Deck 14: Introduction to Multiple Regression

Question 1

In a multiple regression model, which of the following is correct regarding the value of the adjusted r²?

A) It can be negative.
B) It has to be positive.
C) It has to be larger than the coefficient of multiple determination.
D) It can be larger than 1.

Answer 1

It can be negative.

Question 2

TABLE 14-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X?) and how he/she scored on a business aptitude test (X?). A random sample of 8 employees provides the following: $\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y } & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 100 & 10 & 7 \\2 & 90 & 3 & 10 \\3 & 80 & 8 & 9 \\4 & 70 & 5 & 4 \\5 & 60 & 5 & 8 \\6 & 50 & 7 & 5 \\7 & 40 & 1 & 4 \\8 & 30 & 1 & 1\end{array}$

-Referring to Table 14-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b??

A) 0.998
B) 3.103
C) 4.698
D) 21.293

Answer 2

4.698

Question 3

TABLE 14-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X?) and how he/she scored on a business aptitude test (X?). A random sample of 8 employees provides the following: $\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y } & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 100 & 10 & 7 \\2 & 90 & 3 & 10 \\3 & 80 & 8 & 9 \\4 & 70 & 5 & 4 \\5 & 60 & 5 & 8 \\6 & 50 & 7 & 5 \\7 & 40 & 1 & 4 \\8 & 30 & 1 & 1\end{array}$

-Referring to Table 14-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b??

A) 0.998
B) 3.103
C) 4.698
D) 21.293

Answer 3

3.103

Question 4

The coefficient of multiple determination r²Y.₁₂

A) measures the variation around the predicted regression equation.
B) measures the proportion of variation in Y that is explained by X₁ and X₂.
C) measures the proportion of variation in Y that is explained by X₁ holding X₂ constant.
D) will have the same sign as b₁.

Question 5

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r² value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?

A) 98.2
B) 11.1
C) 2.8
D) 1.1

Question 6

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion

Question 7

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X?) and the number of economics courses the employee successfully completed in college (X?). The professor randomly selects 6 workers and collects the following information:
$\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y (\$)} & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$

-Referring to Table 14-2, for these data, what is the value for the regression constant, b??

A) 0.616
B) 1.054
C) 6.932
D) 9.103

Question 8

In a multiple regression problem involving two independent variables, if b₁ is computed to be +2.0, it means that

A) the relationship between X₁ and Y is significant.
B) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant.
C) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, without regard to X₂.
D) the estimated mean of Y is 2 when X₁ equals zero.

Question 9

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, the p-value for GDP is

A) 0.05.
B) 0.01.
C) 0.001.
D) None of the above.

Question 10

TABLE 14-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X?) and how he/she scored on a business aptitude test (X?). A random sample of 8 employees provides the following: $\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y } & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 100 & 10 & 7 \\2 & 90 & 3 & 10 \\3 & 80 & 8 & 9 \\4 & 70 & 5 & 4 \\5 & 60 & 5 & 8 \\6 & 50 & 7 & 5 \\7 & 40 & 1 & 4 \\8 & 30 & 1 & 1\end{array}$

-Referring to Table 14-1, for these data, what is the value for the regression constant, b??

A) 0.998
B) 3.103
C) 4.698
D) 21.293

Question 11

TABLE 14-1
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X?) and how he/she scored on a business aptitude test (X?). A random sample of 8 employees provides the following: $\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y } & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 100 & 10 & 7 \\2 & 90 & 3 & 10 \\3 & 80 & 8 & 9 \\4 & 70 & 5 & 4 \\5 & 60 & 5 & 8 \\6 & 50 & 7 & 5 \\7 & 40 & 1 & 4 \\8 & 30 & 1 & 1\end{array}$

-Referring to Table 14-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?

A) 79.09
B) 60.88
C) 55.62
D) 17.98

Question 12

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, the p-value for the aggregated price index is

A) 0.05.
B) 0.01.
C) 0.001.
D) None of the above.

Question 13

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X?) and the number of economics courses the employee successfully completed in college (X?). The professor randomly selects 6 workers and collects the following information:
$\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y (\$)} & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$

-Referring to Table 14-2, for these data, what is the estimated coefficient for performance rating, b??

A) 0.616
B) 1.054
C) 6.932
D) 9.103

Question 14

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X?) and the number of economics courses the employee successfully completed in college (X?). The professor randomly selects 6 workers and collects the following information:
$\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y (\$)} & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$

-Referring to Table 14-2, for these data, what is the estimated coefficient for the number of economics courses taken, b??

A) 0.616
B) 1.054
C) 6.932
D) 9.103

Question 15

In a multiple regression model, the value of the coefficient of multiple determination

A) has to fall between -1 and +1.
B) has to fall between 0 and +1.
C) has to fall between -1 and 0.
D) can fall between any pair of real numbers.

Question 16

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, the p-value for the regression model as a whole is

A) 0.05.
B) 0.01.
C) 0.001.
D) None of the above.

Question 17

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X?) and the number of economics courses the employee successfully completed in college (X?). The professor randomly selects 6 workers and collects the following information:
$\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y (\$)} & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$

-Referring to Table 14-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate?

A) 10.90
B) 12.20
C) 17.23
D) 25.11

Question 18

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X?) and the number of economics courses the employee successfully completed in college (X?). The professor randomly selects 6 workers and collects the following information:
$\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y (\$)} & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$

-The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by

A) regression sum of squares.
B) error sum of squares.
C) total sum of squares.
D) regression mean squares.

Question 19

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion

Question 20

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X?) and the number of economics courses the employee successfully completed in college (X?). The professor randomly selects 6 workers and collects the following information:
$\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y (\$)} & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$

-Referring to Table 14-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate?

A) 10.90
B) 12.20
C) 24.87
D) 25.70

Question 21

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?

A) 11.43
B) 15.15
C) 24.88
D) 53.87

Question 22

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?

A) $2.52 billion
B) $0.48 billion
C) -$1.33 billion
D) -$2.52 billion

Question 23

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?

A) 0.01
B) 0.025
C) 0.05
D) 0.15

Question 24

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home (House = 100)?

A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand

Question 25

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, to test for the significance of the coefficient on aggregate price index, the p-value is

A) 0.0001.
B) 0.8330.
C) 0.8837.
D) 0.9999.

Question 26

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, what fraction of the variability in house size is explained by income, size of family, and education?

A) 27.0%
B) 33.4%
C) 74.8%
D) 86.5%

Question 27

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, what is the estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?

A) $1.39 billion
B) $2.89 billion
C) $4.75 billion
D) $9.45 billion

Question 28

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home (House = 50)?

A) $44.14 thousand
B) $56.75 thousand
C) $178.33 thousand
D) $211.85 thousand

Question 29

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, to test whether gross domestic product has a positive impact on consumption, the p-value is

A) 0.00005.
B) 0.0001.
C) 0.9999.
D) 0.99995.

Question 30

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, to test whether aggregate price index has a positive impact on consumption, the p-value is

A) 0.0001.
B) 0.4165.
C) 0.5835.
D) 0.8330.

Question 31

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, one individual in the sample had an annual income of $40,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet)for this data point?

A) -6.99
B) -5.35
C) 5.40
D) 16.99

Question 32

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, which of the independent variables in the model are significant at the 5% level?

A) Income, Size, School
B) Income, Size
C) Size, School
D) Income, School

Question 33

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?

A) 0.01
B) 0.025
C) 0.05
D) 0.15

Question 34

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

A) 2.8%
B) 51.8%
C) 72.6%
D) 74.8%

Question 35

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, to test for the significance of the coefficient on aggregate price index, the value of the relevant t-statistic is

A) 2.365.
B) 0.143.
C) -0.219.
D) -1.960.

Question 36

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?

A) 0.0005
B) 0.001
C) 0.01
D) 0.05

Question 37

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet)for this data point?

A) 7.40
B) 2.52
C) -2.52
D) -5.40

Question 38

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?

A) $4.39 billion
B) $0.39 billion
C) -$0.39 billion
D) -$1.33 billion

Question 39

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, to test whether aggregate price index has a negative impact on consumption, the p-value is

A) 0.0001.
B) 0.4165.
C) 0.8330.
D) 0.8837.

Question 40

TABLE 14-3
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\\text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\\text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & &\end{array}$


$\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$

-Referring to Table 14-3, to test for the significance of the coefficient on gross domestic product, the p-value is

A) 0.0001.
B) 0.8330.
C) 0.8837.
D) 0.9999.

Question 41

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, which of the following values for ? is the smallest for which the regression model as a whole is significant?

A) 0.00005
B) 0.001
C) 0.01
D) 0.05

Question 42

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what are the predicted sales (in millions of dollars)for a company spending $500 million on capital and $200 million on wages?

A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98

Question 43

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?

A) 5.286
B) 5.195
C) 3.945
D) -1.509

Question 44

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?

A) 0.0001
B) 0.0299
C) 0.726
D) 45.5340

Question 45

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what is the p-value for Capital?

A) 0.01
B) 0.025
C) 0.05
D) None of the above

Question 46

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what is the p-value for testing whether Capital has a negative influence on corporate sales?

A) 0.05
B) 0.2743
C) 0.5485
D) 0.7258

Question 47

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what is the p-value for testing whether Wages have a positive impact on corporate sales?

A) 0.01
B) 0.05
C) 0.0001
D) 0.00005

Question 48

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r² value of 0.601. What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?

A) 60.1%
B) 31.1%
C) 22.9%
D) 8.8%

Question 49

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, what are the residual degrees of freedom that are missing from the output?

A) 3
B) 46
C) 49
D) 50

Question 50

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what is the p-value for testing whether Wages have a negative impact on corporate sales?

A) 0.05
B) 0.0001
C) 0.00005
D) 0.99995

Question 51

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, the observed value of the F-statistic is missing from the printout. What are the degrees of freedom for this F-statistic?

A) 46 for the numerator, 3 for the denominator
B) 3 for the numerator, 49 for the denominator
C) 46 for the numerator, 49 for the denominator
D) 3 for the numerator, 46 for the denominator

Question 52

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

A) 5.286
B) 5.195
C) 3.945
D) -1.509

Question 53

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what is the p-value for Wages?

A) 0.01
B) 0.05
C) 0.0001
D) None of the above

Question 54

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, what are the regression degrees of freedom that are missing from the output?

A) 3
B) 46
C) 49
D) 50

Question 55

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?

A) School is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) School is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) School is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) School is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.

Question 56

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what is the p-value for testing whether Capital has a positive influence on corporate sales?

A) 0.025
B) 0.05
C) 0.2743
D) 0.5485

Question 57

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$
$\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$

-Referring to Table 14-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model?

A) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
D) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.

Question 58

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?

A) 15,800.00
B) 16,520.07
C) 17,277.49
D) 20,455.98

Question 59

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, which of the independent variables in the model are significant at the 5% level?

A) Capital, Wages
B) Capital
C) Wages
D) None of the above

Question 60

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, what fraction of the variability in sales is explained by spending on capital and wages?

A) 27.0%
B) 50.9%
C) 68.9%
D) 83.0%

Question 61

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic?

A) 25 for the numerator, 2 for the denominator
B) 2 for the numerator, 23 for the denominator
C) 23 for the numerator, 25 for the denominator
D) 2 for the numerator, 25 for the denominator

Question 62

When an explanatory variable is dropped from a multiple regression model, the adjusted r² can increase.

Question 63

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, suppose the microeconomist wants to test whether the coefficient on Capital is significantly different from 0. What is the value of the relevant t-statistic?

A) 0.609
B) 2.617
C) 4.804
D) 25.432

Question 64

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?

A) Capital is significant in explaining corporate sales and should be included in the model because its p-value is less than 0.01.
B) Capital is significant in explaining corporate sales and should be included in the model because its p-value is more than 0.01.
C) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is less than 0.01.
D) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01.

Question 65

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X?) the amount of insulation in inches (X?), the number of windows in the house (X?), and the age of the furnace in years (X?). Given below are the Excel outputs of two regression models.
Model 1
$\begin{array}{|lr}\hline{\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\hline \text { Adjusted R Square } & 0.7568 \\\hline \text { Observations } & 20 \\\hline\end{array}$

$\mathrm{ANOVA}$

$\begin{array}{llrrrrrr}\hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\\hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$
Model 2
$\begin{array}{|lr|}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\hline \text { Adjusted R Square } & 0.7506 \\\hline \text { Observations } & 20 \\\hline\end{array}$


$\text { ANOVA }$
$\begin{array}{|lrrrccc}\hline & & & & & & \text { Significance } \\& d f & \text { SS } & \text { MS } & F & F \\\hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\\text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\\text { Error }\end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\\mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\\hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\\hline\end{array}$


-Referring to Table 14-6 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test H?: ?? = ?? = ?? = ?? = 0 vs. H?: At least one ?? ? 0, j = 1,2,..., 4 using Model 1?

A) Do not reject H? and conclude that the 4 independent variables have significant individual linear effects on heating costs.
B) Reject H? and conclude that the 4 independent variables taken as a group have significant linear effects on heating costs.
C) Do not reject H? and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs.
D) Reject H? and conclude that the 4 independent variables taken as a group do not have significant linear effects on heating costs.

Question 66

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X?) the amount of insulation in inches (X?), the number of windows in the house (X?), and the age of the furnace in years (X?). Given below are the Excel outputs of two regression models.
Model 1
$\begin{array}{|lr}\hline{\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\hline \text { Adjusted R Square } & 0.7568 \\\hline \text { Observations } & 20 \\\hline\end{array}$

$\mathrm{ANOVA}$

$\begin{array}{llrrrrrr}\hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\\hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$
Model 2
$\begin{array}{|lr|}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\hline \text { Adjusted R Square } & 0.7506 \\\hline \text { Observations } & 20 \\\hline\end{array}$


$\text { ANOVA }$
$\begin{array}{|lrrrccc}\hline & & & & & & \text { Significance } \\& d f & \text { SS } & \text { MS } & F & F \\\hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\\text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\\text { Error }\end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\\mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\\hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\\hline\end{array}$


-Referring to Table 14-6, the estimated value of the partial regression parameter ?? in Model 1 means that

A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.
B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51.
C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51.
D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%.

Question 67

When an additional explanatory variable is introduced into a multiple regression model, the coefficient of multiple determination will never decrease.

Question 68

The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

Question 69

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X?) the amount of insulation in inches (X?), the number of windows in the house (X?), and the age of the furnace in years (X?). Given below are the Excel outputs of two regression models.
Model 1
$\begin{array}{|lr}\hline{\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\hline \text { Adjusted R Square } & 0.7568 \\\hline \text { Observations } & 20 \\\hline\end{array}$

$\mathrm{ANOVA}$

$\begin{array}{llrrrrrr}\hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\\hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$
Model 2
$\begin{array}{|lr|}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\hline \text { Adjusted R Square } & 0.7506 \\\hline \text { Observations } & 20 \\\hline\end{array}$


$\text { ANOVA }$
$\begin{array}{|lrrrccc}\hline & & & & & & \text { Significance } \\& d f & \text { SS } & \text { MS } & F & F \\\hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\\text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\\text { Error }\end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\\mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\\hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\\hline\end{array}$


-Referring to Table 14-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?

A) [-6.58, -3.65]
B) [-6.24, -2.78]
C) [-5.94, -3.08]
D) [-2.37, 15.12]

Question 70

The slopes in a multiple regression model are called net regression coefficients.

Question 71

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X?) the amount of insulation in inches (X?), the number of windows in the house (X?), and the age of the furnace in years (X?). Given below are the Excel outputs of two regression models.
Model 1
$\begin{array}{|lr}\hline{\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\hline \text { Adjusted R Square } & 0.7568 \\\hline \text { Observations } & 20 \\\hline\end{array}$

$\mathrm{ANOVA}$

$\begin{array}{llrrrrrr}\hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\\hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$
Model 2
$\begin{array}{|lr|}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\hline \text { Adjusted R Square } & 0.7506 \\\hline \text { Observations } & 20 \\\hline\end{array}$


$\text { ANOVA }$
$\begin{array}{|lrrrccc}\hline & & & & & & \text { Significance } \\& d f & \text { SS } & \text { MS } & F & F \\\hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\\text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\\text { Error }\end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\\mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\\hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\\hline\end{array}$


-Referring to Table 14-6, what is the value of the partial F test statistic for H?: ?? = ?? = 0 vs. H?: At least one ?? ? 0, j = 3, 4?

A) 0.820
B) 1.219
C) 1.382
D) 15.787

Question 72

When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.

Question 73

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?

A) 874.55
B) 622.87
C) -790.69
D) -983.56

Question 74

In calculating the standard error of the estimate, SYX = $$\sqrt { \mathrm { MSE } }$$ , there are n - k - 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.

Question 75

The coefficient of multiple determination r²Y.₁₂ measures the proportion of variation in Y that is explained by X₁ and X₂.

Question 76

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X?) the amount of insulation in inches (X?), the number of windows in the house (X?), and the age of the furnace in years (X?). Given below are the Excel outputs of two regression models.
Model 1
$\begin{array}{|lr}\hline{\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\hline \text { Adjusted R Square } & 0.7568 \\\hline \text { Observations } & 20 \\\hline\end{array}$

$\mathrm{ANOVA}$

$\begin{array}{llrrrrrr}\hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\\hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$
Model 2
$\begin{array}{|lr|}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\hline \text { Adjusted R Square } & 0.7506 \\\hline \text { Observations } & 20 \\\hline\end{array}$


$\text { ANOVA }$
$\begin{array}{|lrrrccc}\hline & & & & & & \text { Significance } \\& d f & \text { SS } & \text { MS } & F & F \\\hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\\text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\\text { Error }\end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\\mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\\hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\\hline\end{array}$


-Referring to Table 14-6, what are the degrees of freedom of the partial F test for H?: = ?? = ?? = 0 vs. H?: At least one ?? ? 0, j = 3, 4?

A) 2 numerator degrees of freedom and 15 denominator degrees of freedom
B) 15 numerator degrees of freedom and 2 denominator degrees of freedom
C) 2 numerator degrees of freedom and 17 denominator degrees of freedom
D) 17 numerator degrees of freedom and 2 denominator degrees of freedom

Question 77

When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.

Question 78

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X?) the amount of insulation in inches (X?), the number of windows in the house (X?), and the age of the furnace in years (X?). Given below are the Excel outputs of two regression models.
Model 1
$\begin{array}{|lr}\hline{\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\hline \text { Adjusted R Square } & 0.7568 \\\hline \text { Observations } & 20 \\\hline\end{array}$

$\mathrm{ANOVA}$

$\begin{array}{llrrrrrr}\hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\\hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$
Model 2
$\begin{array}{|lr|}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\hline \text { Adjusted R Square } & 0.7506 \\\hline \text { Observations } & 20 \\\hline\end{array}$


$\text { ANOVA }$
$\begin{array}{|lrrrccc}\hline & & & & & & \text { Significance } \\& d f & \text { SS } & \text { MS } & F & F \\\hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\\text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\\text { Error }\end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\\mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\\hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\\hline\end{array}$


-Referring to Table 14-6, what can we say about Model 1?

A) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs.
B) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.
C) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs.
D) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.

Question 79

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X?) the amount of insulation in inches (X?), the number of windows in the house (X?), and the age of the furnace in years (X?). Given below are the Excel outputs of two regression models.
Model 1
$\begin{array}{|lr}\hline{\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\hline \text { Adjusted R Square } & 0.7568 \\\hline \text { Observations } & 20 \\\hline\end{array}$

$\mathrm{ANOVA}$

$\begin{array}{llrrrrrr}\hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\\hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$
Model 2
$\begin{array}{|lr|}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\hline \text { Adjusted R Square } & 0.7506 \\\hline \text { Observations } & 20 \\\hline\end{array}$


$\text { ANOVA }$
$\begin{array}{|lrrrccc}\hline & & & & & & \text { Significance } \\& d f & \text { SS } & \text { MS } & F & F \\\hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\\text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\\hline \text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\\text { Error }\end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\\mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\\hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\\hline\end{array}$


-Referring to Table 14-6, what is your decision and conclusion for the test H?: ?? = 0 vs H?: ?? < 0 at the ? = 0.01 level of significance using Model 1?

A) Do not reject H? and conclude that the amount of insulation has a linear effect on heating cots.
B) Reject H? and conclude that the amount of insulation does not have a linear effect on heating costs.
C) Reject H? and conclude that the amount of insulation has a negative linear effect on heating costs.
D) Do not reject H? and conclude that the amount of insulation has a negative linear effect on heating costs.

Question 80

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT
$\begin{array}{l}\text { Regression Statistics }\\\begin{array}{ll}\text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$

ANOVA
$\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text { Residual } & 23 & 7045072780 & 306307512 & & \\\text { Total } & 25 & 22624849820 & & &\end{array}$


$\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$

-Referring to Table 14-5, one company in the sample had sales of $21.439 billion (Sales = 21,439). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?

A) 790.69
B) 648.31
C) -648.31
D) -790.69