Question 1

For the linear probability model y = β0 + β1x + ε,the predicted value of y is always constrained between ________.

Accepted Answer

A)  0 and 1. 
B)  −1 and 1. 
C)  Both 0 and 1,and −1 and 1 are correct. 
D)  None of these choices is correct.

Question 2

A bank manager is interested in assigning a rating to the holders of credit cards issued by her bank.The rating is based on the probability of defaulting on credit cards and is as follows. To estimate this probability,she decided to use the logistic model where y = a binary response variable with value of 1 corresponding to a default,and 0 to a no default x₁ = the ratio of the credit card balance to the credit card limit (in %) x₂ = the ratio of the total debt to the annual income (in %) Using Minitab on the sample data,she arrived at the following estimates: Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients. Bob has a balance ratio of 10%,an annual income of $80,000,and $15,000 in total debt.Only applicants with excellent and good ratings qualify for a loan.Find the maximum amount of loan Bob can get if he is required to maintain his excellent or good rating after getting this amount.

Accepted Answer

The answer of A bank manager is interested in assigning...

Question 3

Consider the following regression model: Humidity = β0 + β1 Temperature + β2 Spring + β3 Summer + β4Fall + β5 Rain + ε,
Where the dummy variables Spring,Summer,and Fall represent the qualitative variable Season (spring,summer,fall,winter),and the dummy variable Rain is defined as Rain = 1 if rainy day,Rain = 0 otherwise.What is the regression equation for the winter days?

Accepted Answer

A)   = (b0 + b3)+b1Temperature + b5Rain 
B)   = (b0 + b2 + b3 + b4)+ b1Temperature + b5Rain 
C)   = b0 + b1Temperature + b5Rain 
D)

Question 4

To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected,and two models were created with the following variables considered: Salary = the monthly salary (excluding fringe benefits and bonuses),
Educ = the number of years of education,
Exper = the number of months of experience,
Train = the number of weeks of training,
Gender = the gender of an individual;1 for males,and 0 for females.
Excel partial outputs corresponding to these models are available and shown below.
Model A: Salary = β0 + β1 Educ + β2 Exper + β3 Train + β4 Gender + ε  Model B: Salary = β0 + β1 Educ + β2 Exper + β3 Gender + ε  Using Model A,which of the following is the estimated average difference between the salaries of male and female employees with the same years of education,months of experience,and weeks of training?

Accepted Answer

A)  About $5,423 
B)  About $619 
C)  About $5,278 
D)  About $615

Question 5

Which of the following variables is not qualitative?

Accepted Answer

A)  Gender of a person 
B)  Religious affiliation 
C)  Number of dependents claimed on a tax return 
D)  Student's status (freshman,sophomore,etc. )

Question 6

A medical researcher is interested in assessing the probability of some symptoms of coronary heart disease (CHD)being present at a given age.For this reason he uses the following data collected on 100 individuals.  Thus,the variable under study is CHD that assumes a value of 1 if coronary heart disease is present,and a value of 0 otherwise.Using Excel and Minitab,the following linear and logistics regression equations have been estimated: Linear Regression:  = - 0.53796 + 0.02181Age
Logistic Regression:  Using the logistic equation,what is the estimated probability of coronary heart disease for a 60-year-old individual?

Accepted Answer

A)  0.4581 
B)  0.3219 
C)  0.7706 
D)  0.7946

Question 7

In a model y = β₀ + β₁x + β₂d + β₃xd + ε,the ______ F test for the joint significance of d and xd can be performed.

Accepted Answer

The answer of In a model y = β₀ +...

Question 8

A researcher wants to examine how the remaining balance on $100,000 loans taken 10 to 20 years ago depends on whether the loan was a prime or subprime loan.He collected a sample of 25 prime loans and 25 subprime loans and recorded the data in the following variables: Balance = the remaining amount of loan to be paid off (in $),
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans,and 0 for subprime loans.
The regression results obtained for the models:
Model A: Balance = β0 + β1Prime + ε
Model B: Balance = β0 + β1Time + β2Prime + β3Time × Prime + ε
Model C: Balance = β0 + β1Prime + β2Time × Prime + ε,
Are summarized in the following table.  Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Using Model C,which of the following is the predicted balance on a $100,000 prime loan taken 15 years ago?

Accepted Answer

A)  $88,020 
B)  $69,486 
C)  $74,591 
D)  $82,183

Question 9

If we include as many dummy variables as there are categories,then their sum will be equal to _____.

Accepted Answer

The answer of If we include as many dummy variables...

Question 10

The logistic model can be estimated through the use of the ordinary least squares method.

Accepted Answer

A) True 
 B)False

Question 11

For the model y = β0 + β1x + β2d + ε,which test is used for testing the significance of a dummy variable d?

Accepted Answer

A)  F test 
B)  chi-square test 
C)  z test 
D)  t test

Question 12

In the model y = β0 + β1x + β2d + β3xd + ε,when d changes from 0 to 1 how does the intercept of the corresponding lines change?

Accepted Answer

A)  From b0 to b0 + b1 
B)  From b0 to b0 + b2 
C)  From b0 to b0 + b3 
D)  From b0 to b0 + b1 + b2

Question 13

Suppose that we have a qualitative variable Month with categories: January,February,etc.How many dummy variables are needed to describe Month?

Accepted Answer

A)  12 
B)  11 
C)  10 
D)  9

Question 14

According to the Center for Disease Control and Prevention,life expectancy at age 65 in America is about 18.7 years.Medical researchers have argued that while excessive drinking is detrimental to health,drinking a little alcohol every day,especially wine,may be associated with an increase in life expectancy.Others have also linked longevity with income and gender.The data relating to the length of life after 65 (Life)were collected.Data also include: average income (in $1,000s)(Income),the average number of alcoholic drinks consumed per day (Drinks),and a dummy variable Woman.The following model was created: Life = β0 + β1Income + β2Drinks + β3Woman + ε.The Excel partial output corresponding to this model is shown below.  Using a p-value approach,which of the following conclusions is correct at 5% significance level?

Accepted Answer

A)  Do not reject H0 and conclude that women live longer than men at the 5% significance level. 
B)  Reject H0 and conclude that women live longer than men at the 5% significance level. 
C)  Do not reject H0 and conclude that men live longer than women at the 5% significance level. 
D)  Reject H0 and conclude that men live longer than women at the 5% significance level.

Question 15

A bank manager is interested in assigning a rating to the holders of credit cards issued by her bank.The rating is based on the probability of defaulting on credit cards and is as follows. To estimate this probability,she decided to use the logistic model where y = a binary response variable with value of 1 corresponding to a default,and 0 to a no default x₁ = the ratio of the credit card balance to the credit card limit (in %) x₂ = the ratio of the total debt to the annual income (in %) Using Minitab on the sample data,she arrived at the following estimates: Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients. What are the conclusions of testing the individual significance of the balance ratio and the debt ratio at the 1% level?

Accepted Answer

The answer of A bank manager is interested in assigning...

Question 16

A model formulated as y = β₀ + β₁x + ε = P(y = 1)+ ε is called a(n)______ probability model.

Accepted Answer

The answer of A model formulated as y = β₀...

Question 17

A realtor wants to predict and compare the prices of homes in three neighboring locations.She considers the following linear models: Model A: Price = β₀ + β₁Size + β₂Age + ε Model B: Price = β₀ + β₁ Size + β₃ Loc1 + β₄ Loc2 + ε Model C: Price = β₀ + β₁Size + β₂Age + β₃ Loc1 + β₄ Loc2 +ε where, Price = the price of a home (in $1,000s) Size = the square footage (in sq.feet) Loc1 = a dummy variable taking on 1 for Location 1,and 0 otherwise Loc2 = a dummy variable taking on 1 for Location 2,and 0 otherwise After collecting data on 52 sales and applying regression,her findings were summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. Using Model B,compute the test statistic for testing the joint significance of the two dummy variables Loc1 and Loc2.

Accepted Answer

The answer of A realtor wants to predict and compare...

Question 18

A realtor wants to predict and compare the prices of homes in three neighboring locations.She considers the following linear models: Model A: Price = β₀ + β₁Size + β₂Age + ε Model B: Price = β₀ + β₁ Size + β₃ Loc1 + β₄ Loc2 + ε Model C: Price = β₀ + β₁Size + β₂Age + β₃ Loc1 + β₄ Loc2 +ε where, Price = the price of a home (in $1,000s) Size = the square footage (in sq.feet) Loc1 = a dummy variable taking on 1 for Location 1,and 0 otherwise Loc2 = a dummy variable taking on 1 for Location 2,and 0 otherwise After collecting data on 52 sales and applying regression,her findings were summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. Using Model C,define the null hypothesis for testing the joint significance of the two dummy variables?

Accepted Answer

The answer of A realtor wants to predict and compare...

Question 19

The model y = β0 + β1x + β2d + β3xd + ε is an example of a ______________________________________.

Accepted Answer

A)  simple linear regression model 
B)  linear regression model with only dummy variable 
C)  linear regression model with dummy variable and quantitative variable 
D)  linear regression model with dummy variable,quantitative variable,and interaction variable

Question 20

Consider the following regression model, Humidity = β0 + β1 Temperature + β2 Spring + β3Summer + β4 Fall + β5 Rain + ε,
Where the dummy variables Spring,Summer,and Fall represent the qualitative variable Season (spring,summer,fall,winter),and the dummy variable Rain is defined as Rain = 1 if rainy day,Rain = 0 otherwise.Assuming the same temperature and precipitation condition,what is the difference between the predicted humidity for summer and winter days?

Accepted Answer

A)  b0 + b1 + b5 
B)  b0 + b3 + b5 
C)  b3 
D)  b0 + b5

Exam 17: Regression Models With Dummy Variables

For the linear probability model y = β₀ + β₁x + ε,the predicted value of y is always constrained between ________.

Which of the following variables is not qualitative?

In a model y = β₀ + β₁x + β₂d + β₃xd + ε,the ______ F test for the joint significance of d and xd can be performed.

If we include as many dummy variables as there are categories,then their sum will be equal to _____.

The logistic model can be estimated through the use of the ordinary least squares method.

For the model y = β₀+ β₁x + β₂d + ε,which test is used for testing the significance of a dummy variable d?

In the model y = β₀ + β₁x + β₂d + β₃xd + ε,when d changes from 0 to 1 how does the intercept of the corresponding lines change?

Suppose that we have a qualitative variable Month with categories: January,February,etc.How many dummy variables are needed to describe Month?

A model formulated as y = β₀ + β₁x + ε = P(y = 1)+ ε is called a(n)______ probability model.

The model y = β₀ + β₁x + β₂d + β₃xd + ε is an example of a ______________________________________.

Exam 17: Regression Models With Dummy Variables

For the linear probability model y = β0 + β1x + ε,the predicted value of y is always constrained between ________.

Which of the following variables is not qualitative?

In a model y = β0 + β1x + β2d + β3xd + ε,the ______ F test for the joint significance of d and xd can be performed.

If we include as many dummy variables as there are categories,then their sum will be equal to _____.

The logistic model can be estimated through the use of the ordinary least squares method.

For the model y = β0 + β1x + β2d + ε,which test is used for testing the significance of a dummy variable d?

In the model y = β0 + β1x + β2d + β3xd + ε,when d changes from 0 to 1 how does the intercept of the corresponding lines change?

Suppose that we have a qualitative variable Month with categories: January,February,etc.How many dummy variables are needed to describe Month?

A model formulated as y = β0 + β1x + ε = P(y = 1)+ ε is called a(n)______ probability model.

The model y = β0 + β1x + β2d + β3xd + ε is an example of a ______________________________________.

For the linear probability model y = β₀ + β₁x + ε,the predicted value of y is always constrained between ________.

In a model y = β₀ + β₁x + β₂d + β₃xd + ε,the ______ F test for the joint significance of d and xd can be performed.

For the model y = β₀+ β₁x + β₂d + ε,which test is used for testing the significance of a dummy variable d?

In the model y = β₀ + β₁x + β₂d + β₃xd + ε,when d changes from 0 to 1 how does the intercept of the corresponding lines change?

A model formulated as y = β₀ + β₁x + ε = P(y = 1)+ ε is called a(n)______ probability model.

The model y = β₀ + β₁x + β₂d + β₃xd + ε is an example of a ______________________________________.