Deck 19: Building Multiple Regression Models

Question 1

Data were collected for a study investigating what factors affect the size of company bonuses.The number of employees at the company and whether or not the employees were unionized (1 = yes, 0 = no) was included in two competing multiple regression models.Which of the following statements is true?

A)Model 2 explains less of the variability in average annual bonus than model 1.
B)The standard deviation of residuals is lower for model 1 compared to model 2.
C)Model 1 includes an interaction term.
D)Model 2 is better than model 1.
E)Model 1 is better than model 2.

Answer 1

Model 2 is better than model 1.

Question 2

A multiple regression model was fit to predict size of company bonuses from number of employees and unionized employees (1 = yes, 0 = no).The resulting model was:
Based on this model, what is the annual average bonus for a company with 7500 employees that are not unionized?

A)$5413
B)$10,259.20
C)$10,666
D)$5253
E)$7980.25

Answer 2

$5413

Question 3

Which of the following statements about building multiple regression models is true?

A)Automatic model building procedures such as "best subsets" and "stepwise" always select the best multiple regression model.
B)When comparing among competing multiple regression models, it is best to use R² rather than the adjusted R² for comparison.
C)It is always preferable to include more rather than fewer predictor variables in a multiple regression model in order to ensure the highest possible value of R.²
D)When comparing among competing multiple regression models, the best models will have the highest values for s_e.
E)None of the above.

Answer 3

None of the above.

Question 4

Which of the following statements about collinearity in a multiple regression model is false?

A)The Variance Inflation Factor can measure the collinearity of a predictor variable.
B)Coefficients of predictor variables will not be affected by collinearity.
C)Collinearity should be suspected if a model has a high R² and large F but no significant predictor variables.
D)All predictors must be considered in determining collinearity in a multiple regression model.
E)None of these are false.

Question 5

Data were collected on the number of employees and whether or not the employees were unionized (1 = yes, 0 = no) for a sample of companies to investigate factors that affect the size of bonuses.Based on the results shown, which of the following statements is true?

A)The indicator variable in the model is not significant.
B)The interaction term in the model is not significant.
C)The indicator variable in the model is significant.
D)The interaction term should be dropped from the model.
E)None of the above.

Question 6

Data were collected on the following variables: turnover rate, job growth, number of employees, and innovative index and fit in a model to explain Turnover Rate.To check for the possibility of collinearity, a regression among predictor variables job growth and employees predicting a third predictor variable, innovative index, was run and was found to have an R² = 8.8% and S=319.23.The Variance Inflation Factor (VIF) for the predictor variable Employees is ________________________ .

A)8.33
B)1.10
C)319.23
D)1.00
E)3.20

Question 7

A diagnostic measure used to identify influential cases that may have greatly affected multiple regression results is ________________________ .

A)Cook's Distance
B)Variance Inflation Factor
C)Variance Influential Factor
D)Residual's Distance
E)Adjusted R²

Question 8

Data were collected on Job Growth (%) and Industry in an attempt to develop a model to predict Turnover Rate in a sample of 22 firms from the high tech (Industry = 1) and the financial services sector (Industry = 0).Based on the output provided, the predicted turnover rate for a firm in the financial services sector with a 2% job growth rate is ________________________ .

A)8.25%
B)7.69%
C)4.56%
D)6.19%
E)None of the above.

Question 9

A point with a leverage value of 0 as an effect on all of the following regression statistics except:

A)Intercept
B)R²
C)F-statistic
D)t-statistic
E)regression slope

Question 10

In a multiple regression model, industry (1=high tech, 0=financial services), job growth, number of employees, and innovative index were used to predict turnover rate in a sample of firms.The coefficient of Industry is -2.8329.This means that for firms with the same innovative index score, job growth and number of employees the turnover rate will, on average, be ________________________ .

A)2.83% less for a firm from high tech industry compared to financial services
B)2.83% less for a firm from the financial services compared to the high tech industry
C)2.83% more for a firm from the high tech industry compared to the financial services
D)6.03% less for a firm from the high tech industry compared to the financial services
E)0.47% less for a firm from the financial services compared to the high tech industry

Question 11

A multiple regression model was fit to data investigating what factors affect the size of company bonuses including number of employees and whether or not the employees were unionized (1 = yes, 0 = no).The regression coefficient of Union is 1259.5.The correct interpretation of this value is that, for unionized companies compared to non-unionized companies of the same size (same number of employees), on average the annual average bonus is ________________________ .

A)$605.80 less
B)$605.80 more
C)$1259.50 less
D)$1259.50 more
E)$208 more

Question 12

Below is a scatterplot of size of company bonuses (Y) by number of employees at the company (X) for unionized and non-unionized employees.What does the scatterplot suggest?

A)Using Union as an indicator variable in this model is appropriate.
B)Using the interaction term Employees*Union in the model is appropriate.
C)Union should not be included in the model as a variable.
D)Employees should not be included in the model as a variable.
E)None of the above.

Question 13

Based on the multiple regression statistics below, how much of the variability in Turnover Rate is explained by this multiple regression model?

A)73.9%
B)95.6%
C)9.3%
D)50.62%
E)None of the above.

Question 14

What does the scatterplot below suggest about developing a multiple regression model to predict turnover rate using job growth and industry as predictor variables?

A)Using Job Growth as an indicator variable in this model is appropriate.
B)Using the interaction term Job Growth*Industry in the model is appropriate.
C)Using Industry as an indicator variable in this model is appropriate.
D)Job Growth should not be included in the model as a variable.
E)None of the above.

Question 15

A multiple regression model was fit to predict size of company bonuses from number of employees and unionized employees (1 = yes, 0 = no).The resulting model was:
Based on this model, what is the annual average bonus for a company with 5000 employees that are unionized?

A)$3195
B)$8176.80
C)$5253
D)$7980.25
E)$10,259.20

Question 16

Data were collected on the following variables: turnover rate, job growth, number of employees, and innovative index and fit in a model to explain Turnover Rate.To check for the possibility of collinearity, a regression among predictor variables job growth and employees predicting a third predictor variable, innovative index, was run and was found to have an R² = 52.5%.The Variance Inflation Factor (VIF) for the predictor variable Innovative Index is ________________________ .

A)52.5
B)13.15
C)3.63
D)2.10
E)1.00