Question 1

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 2

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 3

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

Accepted Answer

The t test is used for testing the significance of a dummy variable in a regression model. This test evaluates whether the coefficient associated with the dummy variable (in this case, β₂ for variable d) is significantly different from zero, indicating that the dummy variable has a statistically significant effect on the dependent variable y.

Question 4

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 5

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?

Accepted Answer

The answer of Exhibit 17.1.A researcher has developed the following...

Question 6

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 7

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:

Accepted Answer

The answer of Consider the model y = β₀ +...

Question 8

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?

Accepted Answer

The regression equation found by Excel for Model A is Salary = 4663.31 + 140.66Educ + 3.36Exper + 1.17Train + 615.15Gender, as indicated by the coefficients (β values) for each variable in the model output.

Question 9

The number of dummy variables representing a qualitative variable should be:

Accepted Answer

The number of dummy variables representing a qualitative variable should be one less than the number of categories of the variable. This is because the dummy variable coding scheme requires one less than the total number of categories to avoid perfect multicollinearity in the regression model. For example, if we have a variable with four categories (e.g. red, blue, green, and yellow), we would create three dummy variables (e.g. red, blue, and green) since having all four would result in perfect multicollinearity.

Question 10

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?

Accepted Answer

The appropriate test for joint significance of multiple variables is the F test. The other tests listed are not appropriate for this scenario.

Question 11

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 12

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?

Accepted Answer

We need to test the null hypothesis H0: β₀ ≥ -500 against the alternative hypothesis Ha: β₀ < -500. Using Model B, we run a one-tailed t-test with the following hypotheses: H0: β₀ = -500 Ha: β₀ < -500 Using a 10% significance level, the critical t-value with 86 degrees of freedom is -1.296. The t-value for the coefficient β₀ is -0.998 with a p-value of 0.166, which is greater than 0.1 (our significance level). Therefore, we do not reject the null hypothesis, and we cannot conclude that the salaries of female managers are lower on average by more than $500.

Question 13

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?

Accepted Answer

The regression equation is: 
Price = 125 + 0.25(Size) + 100(View)

For a bay view unit (View=0) measuring 1500 square feet (Size=1500), the predicted price is: 
Price = 125 + 0.25(1500) + 100(0) = $ 265,000 (in thousands of dollars)

Therefore, the best choice is C.

Question 14

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

Accepted Answer

For a qualitative variable with n categories, n-1 dummy variables are needed to fully describe it. Since there are 12 months, 12-1 = 11 dummy variables are needed.

Question 15

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 16

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?

Accepted Answer

The answer of Exhibit 17.3.Consider the regression model, Humidity =...

Question 17

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?

Accepted Answer

According to the given regression equation, the coefficient of the View variable is -0.05. This means that, holding square footage constant, the predicted difference in prices between an ocean view unit (View=1) and a bay view unit (View=0) is -$50,000. However, since the question asks for the difference in prices of the ocean view and bay view units with the same square footage, we need to ignore the coefficient of the View variable in the prediction. Therefore, the predicted difference in prices is $50,000. The correct answer is D.

Question 18

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 19

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?

Accepted Answer

The answer of Exhibit 17.2.To examine the differences between salaries...

Question 20

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:

Accepted Answer

When the dummy variable d increases from 0 to 1, it means that the coefficient b₂ will be added to the intercept term. Therefore, the change in the intercept is given by b₂.

Quiz 17: Regression Models With Dummy Variables

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

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:

The number of dummy variables representing a qualitative variable should be:

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?

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

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:

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

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:

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?

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: