Deck 17: Regression Models With Dummy Variables

Question 1

Regression models that use a binary variable as the response variable are called binary choice models.

Answer 1

True

Question 2

A dummy variable is commonly used to describe a quantitative variable with discrete or continuous values.

Answer 2

False

Question 3

A binary choice model can be used,for example,to predict the chances of a candidate of winning an election.

Answer 3

True

Question 4

For the model y = β₀ + β₁x + β₂d + β₃xd + ε,in which d is a dummy variable,we can perform standard t tests for the individual significance of x,d,and xd.

Question 5

Consider the regression model y = β₀ + β₁x + β₂d + β₃xd + ε.If the dummy variable d changes from 0 to 1,the estimated changes in the intercept and the slope are b₀ + b₂ and b₂,respectively.

Question 6

A gender is an example of ______ variable.

Question 7

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

Question 8

A dummy variable is a variable that takes on the values of 0 and 1.

Question 9

For the logistic model,the predicted values of the response variables can always be interpreted as probabilities.

Question 10

Using a ______ we can examine whether the particular dummy variable is statistically significant.

Question 11

For the linear probability model y = β₀ + β₁x + ε,the predictions made by = b₀ + b₁x can be always interpreted as probabilities.

Question 12

If the number of dummy variables representing a qualitative variable equals the number of categories of this variable,one deals with the problem of perfect multicollinearity.

Question 13

A dummy variable is also referred to as a(n)_________ variable.

Question 14

In the regression equation = b₀ + b₁x + b₂d,a dummy variable d affects the slope of the line.

Question 15

For the model y = β₀ + β₁x + β₂d + β₃xd+ε,in which d is a dummy variable,we cannot perform the F test for the joint significance of the dummy variable d and the interaction variable xd.

Question 16

For the model y = β₀ + β₁x + β₂d + β₃xd + ε,the dummy variable d causes only a shift in intercept.

Question 17

A model y = β₀ + β₁x + ε,in which y is a binary variable,is called a linear probability model.

Question 18

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

Question 19

The number of dummy variables representing a qualitative variable should be one less than the number of categories of the variable.

Question 20

All variables employed in regression must be quantitative.

Question 21

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

Question 22

Regression models that use a dummy variable as the response variable are called binary or discrete ______ models.

Question 23

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

Question 24

A logit model ensures that the predicted probability of the binary response variable falls between _________.

Question 25

A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, = 40 + 0.15 Size + 50 View,where Price = the price of a unit (in $1,000s),Size = the square footage (in sq.feet),View = a dummy variable taking on 1 for an ocean view unit,and 0 for a bay view unit.Which of the following is the difference in predicted prices of the ocean view and bay view units with the same square footage?

A) $40,000
B) $90,000
C) $500,000
D) $50,000

Question 26

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

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

Question 27

Consider the model y = β₀ + β₁x + β₂d + ε,where x is a quantitative variable and d is a dummy variable.For d = 1,the predicted value of y is computed as

A) = b₀ + b₁x + b₂x
B) = b₀ + b₁x
C) = (b₀ +b₁)x + b₂
D)

Question 28

The maximum likelihood estimation (MLE)produces estimates for the ________ parameters β₀ and β₁.

Question 29

Which of the following variables is not qualitative?

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 30

Consider the model y = β₀ + β₁x + β₂d + ε,where x is a quantitative variable and d is a dummy variable.We can use sample data to estimate the model as _______________.

A) = b₀+ b₁x + b₂d
B) = b₀ + b₁x
C) = b₀ + b₂d
D)

Question 31

Consider the regression equation = b₀ + b₁x + b₂d with a dummy variable d.If d increases from 0 to 1,the change in the intercept is given by:

A) b₀
B) b₀ + b₁
C) b₂
D) b₀ + b₂

Question 32

A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, = 40 + 0.15 Size + 50 View,where Price = the price of a unit (in $1,000s),Size = the square footage (in sq.feet),View = a dummy variable taking on 1 for an ocean view unit,and 0 for a bay view unit.Which of the following is the predicted price of a bay view unit measuring 1,500 square feet?

A) $315,000
B) $2,650,000
C) $265,000
D) $225,000

Question 33

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 Which of the following explanatory variables in Model A is most likely to be tested for the individual significance?

A) Educ
B) Exper
C) Train
D) Gender

Question 34

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 Which of the following is the regression equation found by Excel for Model A?

A) = 4663.31 + 140.66Educ + 3.36Exper + 1.17Train + 615.15Gender
B) = 365.37 + 20.16Educ + 0.47Exper + 3.72Train + 97.33Gender
C) = 12.76 + 6.98Educ + 7.15Exper + 0.31Train + 6.32Gender
D)

Question 35

A dummy variable can be used to create a(n)_______ variable,which allows the estimated change in y to vary across the values of x.

Question 36

Quantitative variables assume meaningful ____,where as qualitative variables represent some ____.

A) categories,numeric values
B) numeric values,categories
C) categories,responses
D) responses,categories

Question 37

To avoid the dummy variable _____,the number of dummy variables should be one less than the number of categories.

Question 38

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?

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

Question 39

A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, = 40 + 0.15 Size + 50 View,where Price = the price of a unit (in $1,000s),Size = the square footage (in sq.feet),View = a dummy variable taking on 1 for an ocean view unit,and 0 for a bay view unit.Which of the following is the predicted price of an ocean view unit with 1,500 square feet?

A) $315,000
B) $3,150,000
C) $265,000
D) $275,000

Question 40

The logit model cannot be estimated with standard ______ least squares procedures.

Question 41

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 Under the assumption of the same years of education and months of experience,what is the p-value for testing whether the mean salary of males is greater than the mean salary of females using Model B?

A) At least 0.025
B) Less than 0.025 but at least 0.01
C) Less than 0.01 but at least 0.005
D) Less than 0.005

Question 42

For the model y = β₀ + β₁x + β₂d₁ + β₃d₂ + ε,which of the following tests is used for testing the joint significance of the dummy variables d₁ and d₂?

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

Question 43

Consider the regression equation = b₀ + b₁xd with b₁ > 0 and a dummy variable d.If d changes from 0 to 1,which of the following is true?

A) The intercept increases by b₀ + b₁.
B) The intercept increases by b₁.
C) The slope increases by b₀ + b₁.
D) The slope increases by b₁.

Question 44

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?

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

Question 45

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 + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Using Model B,what is the regression equation found by Excel for males?

A) = 4,713.2506 + 139.5366Educ + 3.3488Exper + 609.2505Gender
B) = 5,322.5011 + 139.5366Educ + 3.3488Exper
C) = 4,713.2506 + 139.5366Educ + 3.3488Exper
D)

Question 46

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

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 47

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.What is the regression equation for the winter rainy days?

A) = (b₀ + b₃)+ b₁Temperature + b₅Rain
B) = (b₀ + b₅)+ b₁Temperature
C) = (b₀ + b₂ + b₃ + b₄ + b₅)+ b₁Temperature
D)

Question 48

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.What is the regression equation for the summer days?

A) = (b₀ + b₃)+ b₁Temperature + b₅Rain
B) = b₀ + b₁Temperature + b₅Rain
C) = b₀ + b₁Temperature + b₂Spring + b₅Rain
D)

Question 49

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 A group of female managers considers a discrimination lawsuit if on average their salaries can be statistically proven to be lower by more than $500 than the salaries of their male peers with the same level of education and experience.Using Model B,what is the alternative hypothesis for testing the lawsuit condition?

A) H_A: β₃ ≤ 500
B) H_A: β₃< 500
C) H_A: β₃ ≠ 500
D) H_A: β₃ > 500

Question 50

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

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

Question 51

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 A group of female managers considers a discrimination lawsuit if on average their salaries could be statistically proven to be lower by more than $500 than the salaries of their male peers with the same level of education and experience.Using Model B,what is the conclusion of the appropriate test at 10% significance level?

A) Do not reject H₀;the salaries of female managers cannot be proven to be lower on average by more than $500.
B) Reject H₀;the salaries of female managers cannot be proven to be lower on average by more than $500.
C) Do not reject H₀;the salaries of female managers are lower on average by more than $500.
D) Reject H₀;the salaries of female managers are lower on average by more than $500.

Question 52

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 + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Using Model B,what is the regression equation found by Excel for females?

A) = 4,713.2506 + 139.5366Educ + 3.3488Exper + 609.2505Gender
B) = 5,322.5011 + 139.5366Educ + 3.3488Exper
C) = 4,713.2506 + 139.5366Educ + 3.3488Exper
D)

Question 53

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 Under the assumption of the same years of education and months of experience,what is the null hypothesis for testing whether the mean salary of males is greater than the mean salary of females using Model B?

A) H₀: β₃ ≤ 0
B) H₀: β₃ ≥ 0
C) H₀: β₃> 0
D) H₀: β₃ = 0

Question 54

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?

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

Question 55

Which of the following regression models does not include an interaction variable?

A) y = β₀ + β₁x + β₂xd + ε
B) y = β₀ + β₁x + β₂x² + ε
C) y = β₀ + β₁d + β₂xd + ε
D) y = β₀ + β₁x + β₂d + β₃xd + ε

Question 56

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 fall days?

A) b₀ + b₃ - b₄
B) b₃ - b₄
C) b₃ + b₄
D) b₀ + b₄ - b₃

Question 57

In the model y = β₀ + β₁x + β₂d + β₃xd + ε,the dummy variable and the interaction variable cause ____________________________________.

A) a change in just the intercept
B) a change in just the slope
C) a change in both the intercept as well as the slope
D) None of these choices is correct.

Question 58

The number of dummy variables representing a qualitative variable should be ____________________________.

A) one less than the number of categories of the variable
B) two less than the number of categories of the variable
C) the same number as the number of categories of the variable
D) None of these choices is correct.

Question 59

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 When testing the individual significance of Train in Model A,what is the test conclusion at 10% significance level?

A) Do not reject H₀;Train is significant.
B) Reject H₀;Train is significant.
C) Reject H₀;Train does not seem to be significant.
D) Do not reject H₀;Train does not seem to be significant.

Question 60

Consider the following regression model: Humidity = β₀ + β₁ Temperature + β₂ Spring + β₃ Summer + 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.What is the regression equation for the summer rainy days?

A) = (b₀ + b₃)+ b₁Temperature
B) = (b₀ + b₅)+ b₁Temperature
C) = b₀ + b₁Temperature + b₂Spring + b₄Fall
D)

Question 61

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.
Which of the following three models would you choose to make the predictions of the remaining loan balance?

A) Model A
B) Model B
C) Model C
D) Any model

Question 62

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 B,what is the value of the test statistic for testing the joint significance of the variable Time and the interaction variable Time × Prime?

A) −0.64
B) −5.36
C) 2.03
D) 2.74

Question 63

Which of the following predictions cannot be described by a binary choice model?

A) Predict the ability to swim through the English Channel.
B) Predict the chances of a candidate winning the next presidential election.
C) Predict today's number of cars crossing the Golden Gate Bridge.
D) Predict the occurrence of a hurricane in Florida next year.

Question 64

In the model y = β₀ + β₁x + β₂d + β₃xd + ε,for a given x and d = 1,the predicted value of y is given by _________________________.

A) = b₀ + b₁x + b₂ + b₃x
B) = b₀ + b₂ + b₁x + b₃x
C) = (b₀ + b₂)+ (b₁ + b₃)x
D) All of these choices are correct.

Question 65

For the model y = β₀ + β₁x + β₂xd + ε,which of the following are the hypotheses for testing the individual significance of the interaction variable xd?

A) H₀: xd = 0,H_A: xd ≠ 0
B) H₀: b₂ = 0,H_A: b₂ ≠ 0
C) H₀: β₂ = 0,H_A: β₂ ≠ 0
D) H₀: β₂ ≠ 0,H_A: β₂ = 0

Question 66

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) 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 67

The major shortcoming of the general linear probability model y = β₀ + β₁x₁ + β₂x₂ + … + β_kx_k+ ε,is that the predicted values of y can be sometimes _______________________.

A) greater than 0 and less than 1
B) at least 0 and no more than 1
C) less than 1 but more than 0
D) less than 0 or greater than 1

Question 68

A logistic model can be estimated with the method of _____________________.

A) ordinary least squares
B) maximum likelihood estimation
C) ANOVA
D) nonparametric estimation

Question 69

In the regression equation = b₀ + b₁x + b₂dx with a dummy variable d,when d changes from 0 to 1,the change in the slope of the corresponding lines is given by ______.

A) b₀
B) b₀ + b₁
C) b₂
D) b₀ + b₂

Question 70

Which of the following is an estimated logistic model?

A)
B)
C)
D)

Question 71

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

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 72

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 B,what is the null hypothesis for testing the joint significance of the variable Time and the interaction variable Time × Prime?

A) H₀: β₁ = β₂ = β₃ = 0
B) H₀: β₁ = 0 and β₃ = 0
C) H₀: β₁ = 0 or β₃ = 0
D) H₀: β₁ ≠ 0 or β₃ ≠ 0

Question 73

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 B,what is the conclusion for testing the joint significance of the variable Time and the interaction variable Time × Prime at 5% significance level?

A) Reject H₀;Time and Time × Prime are jointly significant.
B) Do not reject H₀;Time and Time × Prime are jointly significant.
C) Reject H₀;Time and Time × Prime cannot be proven to be jointly insignificant.
D) Do not reject H₀;Time and Time × Prime cannot be proven to be jointly significant.

Question 74

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?

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

Question 75

The major advantage of a logistic model over the corresponding linear probability model is that the predicted values of y are always between _________.

A) −1 and 1
B) 0 and 2
C) 0 and 1
D) −1 and 0

Question 76

Which of the following predictions can be described by a binary choice model?

A) Predict the day's temperature in degrees Fahrenheit.
B) Predict whether a student will pass or fail a test.
C) Predict today's price of gasoline per gallon in dollars.
D) Predict the rainfall in millimeters today.

Question 77

Which of the following represents a logistic regression model?

A) P = β₀ + β₁x
B)
C) P = β₀ + β₁ ln(x)
D) P = exp(β₀ + β₁x)

Question 78

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 B,which of the following is the alternative hypothesis for testing the significance of Time?

A) H_A: β₁ = 0
B) H_A: β₁ = 0 and β₃ = 0
C) H_A: β₁ ≠ 0
D) H_A: β₁ ≠ 0 or β₃ ≠ 0

Question 79

For a linear regression model with a dummy variable d and an interaction variable xd,we _______________________________________________________________.

A) cannot conduct the F test for the joint significance of d and xd
B) can conduct the F test for the joint significance of d and xd
C) cannot conduct t test for the individual significance of d and xd
D) can conduct the chi-square test for testing the independence of attributes

Question 80

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.
Which of the following is the p-value for testing the individual significance of Time in Model B?

A) Less than 0.10
B) Less than 0.20 but at least 0.10
C) Less than 0.40 but at least 0.20
D) More than 0.40