Deck 17: Regression Models With Dummy Variables

Question 1

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

Answer 1

False

Question 2

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

Answer 2

indicator

Question 3

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

Answer 3

False

Question 4

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 5

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 6

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 7

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

Question 8

A binary choice model is also referred to as a discrete choice model.

Question 9

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

Question 10

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

Question 11

Using a ________ we can determine if a particular dummy variable is statistically significant.

Question 12

The logit model can be estimated with standard ordinary least squares.

Question 13

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

Question 14

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 15

A dummy variable is also called an interaction variable.

Question 16

Including as many dummy variables as there are categories is referred to as the dummy variable ________.

Question 17

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

Question 18

Gender is an example of ________ variable.

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

Variables employed in a regression model can be quantitative or qualitative.

Question 21

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

Question 22

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

A) b_{0
B) b0} + b_{1
C) b2
D) b0} + b₂

Question 23

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

Question 24

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 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 25

A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, = 40 + 0.15Size + 50View, where Price = the price of a unit (in $1,000s), Size is the square footage (in sq. feet), and View is 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) $50,000
C) $265,000
D) $40,000

Question 26

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 + β₃ Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Which of the following explanatory variables in Model A is not significant at the 5% level?

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

Question 27

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) Class level of a student (freshman, sophomore, etc.)

Question 28

The method of maximum likelihood estimation (MLE) is used to ________ the parameters of a logit model.

Question 29

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

Question 30

A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, = 40 + 0.15Size + 50View, where Price is the price of a unit (in $1,000s), Size is the square footage (in sq. feet), and View is 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) $315,000
B) $50,000
C) $265,000
D) $40,000

Question 31

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

Question 32

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

Question 33

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

A) = b₀ + b₁x + b₂x
B) = b₀ + b₁x
C) = (b₀ + b₁)x + b_2
D) = (b₀ + b₂) + b₁x

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 + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + 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) = 140.66Educ + 3.36Exper + 1.17Train + 615.15Gender

Question 35

Quantitative variables assume meaningful ________, whereas qualitative variables represent some ________.

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

Question 36

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

Question 37

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 38

Consider the model y = β₀ + β₁x + β₂d + ε, where x is a quantitative variable and d is a dummy variable. When d = 0, the predicted value of y is ________.

A) = b₀+ b₁x + b₂d
B) = b₀ + b₁x
C) = b₀ + b₂d
D) = b₀ + b₁(x + d)

Question 39

A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, = 40 + 0.15Size + 50View, where Price is the price of a unit (in $1,000s), Size is the square footage (in sq. feet), and View is 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) $50,000
C) $265,000
D) $40,000

Question 40

A dummy variable can be used to create a(n) ________ variable between the dummy variable and a quantitative variable x, which allows the predicted y to differ between the two categories by a varying amount across the values of x.

Question 41

Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + 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) = (b₀ + b₅) + b₁Temperature + b₅Rain

Question 42

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 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 43

Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + 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 - b_{4
B) b3} - b_{4
C) b3} + b_{4
D) b0} + b₄ - b₃

Question 44

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 45

Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + 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) = (b₀ + b₃ + b₅) + b₁Temperature

Question 46

Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + 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 + b_{5
B) b0} + b₃ + b_{5
C) b3
D) b0} + b₅

Question 47

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 For a test of individual significance about gender, what is the conclusion at 5% significance level?

A) Do not reject H₀; we can conclude gender is significant.
B) Reject H₀; we can conclude gender is significant.
C) Reject H₀; we cannot conclude gender is significant.
D) Do not reject H₀; we cannot conclude gender is significant.

Question 48

Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + 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) = b₀ + b₁Temperature + b₂Spring + b₄Fall + b₅Rain

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 + 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) = 4,713.26 + 139.5366Educ + 3.3488Exper + 609.25Gender
B) = 5,322.51 + 139.5366Educ + 3.3488Exper
C) = 4,713.26 + 139.5366Educ + 3.3488Exper
D) = 4,663.31 + 140.6634Educ + 3.3566Exper

Question 50

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 Assuming 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 51

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

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

Question 52

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 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 + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Assuming 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 54

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 55

Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + 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) = (b₀ + b₂ + b₃ + b₄) + b₁Temperature

Question 56

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 for males?

A) = 4,713.26 + 139.5366Educ + 3.3488Exper + 609.25Gender
B) = 5,322.51 + 139.5366Educ + 3.3488Exper
C) = 4,713.26 + 139.5366Educ + 3.3488Exper
D) = 4,663.31 + 140.6634Educ + 3.3566Exper

Question 57

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 58

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 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 + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε The variable Train is deleted from Model A which results in Model B. Which of the following justifies this choice?

A) The adjusted R² Model B is lower than the adjusted R² of Model A, and the variable is individually significant in Model A.
B) The adjusted R² of Model B is higher than the adjusted R² of Model A, and the variable is individually significant in Model A.
C) The adjusted R² of Model B is lower than the adjusted R² of Model A, and the variable is not individually significant in Model A.
D) The adjusted R² of Model B is higher than the adjusted R² of Model A, and the variable is not individually significant in Model A.

Question 60

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.
The 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 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 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.
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 62

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 + b_1
B) From b₀ to b₀ + b₂
C) From b₀ to b₀ + b₃
D) From b₀ to b₀ + b₁ + b₂

Question 63

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 64

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 are correct.

Question 65

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 66

An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly found in older patients. Thirteen patients are given the new drug and 13 patients are given the old drug. To avoid bias in the experiment, they are not told which drug is given to them. To check how the effectiveness depends on the age of patients, the following data have been collected. The variables are Effectiveness = the response variable measured on a scale from 0 to 100,
Age = the age of a patient (in years),
Drug = a dummy variable that is 1 for the new drug and 0 for the old drug.
The regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug, is estimated and the following results are obtained. Which of the following is the estimated regression model for the new drug?

A) = 47.04 + 0.34Age
B) = 6.18 + 1.04Age
C) = 47.04 + 0.34Age + 0.70Age × Drug
D) = 47.04 + 0.34Age - 40.86Drug + 0.70Age × Drug

Question 67

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.
Suppose that at a 10% significance level, you do not reject the null hypothesis, H₀: β₁ = 0, when testing the individual significance of Time in Model B. Would you delete Time from Model B?

A) Yes, removing Time from Model B results in Model C which has a higher adjusted R².
B) No, removing Time from Model B results in Model C which has a with lower R².
C) No, Model B has the highest R², so it should be used for making predictions.
D) Yes, Time should be deleted because we could not prove its significance even for α = 0.10.

Question 68

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, what is the predicted balance on a $100,000 subprime loan taken 15 years ago?

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

Question 69

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

Question 70

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

A) cannot conduct a partial F test for the joint significance of d and xd
B) can conduct a partial F test for the joint significance of d and xd
C) cannot conduct t tests for the individual significance of d and xd
D) can conduct a t test for the joint significance of d and xd

Question 71

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

A) Reject H₀; we can conclude Time and Time × Prime are jointly significant.
B) Do not reject H₀; we can conclude Time and Time × Prime are jointly significant.
C) Reject H₀; we cannot conclude Time and Time × Prime are jointly insignificant.
D) Do not reject H₀; we cannot conclude Time and Time × Prime are jointly significant.

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.
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 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.
Suppose that at the 5% significance level you do not reject the null hypothesis, H₀: β₁ = β₃ = 0, when testing the joint significance of Time and Time × Prime in Model B. Should you delete both Time and Time × Prime from Model B?

A) No, because Model B has the highest R².
B) No, because Model B reduces then to Model A with a lower adjusted R².
C) No, because Model B reduces than to Model A with lower R².
D) Yes, because Model B reduces than to Model C with higher adjusted R².

Question 75

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 76

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) b_{0
B) b0} + b_{1
C) b2
D) b0} + b₂

Question 77

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 78

An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly found in older patients. Thirteen patients are given the new drug and 13 patients are given the old drug. To avoid bias in the experiment, they are not told which drug is given to them. To check how the effectiveness depends on the age of patients, the following data have been collected. The variables are Effectiveness = the response variable measured on a scale from 0 to 100,
Age = the age of a patient (in years),
Drug = a dummy variable that is 1 for the new drug and 0 for the old drug,
The regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug,is estimated and the following results are obtained. Which of the following is the estimated regression model for the old drug?

A) = 47.04 + 0.34Age
B) = 6.18 + 1.04Age
C) = 47.04 + 0.34Age + 0.70Age × Drug
D) = 47.04 + 0.34Age - 40.86Drug + 0.70Age × Drug

Question 79

An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly found in older patients. Thirteen patients are given the new drug and 13 patients are given the old drug. To avoid bias in the experiment, they are not told which drug is given to them. To check how the effectiveness depends on the age of patients, the following data have been collected. The variables are Effectiveness = the response variable measured on a scale from 0 to 100,
Age = the age of a patient (in years),
Drug = a binary variable with 1 for the new drug and 0 for the old drug.
The regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug, is estimated and the following results are obtained. Which of the following is the estimated regression model?

A) = 0.34Age - 40.86Drug + 0.70Age × Drug
B) = 3.15 + 0.07Age - 4.08Drug + 0.09Age × Drug
C) = 14.94 + 5.06Age - 10.02Drug + 7.94Age × Drug
D) = 47.04 + 0.34Age - 40.86Drug + 0.70Age × Drug

Question 80

An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly found in older patients. Thirteen patients are given the new drug and 13 patients are given the old drug. To avoid bias in the experiment, they are not told which drug is given to them. To check how the effectiveness depends on the age of patients, the following data have been collected. The variables are Effectiveness = the response variable measured on a scale from 0 to 100,
Age = the age of a patient (in years),
Drug = a dummy variable that is 1 for the new drug and 0 for the old drug.
The regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug, is estimated and the following results are obtained. Which of the following is the percentage of variation in Effectiveness explained by the model?

A) 97.61%
B) 95.27%
C) 94.63%
D) 32.35%