Question 1

A binary (categorical) predictor should not be used along with nonbinary (numerical) predictors.

Accepted Answer

A) True 
 B)False  False

Question 2

Which estimated multiple regression has nonlinearity tests?

Accepted Answer

A)    y^=−92−5x1+6x12+18x2−12x22\hat { y } = - 92 - 5 x _ { 1 } + 6 x _ { 1 } ^ { 2 } + 18 x _ { 2 } - 12 x _ { 2 } ^ { 2 }y^​=−92−5x1​+6x12​+18x2​−12x22​ 
B)    y^=47−18x1−3x2+6x3+36x4\hat { y } = 47 - 18 x _ { 1 } - 3 x _ { 2 } + 6 x _ { 3 } + 36 x _ { 4 }y^​=47−18x1​−3x2​+6x3​+36x4​  .
C)    y^=88+11x1+7x1x2+5x2\hat { y } = 88 + 11 x _ { 1 } + 7 x _ { 1 } x _ { 2 } + 5 x _ { 2 }y^​=88+11x1​+7x1​x2​+5x2​ A

Question 3

A high variance inflation factor (VIF) indicates a significant predictor in the regression.

Accepted Answer

A) True 
 B)False  False

Question 4

Based on the following regression ANOVA table, what is the R2? $$\begin{array} { l r r r r } 
\hline \text { Source } & d f & \text { SS } & M S & F \
\hline \text { Regression } & 4 & 1793.2356 & 448.3089 & 7.485401 \
\text { Residual } & 45 & 2695.0996 & 59.8911 & \
\text { Total } & 49 & 4488.3352 & & \
\hline
\end{array}$$

Accepted Answer

A)  0.1336
B)  0.6005
C)  0.3995
D)  Insufficient information to answer

Question 5

For a certain firm, the regression equation Bonus = 2,000 + 257 Experience + 0.046 Salary describes employee bonuses with a standard error of 125. John has 10 years' experience, earns $50,000, and earned a bonus of $7,000. John is an outlier.

Accepted Answer

A) True 
 B)False

Question 6

A fitted multiple regression equation is Y = 12 + 3X1 - 5X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as well, while X3 and X4 remain unchanged, what change would you expect in your estimate of Y?

Accepted Answer

A)  Decrease by 2
B)  Decrease by 4
C)  Increase by 2
D)  No change in Y

Question 7

If the standard error is 18, an approximate prediction interval for Y is:

Accepted Answer

A)  ±36.
B)  ±24.
C)  ±18.
D)  impossible to determine without an F table.

Question 8

A squared predictor is used to test for nonlinearity in the predictor's relationship to Y.

Accepted Answer

A) True 
 B)False

Question 9

When the predictor units of measurement differ greatly in magnitude, which might be useful?

Accepted Answer

A)  Stepwise regression to detect which predictors are best.
B)  Decimal transformations to improve data conditioning.
C)  Logistic regression to produce probability predictions.
D)  Best subsets regression to find the best model.

Question 10

Multicollinearity can be detected from t tests of the predictor variables.

Accepted Answer

A) True 
 B)False

Question 11

Using data for a large sample of cars (n = 93), a statistics student calculated a matrix of correlation coefficients for selected variables describing each car. (a) In the spaces provided, write the two-tailed critical values of the correlation coefficient for α = .05 and α = .01 respectively. Show how you derived these critical values. (b) Mark with * all correlations that are significant at α = .05, and mark with ** those that are significant at α = .01. (c) Why might you expect a negative correlation between Weight and HwyMPG? (d) Why might you expect a positive correlation between HPMax and Length? Explain your reasoning. (e) Why is the matrix empty above the diagonal?
Correlation Matrix ( $n = 93$ cars)

$\begin{array}{|c|c|c|c|c|c|c|}
\text { MidPr}&\text { CityMPG}&\text { HwyMPG}&\text { EngSize}&\text { HPMax}&\text {Length}& \text {Weight }\
\hline \text { MidPr}&1.000 & & & & & & \
\hline\text { CityMPG}&-0.595 & 1.000 & & & & & \
\hline\text { HwyMPG}&-0.561 & 0.944 & 1.000 & & & & \
\hline\text { EngSize}&0.597 & -0.710 & -0.627 & 1.000 & & & \
\hline \text { HPMax}&0.788 & -0.673 & -0.619 & 0.732 & 1.000 & & \
\hline \text {Length}& 0.504 & -0.666 & -0.543 & 0.780 & 0.551 & 1.000 & \
\hline \text {Weight }&0.647 & -0.843 & -0.811 & 0.845 & 0.739 & 0.806 & 1.000 \
\hline
\end{array}$

MidPr = midrange price (in $\$ 1,000 )$ - average of min and max prices
CityMPG = city MPG (miles per gallon by EPA rating)
HwyMPG highway MPG
EngSize = engine size (liters)
HPMax = horsepower (maximum)
Length $=$ length (inches)
Weight = weight (pounds)
Critical value for $.05$
Critical value for .01

Accepted Answer

The answer of Using data for a large sample of...

Question 12

The regression equation Salary = 45,000 + 1500 YearsExperience + 2800 YearsCollege describes employee salaries at Terminus Fissile Labs. The standard error is 2500. Lars has 15 years' experience and 4 years of college. His salary is $70,500. If this regression is valid, we conclude that:

Accepted Answer

A)  Lars is underpaid, but is not an outlier.
B)  Lars is underpaid, and his salary is an outlier.
C)  Lars is overpaid, but is not an outlier.
D)  Lars is overpaid, and his salary is an outlier.

Question 13

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. $$\begin{array} { l r r r r } 
\hline \text { Variable } & \text { Coefficients } & \text { Standard Error } & \text { t-Stat } & \text { P-value } \
\hline \text { Intercept } & 128.93746 & 2.6205302 & 49.203 & 8.93 \mathrm { E } - 20 \
\text { Size } & & 1.2072436 & 11.439 & 2.09 \mathrm { E } - 09 \
\text { FP } & 6.47601954 & 1.9803612 & 3.27 & 0.004512 \
\hline
\end{array}$$ Which statement is supported by the regression output?

Accepted Answer

A)  At ? = .05, FP is not a significant predictor in a two-tailed test.
B)  A fireplace adds around $6476 to the selling price of the average house.
C)  A large house with no fireplace will sell for more than a small house with a fireplace.
D)  FP is a more significant predictor than Size.

Question 14

In a regression with n = 50 observations and k = 3 predictors, the criterion for high leverage is:

Accepted Answer

A)  hi ≥ .33
B)  hi ≥ .25
C)  hi ≥ .21
D)  hi ≥ .16

Question 15

Multicollinearity refers to relationships among the independent variables.

Accepted Answer

A) True 
 B)False

Question 16

The random error term in a regression model reflects all factors omitted from the model.

Accepted Answer

A) True 
 B)False

Question 17

Which of the following is not true of the standard error of the regression?

Accepted Answer

A)  It is a measure of the accuracy of the prediction.
B)  It is based on squared vertical deviations between the actual and predicted values of Y.
C)  It would be negative when there is an inverse relationship in the model.
D)  It is used in constructing confidence and prediction intervals for Y.

Question 18

Autocorrelation may be detected by looking at a plot of the residuals against time.

Accepted Answer

A) True 
 B)False

Question 19

When the dependent variable is binary (0 or 1), we need:

Accepted Answer

A)  stepwise regression.
B)  data transformation to improve conditioning.
C)  logistic regression.
D)  best subsets regression.

Question 20

In the following regression (n = 91), which coefficients differ from zero in a two-tailed test at ? = .05? $$\begin{array} { l r r r } 
& &  { \text { Confidence Interval } } \
\hline \text { Variables } & \text { Coefficients } & \text { 95\%lower } & \text { 95\% upper } \
\hline \text { Intercept } & 9.8080 & - 23.9968 & 43.6129 \
\text { NumCyl } & - 1.6804 & - 2.8260 & - 0.5349 \
\text { HPMax } & - 0.0369 & - 0.0648 & - 0.0090 \
\text { ManTran } & 0.2868 & - 2.2604 & 2.8341 \
\text { Length } & 0.1109 & - 0.0087 & 0.2305 \
\text { Wheelbase } & - 0.0701 & - 0.4111 & 0.2709 \
\text { Width } & 0.4079 & - 0.1735 & 0.9893 \
\text { RearStRm } & - 0.0085 & - 0.4100 & 0.3931 \
\text { Weight } & - 0.0025 & - 0.0064 & 0.0014 \
\text { Domestic } & - 1.2291 & - 3.4955 & 1.0374 \
\hline
\end{array}$$

Accepted Answer

A)  NumCyl, HPMax
B)  Intercept, ManTran
C)  Intercept, NumCyl, Domestic
D)  Intercept, Domestic

Exam 13: Multiple Regression

A binary (categorical) predictor should not be used along with nonbinary (numerical) predictors.

Which estimated multiple regression has nonlinearity tests?

A high variance inflation factor (VIF) indicates a significant predictor in the regression.

For a certain firm, the regression equation Bonus = 2,000 + 257 Experience + 0.046 Salary describes employee bonuses with a standard error of 125. John has 10 years' experience, earns $50,000, and earned a bonus of $7,000. John is an outlier.

A fitted multiple regression equation is Y = 12 + 3X₁ - 5X₂ + 7X₃ + 2X₄. When X₁ increases 2 units and X₂ increases 2 units as well, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y?

If the standard error is 18, an approximate prediction interval for Y is:

A squared predictor is used to test for nonlinearity in the predictor's relationship to Y.

When the predictor units of measurement differ greatly in magnitude, which might be useful?

Multicollinearity can be detected from t tests of the predictor variables.

The regression equation Salary = 45,000 + 1500 YearsExperience + 2800 YearsCollege describes employee salaries at Terminus Fissile Labs. The standard error is 2500. Lars has 15 years' experience and 4 years of college. His salary is $70,500. If this regression is valid, we conclude that:

In a regression with n = 50 observations and k = 3 predictors, the criterion for high leverage is:

Multicollinearity refers to relationships among the independent variables.

The random error term in a regression model reflects all factors omitted from the model.

Which of the following is not true of the standard error of the regression?

Autocorrelation may be detected by looking at a plot of the residuals against time.

When the dependent variable is binary (0 or 1) , we need: