Question 1

Plotting the residuals against a binary predictor (X = 0, 1) reveals nothing about heteroscedasticity.

Accepted Answer

A) True 
 B)False

Question 2

A disadvantage of Excel's Data Analysis regression tool is that it expects the independent variables to be in a block of contiguous columns, so you must delete a column if you want to eliminate a predictor from the model.

Accepted Answer

A) True 
 B)False

Question 3

To find which predictors are most helpful in increasing R2, we might consider:

Accepted Answer

A) Log transformations. 
B) Stepwise regression. 
C) Logistic regression. 
D) Nonlinear regression. 
A) Log transformations. 
B) Stepwise regression. 
C) Logistic regression. 
D) Nonlinear regression.

Question 4

Which estimated multiple regression allows a test for nonlinearity?

Accepted Answer

A)  $\hat { y } = 47 - 12 x _ { 1 } + 8 x _ { 1 } x _ { 2 } - 5 x _ { 2 }$ . 
B)  $\hat { y } = 47 - 12 x _ { 1 } + 8 x _ { 1 } ^ { 2 } - 5 x _ { 2 } + 25 x _ { 2 } ^ { 2 }$ 
C)  $\hat { y } = 47 - 12 x _ { 1 } + 5 x _ { 2 } + 13 x _ { 3 }$ 
A)  $\hat { y } = 47 - 12 x _ { 1 } + 8 x _ { 1 } x _ { 2 } - 5 x _ { 2 }$ . 
B)  $\hat { y } = 47 - 12 x _ { 1 } + 8 x _ { 1 } ^ { 2 } - 5 x _ { 2 } + 25 x _ { 2 } ^ { 2 }$ 
C)  $\hat { y } = 47 - 12 x _ { 1 } + 5 x _ { 2 } + 13 x _ { 3 }$

Question 5

In a regression with 7 predictors and 62 observations, degrees of freedom for a t test for each coefficient would use how many degrees of freedom?

Accepted Answer

A) 61 
B) 60 
C) 55 
D) 54 
A) 61 
B) 60 
C) 55 
D) 54

Question 6

A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). The regression output is provided below. Some of the information has been omitted. $$\begin{array} { l c r c c } 
\hline \text { Source of variation } & \text { SS } & d f & \text { MS } & F \
\hline \text { Regression } & 3177.17 & 2 & 1588.584 & \
\text { Residual } & & 17 & 17.71713 & \
\text { Total } & 3478.36 & 19 & & \
\hline
\end{array}$$ Which of the following conclusions can be made based on the F-test?

Accepted Answer

A) The p-value on the F-test will be very high. 
B) At least one of the predictors is useful in explaining Y. 
C) The model is of no use in predicting selling prices of houses. 
D) The estimates were based on a sample of 19 houses. 
A) The p-value on the F-test will be very high. 
B) At least one of the predictors is useful in explaining Y. 
C) The model is of no use in predicting selling prices of houses. 
D) The estimates were based on a sample of 19 houses.

Question 7

Based on these regression results, in your judgment which statement is most nearly correct (Y = highway miles per gallon in 91 cars)? $$\begin{array}{l}
\begin{array} { r r r r } 
\mathrm { R } ^ { 2 } & 0.499 & & \
\text { Adjusted } \mathrm { R } ^ { 2 } & 0.444 & \mathrm { n } & 91 \
\mathrm { R } & 0.707 & \mathrm { k } & 9
\end{array}\
\begin{array} { l l l } 
\text { Std. Error } & 4.019 & \text { Dep. Var. HwyMPG }
\end{array}\
\begin{array} { l r r r r r } 
\hline \text { Source } & \text { SS } & d f & M S & F & p \text {-value } \
\hline \text { Regression } & 1,305.7251 & 9 & 145.0806 & 8.98 & .0000 \
\text { Residual } & 1,308.3848 & 81 & 16.1529 & & \
\hline \text { Total } & 2,614.1099 & 90 & & & \
\hline
\end{array}
\end{array}$$

Accepted Answer

A) The number of predictors is rather small. 
B) Some predictors are not contributing much. 
C) Prediction intervals would be fairly narrow in terms of MPG. 
D) The overall model lacks significance and/or predictive power. 
A) The number of predictors is rather small. 
B) Some predictors are not contributing much. 
C) Prediction intervals would be fairly narrow in terms of MPG. 
D) The overall model lacks significance and/or predictive power.

Question 8

In a multiple regression with five predictors in a sample of 56 U.S. cities, what would be the critical value for an F-test of overall significance at α = .05?

Accepted Answer

A) 2.45 
B) 2.37 
C) 2.40 
D) 2.56 
A) 2.45 
B) 2.37 
C) 2.40 
D) 2.56

Question 9

The regression equation Bonus = 2,812 + 27 Experience + 0.046 Salary says that Experience is the most significant predictor of Bonus.

Accepted Answer

A) True 
 B)False

Question 10

A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). The regression output is provided below. Some of the information has been omitted. $$\begin{array} { l c c c c } 
\hline \text { Source of variation } & \text { SS } & d f & M S & F \
\hline \text { Regression } & 3177.17 & 2 & 1588.6 & \
\text { Residual } & & 17 & 17.717 & \
\text { Total } & 3478.36 & 19 & & \
\hline
\end{array}$$ How many predictors (independent variables) were used in the regression?

Accepted Answer

A) 20 
B) 18 
C) 3 
D) 2 
A) 20 
B) 18 
C) 3 
D) 2

Question 11

A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). Part of the regression output is provided below, based on a sample of 20 homes. Some of the information has been omitted. $$\begin{array} { l r r r } 
\hline \text { Variable } & \text { Coefficients } & \text { Standard Error } & t \text {-Stat } \
\hline \text { Intercept } & 128.93746 & 2.6205302 & 49.203 \
\text { Size } & & 1.2072436 & 11.439 \
\text { FP } & 6.47601954 & 1.9803612 & 3.27 \
\hline
\end{array}$$ The estimated coefficient for Size is approximately:

Accepted Answer

A) 9.5. 
B) 13.8. 
C) 122.5. 
D) 1442.6. 
A) 9.5. 
B) 13.8. 
C) 122.5. 
D) 1442.6.

Question 12

In the following regression, which statement best describes the degree of multicollinearity? $\begin{array}{lrrrrr}
\hline \text { Variables } & \text { Coefficients } & \text { Std. Error } & t(d f=81) & p \text {-value } & \text { VFF } \
\hline \text { Intercept } & 9.8080 & 16.9900 & 0.577 & 5654 & \
\text { NumCyl } & -1.6804 & 0.5757 & -2.919 & 0045 & 3.159 \
\text { HPMax } & -0.0369 & 0.0140 & -2.630 & 0102 & 3.068 \
\text { ManTran } & 0.2868 & 1.2802 & 0.224 & 8233 & 2.105 \
\text { Length } & 0.1109 & 0.0601 & 1.845 & 0686 & 4.339 \
\text { Wheelbase } & -0.0701 & 0.1714 & -0.409 & 6836 & 7.553 \
\text { Width } & 0.4079 & 0.2922 & 1.396 & 1665 & 6.857 \
\text { RearStRm } & -0.0085 & 0.2018 & -0.042 & 9666 & 2.015 \
\text { Weight } & -0.0025 & 0.0020 & -1.266 & 2090 & 7.670 \
\text { Domestic } & -1.2291 & 1.1391 & -1.079 & 2838 & 1.825 \
\hline
\end{array}$

Accepted Answer

A) Very little evidence of multicollinearity. 
B) Much evidence of multicollinearity. 
C) Only NumCyl and HPMax are collinear. 
D) Only ManTran and RearStRm are collinear. 
A) Very little evidence of multicollinearity. 
B) Much evidence of multicollinearity. 
C) Only NumCyl and HPMax are collinear. 
D) Only ManTran and RearStRm are collinear.

Question 13

If the standard error is 12, the width of a quick prediction interval for Y is:

Accepted Answer

A) ±15. 
B) ±24. 
C) ±19. 
D) impossible to determine without an F table. 
A) ±15. 
B) ±24. 
C) ±19. 
D) impossible to determine without an F table.

Question 14

In the following regression, which are the three best predictors? $$\begin{array} { l r r r r } 
\hline \text { Variables } & \text { Coefficients } & \text { Std. Error } & t ( d f = 81 ) & p \text {-value } \
\hline \text { Intercept } & 9.8080 & 16.9900 & 0.577 & .5654 \
\text { NumCyl } & - 1.6804 & 0.5757 & - 2.919 & .0045 \
\text { HPMax } & - 0.0369 & 0.0140 & - 2.630 & .0102 \
\text { ManTran } & 0.2868 & 1.2802 & 0.224 & .8233 \
\text { Length } & 0.1109 & 0.0601 & 1.845 & .0686 \
\text { Wheelbase } & - 0.0701 & 0.1714 & - 0.409 & .6836 \
\text { Width } & 0.4079 & 0.2922 & 1.396 & 1665 \
\text { RearStRm } & - 0.0085 & 0.2018 & - 0.042 & .9666 \
\text { Weight } & - 0.0025 & 0.0020 & - 1.266 & .2090 \
\text { Domestic } & - 1.2291 & 1.1391 & - 1.079 & .2838 \
\hline
\end{array}$$

Accepted Answer

A) ManTran, Wheelbase, RearStRm 
B) ManTran, Length, Width 
C) NumCyl, HPMax, Length 
D) Cannot be ascertained from given information 
A) ManTran, Wheelbase, RearStRm 
B) ManTran, Length, Width 
C) NumCyl, HPMax, Length 
D) Cannot be ascertained from given information

Question 15

When predictor variables are strongly related to each other, the __________ of the regression estimates is questionable.

Accepted Answer

A) logic 
B) fit 
C) parsimony 
D) stability 
A) logic 
B) fit 
C) parsimony 
D) stability

Question 16

In a regression with n = 100 observations and k = 5 predictors, the criterion for high leverage is:

Accepted Answer

A) hi ≥ .06 
B) hi ≥ .12 
C) hi ≥ .18 
D) hi ≥ .24 
A) hi ≥ .06 
B) hi ≥ .12 
C) hi ≥ .18 
D) hi ≥ .24

Question 17

If the probability plot of residuals resembles a straight line, the residuals show a fairly good fit to the normal distribution.

Accepted Answer

A) True 
 B)False

Question 18

The regression equation Salary = 35,000 + 3500 YearsExperience + 1200 YearsCollege describes employee salaries at Streeling Research Labs. The standard error is 2500. Doris has 20 years' experience and 4 years of college. Her salary is $113,000. What is Doris's standardized residual?

Accepted Answer

A) +1.28 
B) -0.24 
C) -1.28 
D) +3.20 
A) +1.28 
B) -0.24 
C) -1.28 
D) +3.20

Question 19

In a multiple regression with five predictors in a sample of 56 U.S. cities, we would use F5,50 in a test of overall significance.

Accepted Answer

A) True 
 B)False

Question 20

A disadvantage of Excel's regression is that it does not give as much accuracy in the estimated regression coefficients as a package like Minitab.

Accepted Answer

A) True 
 B)False

Plotting the residuals against a binary predictor (X = 0, 1) reveals nothing about heteroscedasticity.

A disadvantage of Excel's Data Analysis regression tool is that it expects the independent variables to be in a block of contiguous columns, so you must delete a column if you want to eliminate a predictor from the model.

To find which predictors are most helpful in increasing R², we might consider:

Which estimated multiple regression allows a test for nonlinearity?

In a regression with 7 predictors and 62 observations, degrees of freedom for a t test for each coefficient would use how many degrees of freedom?

In a multiple regression with five predictors in a sample of 56 U.S. cities, what would be the critical value for an F-test of overall significance at α = .05?

The regression equation Bonus = 2,812 + 27 Experience + 0.046 Salary says that Experience is the most significant predictor of Bonus.

If the standard error is 12, the width of a quick prediction interval for Y is:

When predictor variables are strongly related to each other, the __________ of the regression estimates is questionable.

In a regression with n = 100 observations and k = 5 predictors, the criterion for high leverage is:

If the probability plot of residuals resembles a straight line, the residuals show a fairly good fit to the normal distribution.

The regression equation Salary = 35,000 + 3500 YearsExperience + 1200 YearsCollege describes employee salaries at Streeling Research Labs. The standard error is 2500. Doris has 20 years' experience and 4 years of college. Her salary is $113,000. What is Doris's standardized residual?

In a multiple regression with five predictors in a sample of 56 U.S. cities, we would use F_5,50 in a test of overall significance.

A disadvantage of Excel's regression is that it does not give as much accuracy in the estimated regression coefficients as a package like Minitab.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

Exam 13: Multiple Regression

Plotting the residuals against a binary predictor (X = 0, 1) reveals nothing about heteroscedasticity.

A disadvantage of Excel's Data Analysis regression tool is that it expects the independent variables to be in a block of contiguous columns, so you must delete a column if you want to eliminate a predictor from the model.

To find which predictors are most helpful in increasing R2, we might consider:

Which estimated multiple regression allows a test for nonlinearity?

In a regression with 7 predictors and 62 observations, degrees of freedom for a t test for each coefficient would use how many degrees of freedom?

In a multiple regression with five predictors in a sample of 56 U.S. cities, what would be the critical value for an F-test of overall significance at α = .05?

The regression equation Bonus = 2,812 + 27 Experience + 0.046 Salary says that Experience is the most significant predictor of Bonus.

If the standard error is 12, the width of a quick prediction interval for Y is:

When predictor variables are strongly related to each other, the __________ of the regression estimates is questionable.

In a regression with n = 100 observations and k = 5 predictors, the criterion for high leverage is:

If the probability plot of residuals resembles a straight line, the residuals show a fairly good fit to the normal distribution.

The regression equation Salary = 35,000 + 3500 YearsExperience + 1200 YearsCollege describes employee salaries at Streeling Research Labs. The standard error is 2500. Doris has 20 years' experience and 4 years of college. Her salary is $113,000. What is Doris's standardized residual?

In a multiple regression with five predictors in a sample of 56 U.S. cities, we would use F5,50 in a test of overall significance.

A disadvantage of Excel's regression is that it does not give as much accuracy in the estimated regression coefficients as a package like Minitab.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

To find which predictors are most helpful in increasing R², we might consider:

In a multiple regression with five predictors in a sample of 56 U.S. cities, we would use F_5,50 in a test of overall significance.