan default.
Reject the null hypothesis. There is insufficient evidence to conclude there is a curvilinear
relationship between income and the likelihood of loan default.
Do not reject the null hypothesis. There is sufficient evidence to conclude there is a curvilinear
relationship between income and the likelihood of loan default.
Regardless of your conclusions above, use the full model for the remainder of these questions.
(e) Switching focus: State the odds ratio for Balance. (Round your answer to three decimal places.)
OR =
1.843
Choose the proper interpretation of the odds ratio you calculated immediately above.
For every additional dollar on the customer's average balance, they are approximately _____
times more likely to NOT be in default.
An applicant without a balance is _____ times as likely than one with a balance to be in default.
For every additional dollar on the customer's average balance, they are approximately _____
times more likely to be in default.
An applicant with a balance is _____ times as likely than one without a balance to NOT be in
default.
An applicant with a balance is _____ times as likely than one without a balance to be in default.
An applicant without a balance is _____ times as likely than one with a balance to NOT be in
default.
(f) Compute the percent increase/decrease associated with the variable Balance (Enter your answer
rounded to two decimal places).
84.26
%
Choose the proper interpretation of the percent increase/decrease you calculated immediately above by
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
mentally inserting the ABSOLUTE VALUE of that number in the blanks below.
The likelihood that a customer is in default decreases by _____% for every additional dollar on the
customer's average balance.
The likelihood that a customer is in default increases by _____% for every additional dollar on the
customer's average balance.
The likelihood that a customer is NOT in default is _____% times greater for every additional
dollar on the customer's average balance.
The likelihood that a customer is in default is _____% times greater for those with a balance.
The likelihood that a customer is in default is _____% times greater for those with a balance.
The likelihood that a customer is NOT in default increases by _____% for every additional dollar
on the customer's average balance.
(g) What is the predicted probability that a new customer will default on a loan when that customer is a
student who has an average balance of $2,000.00 and an income of $10,000.00 (Enter your answer
rounded to four decimal places)?
P(The Customer will Default) =
0.998
What is the predicted probability that a new customer will default on a loan when that customer is NOT a
student, but has an average balance of $2,500.00 and an income of $30,000.00 (Enter your answer
rounded to four decimal places)?
P(The Customer will Default) =
0.9950
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10.
BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
[21/21 Points]
DETAILS
PREVIOUS ANSWERS
MY NOTES
Sales Management: A large wholesaler of groceries, other food stuffs, and consumer products in Portugal has
recently identified that the majority of its customers fall into one of two categories: Either Hotel/Restaurant/Cafe
or Retail. The company wishes to better understand the differences between these two types of customers. The
available variables are contained in the worksheet "Wholesale" and defined as follows.
Channel: (Customer Type) Coded as 1 for Hotel/Restaurant/Cafe or 2 for Retail.
Grocery: Annual spending on grocery products (in thousands of monetary units (m.u.)).
Frozen: Annual spending on frozen products (in thousands of m.u.).
Fit the proper regression model to predict whether or not a customer is Retail or Hotel/Restaurant/Cafe. Fit the
model so that the event being modeled is "Retail". Furthermore, an interaction is hypothesized to exist between
Grocery and Frozen products - in other words, the effect of Grocery spending on the likelihood of being a Retail
customer is hypothesized to be moderated by the amount of spending on Frozen products and vice versa. Create
the appropriate variable(s) and fit the interaction model to test this hypothesis and others.
(a) Complete the following statement (Enter your first answer as a whole number and the percent
rounded to two decimal places).
Out of a total of n = 440
customers in the sample, 67.73
% were
Retail customers.
(b) State the model equation.
P(Y = Retail) =
1
1+e−(𝛽0+𝛽1x1+𝛽2x2+𝛽3x3)
ŷ = 𝛽0 + 𝛽1x1 + 𝛽2x2 + 𝛽3x3
P(Y = Retail) =
1
1+e−(𝛽0+𝛽1x1+𝛽2x2)
ŷ = 𝛽0 + 𝛽1x1 + 𝛽2x2
ŷ = 𝛽0 + 𝛽1x1 + 𝛽2x2 + 𝛽3x1x2
P(Y = Retail) =
1
1+e−(𝛽0+𝛽1x1+𝛽2x2+𝛽3x1x2)
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
(c) Test the fit of the overall model. Use a 10% significance level.
State the hypotheses to be tested.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 = 0
Ha: At least one of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 0
Ha: At least one of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 0
Ha: At least of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 0
Ha: At least one of the coefficients is not equal to 0.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 = 0
Ha: All of the coefficients are equal to zero.
State the decision rule.
Reject H0 if p > 0.05.
Do not reject H0 if p ≤ 0.05.
Reject H0 if p < 0.10.
Do not reject H0 if p ≥ 0.10.
Reject H0 if p < 0.05.
Do not reject H0 if p ≥ 0.05.
Reject H0 if p > 0.10.
Do not reject H0 if p ≤ 0.10.
State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated pvalue (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places,
and the p-value to four decimal places).
χ2
(3
) = 305.566
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,p <
0.0001
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
State your decision.
Reject the null hypothesis. At least one of the coefficients is not equal to 0. In other words, at
least one of the variables is helpful in predicting customer type.
Do not reject the null hypothesis. At least one of the coefficients is not equal to 0. In other
words, at least one of the variables is helpful in predicting customer type.
Do not reject the null hypothesis. All of the coefficients may be equal to 0. In other words, none
of the variables are helpful in predicting customer type.
Reject the null hypothesis. All of the coefficients may be equal to 0. In other words, none of the
variables are helpful in predicting customer type.
(d) Does an interaction exist between Grocery and Frozen? Use a 10% significance level.
State the hypotheses to be tested.
H0: 𝛽3 ≥ 0
Ha: 𝛽3 < 0
H0: 𝛽4 = 0
Ha: 𝛽4 ≠ 0
H0: 𝛽1 = 0
Ha: 𝛽1 ≠ 0
H0: 𝛽0 ≥ 0
Ha: 𝛽0 < 0
H0: 𝛽3 = 0
Ha: 𝛽3 ≠ 0
State the appropriate test statistic name, test statistic value, and the associated p-value (Enter the test
statistic value to three decimal places and the p-value to four decimal places).
χ2
= 7.114
,p =
0.0076
State your decision.
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BUSN 4000: Homework 11 - BUSN 4000, section MORSE, Fall 2021 | WebAssign
Reject the null hypothesis. Yes, there is sufficient statistical evidence that an interaction exists
between spending on groceries and spending on frozen products.
Do not reject the null hypothesis. Yes, there is sufficient statistical evidence that an interaction
exists between spending on groceries and spending on frozen products.
Reject the null hypothesis. No, there is insufficient statistical evidence that an interaction exists
between spending on groceries and spending on frozen products.
Do not reject the null hypothesis. No, there is insufficient statistical evidence that an interaction
exists between spending on groceries and spending on frozen products.
Regardless of your conclusions above, use the full model for the remainder of these questions.
(e) What is the predicted probability that a new customer is in Retail when the customer spends 500 m.u.
on groceries and 2,500 m.u. on frozen products wholesale? (Enter your answer rounded to four decimal
places)?
P(The Customer is in Retail) =
0.9910
What is the predicted probability that a new customer is in Hotel/Restaurant/Cafe when the customer
spends 500 m.u. on groceries and 2,500 m.u. on frozen products wholesale? (Enter your answer rounded
to four decimal places)?
P(The Customer is in Hotel/Restaurant/Cafe) =
0.0090
What is the predicted probability that a new customer is in Retail when the customer spends 1,000 m.u.
on groceries and 2,000 m.u. on frozen products wholesale? (Enter your answer rounded to four decimal
places)?
P(The Customer is in Retail) =
0.9960
What is the predicted probability that a new customer is in Hotel/Restaurant/Cafe when the customer
spends 1,000 m.u. on groceries and 2,000 m.u. on frozen products wholesale? (Enter your answer
rounded to four decimal places)?
P(The Customer is in Hotel/Restaurant/Cafe) =
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