Question 1

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

Accepted Answer

The coefficient of sex is rather small and it's not statistically significant.We have no evidence that it contributes significantly to weight.

Question 2

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

Accepted Answer

It appears that there is a problem with the independence assumption as there is a clear pattern in the residual plot.

Question 3

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?

Accepted Answer

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

Question 4

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

Accepted Answer

After allowing for the effects

Question 5

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 $$\begin{array} { c } 
& \text { Sum of } & &{ \text { Mean } } \
\text { Source } & \text { Squares } & \text { DF } & \text { Square } & \text { F-ratio } \
\text { Regression } & 21671 & 3 & 7223.67 & 123.23 \
\text { Residual } & 1406.88 & 24 & 58.62 &
\end{array}$$ $$\begin{array} { l r c r r } 
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Intercept } & - 167.52 & 7.47 & - 22.43 & < 0.0001 \
\text { Chest } & 3.01 & 2.98 & 1.01 & 0.3218 \
\text { Length } & 4.05 & 1.53 & 2.65 & 0.0135 \
\text { Sex } & - 2.03 & 2.14 & - 0.95 & 0.3509
\end{array}$$ 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?

Accepted Answer

Omitting the two values significantly ch

Question 6

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

Accepted Answer

It appears that there is a pro

Question 7

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: $\text { Salary } = 40,000 + 2,500 x + 1,500 \mathrm {~g} + 1,000 \mathrm { xg }$ Interpret the value of the coefficient of gender (g).

Accepted Answer

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. 
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 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 $$\begin{array} { l r r r r } 
& \text { Sum of } & & { \text { Mean } } \
\text { Source } & \text { Squares } & \text { DF } & \text { Square } & \text { F-ratio } \
\text { Regression } & 7455.0 & 3 & 2485 & 238.26 \
\text { Residual } & 166.89 & 16 & 10.43 &
\end{array}$$ $$\begin{array} { l r c r r } 
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Intercept } & - 169.16 & 3.23 & - 52.37 & < 0.0001 \
\text { Chest } & 0.84 & 0.58 & 1.45 & 0.1590 \
\text { Length } & 5.59 & 2.14 & 2.61 & 0.0148 \
\text { Sex } & - 1.19 & 1.98 & - 0.60 & 0.5537
\end{array}$$ 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?

Accepted Answer

Omitting the values changes the coeffici

Question 9

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

Accepted Answer

The scatterplot of the residuals against

Question 10

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?

Accepted Answer

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

Question 11

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?

Accepted Answer

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 
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 12

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

Accepted Answer

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. 
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.

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: $\text { Salary } = 40,000 + 2,500 x + 1,500 \mathrm {~g}$ What is the least-squares regression line for predicting the salary of female employees?

Accepted Answer

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

Question 14

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

Accepted Answer

There is only one high-leverag

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: $\text { Salary } = 40,000 + 2,500 \mathrm { x } + 1,500 \mathrm {~g} + 1,000 \mathrm { xg }$ Interpret the value of the coefficient of the interaction term xg.

Accepted Answer

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. 
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 16

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: $\text { Salary } = 40,000 + 2,500 \mathrm { x } + 1,500 \mathrm {~g} + 1,000 \mathrm { xg }$ What is the least-squares regression line for predicting the salary of male employees?

Accepted Answer

A)  $\text { Salary }$ = 41,500 + 3,500x 
B)  $\text { Salary }$ = 40,000 + 3,500x 
C)  $\text { Salary }$ = 40,000 + 2,500x 
D)  $\text { Salary }$ = 41,500 + 1,500g 
E)  $\text { Salary }$ = 40,000 + 4,000x 
A)  $\text { Salary }$ = 41,500 + 3,500x 
B)  $\text { Salary }$ = 40,000 + 3,500x 
C)  $\text { Salary }$ = 40,000 + 2,500x 
D)  $\text { Salary }$ = 41,500 + 1,500g 
E)  $\text { Salary }$ = 40,000 + 4,000x

Question 17

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

Accepted Answer

It appears that the Studentize

Question 18

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: $\text { Salary } = 40,000 + 2,500 \mathrm { x } + 1,500 \mathrm {~g} + 1,000 \mathrm { xg }$ Predict the salary for a male employee with 15 years of experience.

Accepted Answer

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

Question 19

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?

Accepted Answer

The 14th employee has a high leverage an

Question 20

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?

Accepted Answer

The points currently keep the

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

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

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

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

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

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

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

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

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?

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?

Stats Starts Here

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Regression Wisdom

Understanding Randomness

Sample Surveys

Experiments and Observational Studies

From Randomness to Probability

Probability Rules

Random Variables

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Rank-Based Nonparametric Tests

The Bootstrap

Filters

Exam 28: Multiple Regression Wisdom

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

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

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

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

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

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

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

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

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?

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?

Stats Starts Here

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Regression Wisdom

Understanding Randomness

Sample Surveys

Experiments and Observational Studies

From Randomness to Probability

Probability Rules

Random Variables

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Rank-Based Nonparametric Tests

The Bootstrap

Filters