Deck 28: Multiple Regression Wisdom

Question 1

What is the purpose of an indicator variable in a regression model?

A)An indicator variable allows us to increase our R-squared value.
B)An indicator variable allows us to include quantitative variables in our model.
C)An indicator variable allows us to fix violations of our constant variance assumption.
D)An indicator variable allows us to fix violations of our normality assumption.
E)An indicator variable allows us to include categorical variables in our model.

Answer 1

An indicator variable allows us to include categorical variables in our model.

Question 2

An actuary wishes to predict the life expectancy of a person based on several variables.One categorical variable of interest is their relationship status - single,married,divorced,widowed,or common-law.If the actuary wished to include "relationship status" in a regression model,how many indicator variables would he/she need to use in the model?

A)4
B)2
C)3
D)5
E)1

Answer 2

4

Question 3

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: What is the least-squares regression line for predicting the salary of female employees?

A) = 40,000 + 4,000x
B) = 41,500 + 1,500g
C) = 40,000 + 2,500x
D) = 40,000 + 3,500x
E) = 41,500 + 3,500x

Answer 3

= 40,000 + 2,500x

Question 4

Here are histograms of the leverage and Studentized residuals for the regression model: Comment on what these diagnostic displays indicate.

Question 5

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: Predict the salary for a male employee with 15 years of experience.

A)$94,000
B)$77,500
C)$79,000
D)$80,000
E)$86,500

Question 6

A histogram of the externally Studentized residuals looks like this: Comment on the distribution of the Studentized Residuals.

Question 7

How would you interpret the coefficient of sex in this model?

Question 8

Here are plots of data for Studentized residuals against Length. Here is the same regression with all of the points at 70 removed.
Dependent variable is: Weight
30 total bears of which 10 are missing
R-squared = 97.8% R-squared (adjusted)= 97.3%
s = 2.96 with 20 - 4 = 16 degrees of freedom Compare the regression with the previous one.In particular,which model is likely to make the best prediction of weight? Which seems to fit the data better?

Question 9

Here is the scatterplot of externally Studentized residuals against predicted values: Comment on what this diagnostic display indicates.

Question 10

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: Interpret the value of the coefficient of gender (g).

A)We predict that a woman with 0 years of experience will make $1,500 more than a man with 0 years of experience.
B)We predict that a man with 0 years of experience will make $1,000 more than a woman with 0 years of experience.
C)We predict that a man with 0 years of experience will make $2,500 more than a woman with 0 years of experience.
D)We predict that a man with 0 years of experience will make $1,500 more than a woman with 0 years of experience.
E)We predict that a woman with 0 years of experience will make $2,500 more than a man with 0 years of experience.

Question 11

Here are plots of data for Studentized residuals against Length. Interpret this plot of the residuals.

Question 12

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: Interpret the value of the coefficient of the interaction term xg.

A)We predict that the growth rate of a male employee's salary will be $1,000 per year higher than that of a female employee.
B)We predict that a man with 0 years of experience will make $1,000 more than a woman with 0 years of experience.
C)We predict that the growth rate of a male employee's salary will be $1,000 per year.
D)We predict that a woman with 0 years of experience will make $1,000 more than a man with 0 years of experience.
E)We predict that the growth rate of a female employee's salary will be $1,000 per year.

Question 13

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: What is the least-squares regression line for predicting the salary of male employees?

A) = 41,500 + 3,500x
B) = 40,000 + 3,500x
C) = 40,000 + 2,500x
D) = 41,500 + 1,500g
E) = 40,000 + 4,000x

Question 14

Here are histograms of the leverage and Studentized residuals for the regression model: The 14th employee who was hired is highlighted in both displays.Do you think this employee is an influential case?

Question 15

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: What is the least-squares regression line for predicting the salary of female employees?

A) = 40,000 + 2,500x
B) = 40,000 + 2,500x + 1,500 g
C) = 40,000 + 4,000x
D) = 41,500 + 1,500g
E) = 41,500 + 2,500x

Question 16

Here are plots for Studentized residuals against Chest. Here is the same regression with the two data points with residuals above 2 removed:
Dependent variable is: Weight
30 total bears of which 2 are missing
R-squared = 93.8% R-squared (adjusted)= 93.0%
s = 7.22 with 28 - 4 = 24 degrees of freedom Compare the regression with the previous one.In particular,which model is likely to make the best prediction of weight? Which seems to fit the data better?

Question 17

Here are plots of data for Studentized residuals against Chest. Interpret this plot of the residuals.

Question 18

Here is a histogram of leverages for this regression: Without doing any calculating,how would you expect the coefficient and t-statistic of English to change if we were to omit the 6 highest leverage points?

Question 19

How would you interpret the coefficient of Science in the multiple regression?

Question 20

The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: $\text { Salary } = 40,000 + 2,500 \mathrm { x } + 1,500 \mathrm {~g}$ What is the least-squares regression line for predicting the salary of male employees?

A) $\text { Salary }$ = 40,000 + 2,500x
B) $\text { Salary }$ = 40,000 + 4,000x
C) $\text { Salary }$ = 40,000 + 2,500x + 1,500 g
D) $\text { Salary }$ = 41,500 + 2,500x
E) $\text { Salary }$ = 41,500 + 1,500g

Question 21

A real estate agent wishes to predict the selling price of a home based on several variables.One categorical variable of interest is the quality of the home - low,medium,or high.If the real estate agent wished to include "quality" in a regression model,how many indicator variables would he/she need to use in the model?

A)4
B)3
C)0
D)1
E)2