Deck 17: Regression Models With Dummy Variables

Question 1

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Answer 1

Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.8.Which of the three models would you choose to make the predictions of the home prices?

Question 2

Exhibit 17.9.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.

Answer 2

To estimate this probability,she decided to use the logistic model: ,
where,
y = a binary response variable with value 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 percent),
x₂ = the ratio of the total debt to the annual income (in percent).
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.
Refer to Exhibit 17.9.Assuming the debt ratio 30%,compute the increase in the probability of defaulting when the balance ratio goes up from 5% to 15%.

Question 3

Exhibit 17.7.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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,
Gender = the gender of an individual;1 for males,and 0 for females.
The regression results for the models,
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + β₄Exper × Gender + ε,
Model B: Salary = β₀ + β₁Educ + β₂Exper + ε,are summarized below.

Answer 3

Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.7.What is the alternative hypothesis for testing the joint significance of Exper and Exper × Gender in Model A?

Question 4

Exhibit 17.7.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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,
Gender = the gender of an individual;1 for males,and 0 for females.
The regression results for the models,
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + β₄Exper × Gender + ε,
Model B: Salary = β₀ + β₁Educ + β₂Exper + ε,are summarized below.

Question 5

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 6

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 7

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 8

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 9

Exhibit 17.9.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.

Question 10

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 11

Exhibit 17.9.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.

Question 12

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 13

Exhibit 17.9.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.

Question 14

Exhibit 17.9.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.

Question 15

Exhibit 17.9.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.

Question 16

Exhibit 17.9.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.

Question 17

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 18

Exhibit 17.7.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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,
Gender = the gender of an individual;1 for males,and 0 for females.
The regression results for the models,
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + β₄Exper × Gender + ε,
Model B: Salary = β₀ + β₁Educ + β₂Exper + ε,are summarized below.

Question 19

Exhibit 17.9.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.

Question 20

Exhibit 17.8.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 + β₁Size + β₂Loc1 + β₃Loc2 + ε,
Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε,
where,
Price = the price of a home (in $thousands),
Size = the square footage (in square 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.

Question 21

All variables employed in regression must be quantitative.

Question 22

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 23

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

Question 24

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

Question 25

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

Question 26

Exhibit 17.9.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.

Question 27

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

Question 28

In the regression equation ,a dummy variable d affects the slope of the line.

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

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

Question 31

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

Question 32

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 33

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 34

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 35

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 36

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

Question 37

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

Question 38

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

Question 39

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

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

Question 40

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

Question 41

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.Using Model B,what is the regression equation found by Excel for females?

A) = 4713.2506 + 139.5366Educ + 3.3488Exper + 609.2505Gender
B) = 5322.5011 + 139.5366Educ + 3.3488Expe
C) = 4713.2506 + 139.5366Educ + 3.3488Expe
D)

Question 42

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.Using Model B,what is the regression equation found by Excel for males?

A) = 4713.2506 + 139.5366Educ + 3.3488Exper + 609.2505Gender
B) = 5322.5011 + 139.5366Educ + 3.3488Expe
C) = 4713.2506 + 139.5366Educ + 3.3488Expe
D)

Question 43

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 44

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.Using Model A,what 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 $(4663 + 141 + 3 + 1 + 615)= $5423
B)About $(3 + 1 + 615)= $619
C)About $(4663 + 615)= $5278
D)About $615

Question 45

Exhibit 17.1.A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, , where
Price = the price of a unit (in $thousands),
Size = the square footage (in square feet),
View = a dummy variable taking on 1 for an ocean view unit,and 0 for a bay view unit.
Refer to Exhibit 17.1.What is the predicted price of an ocean view unit with 1500 square feet?

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

Question 46

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.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 47

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 48

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.What is the regression equation found by Excel for Model A?

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

Question 49

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 the above.

Question 50

For the model y = β₀ + β₁x + β₂d₁ + β₃d₂ + ε,which test 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 51

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.Which of the explanatory variables in Model A is most likely to be tested for the individual significance?

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

Question 52

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.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 mangers are lower on average by more than $500.
D)Reject H₀;the salaries of female mangers are lower on average by more than $500.

Question 53

Exhibit 17.1.A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, , where
Price = the price of a unit (in $thousands),
Size = the square footage (in square feet),
View = a dummy variable taking on 1 for an ocean view unit,and 0 for a bay view unit.
Refer to Exhibit 17.1.What is the predicted price of a bay view unit measuring 1500 square feet?

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

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

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.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 56

Exhibit 17.3.Consider the 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.
Refer to Exhibit 17.3.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 57

Exhibit 17.1.A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, , where
Price = the price of a unit (in $thousands),
Size = the square footage (in square feet),
View = a dummy variable taking on 1 for an ocean view unit,and 0 for a bay view unit.
Refer to Exhibit 17.1.What is the predicted difference in 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 58

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.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 59

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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.
Also,the following Excel partial outputs corresponding to the following models are available:
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.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 60

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 61

Exhibit 17.3.Consider the 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.
Refer to Exhibit 17.3.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 62

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 the above

Question 63

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 64

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 65

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars),
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.4.What is the p-value for testing the 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 66

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars),
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.4.Which of the 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 67

For the model y = β₀ + β₁x + β₂xd + ε,what 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 68

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 the above.

Question 69

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars),
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.4.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 70

Exhibit 17.3.Consider the 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.
Refer to Exhibit 17.3.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 71

Exhibit 17.3.Consider the 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.
Refer to Exhibit 17.3.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 72

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 73

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 74

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 75

Exhibit 17.3.Consider the 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.
Refer to Exhibit 17.3.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 76

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars),
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.4.Using Model C,what 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 77

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars),
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.4.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 78

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 79

Exhibit 17.3.Consider the 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.
Refer to Exhibit 17.3.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 80

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars),
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Refer to Exhibit 17.4.Using Model B,what 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