Deck 14: Introduction to Multiple Regression

Question 1

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average 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 (X₁), the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the EXCEL outputs of two regression models.
$\begin{array}{ll}\text { Model } 1 \\\text { Regression Statistics } \\\hline \text { R Square }& 0.8080 \\\text { AdjustedR S quare }& 0.7568 \\\text { Observations } &20 \end{array}$

ANOVA
$\begin{array}{lrrccc} & \text { df } &{S S} & M S & F & \text { Signuficance F } \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 E-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} && \text { Standard } & & \text {Lower} & \text {Upper }\\& \text {Coefficients} & \text {Error} & \text { t Stat } & \text {p -value} & 90.0 \% & 90.0 \% \\ \hline \text { Intercept }& 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05& 284.9327 & 557.9227 \\ \text { X{1} (Temperature)} & -4.5098 & 0.8129 & -5.5476 &5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \text {X{2} (Insulation) }& -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \text { X{3} (Windows) }& 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \text { X{4} (Furnace Age)} & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \\\hline\end{array}$

$\begin{array}{ll} \text { Model 2} \\\hline \text {Regression Statistics} \\\hline \text {R Square }& 0.7768\\ \text {Adjusted R Square }&0.7506 \\ \text {Observations }& 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrcc}\hline & \text { d f} & \text { SS } & \text { MS } & \text {SS } & \text {Significance F } \\\hline \text {Regression} & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text {Residual }& 17 & 46807.5222 & 2753.384 & & \\ \text {Total }& 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lcccccc} && \text { Standard } & &\text { Lower} &\text { Upper} \\& \text {Coefficients }&\text { Error }&\text { t Stat }& \text { p -value} &95 \%& 95 \% \\\hline \text {Intercept }& 489.3227 & 43.982611 .1253 &3.17 \mathrm{E}-09& 396.5273 & 582.1180 \\\text { X{1} (Temperature) }& -5.1103 & 0.6951-7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\text { X{2} (Insulation) }& -14.7195 & 4.8864-3.0123 & 0.0078 & -25.0290 & -4.4099 \\\hline\end{array}$

-Referring to Table 14-6, the estimated value of the partial regression parameter þ1 in Model 1 means that

A) all else equal, a 1 degree increase in the daily minimum outside temperature results in an estimated expected decrease in average heating costs by $4.51.
B) all else equal, a 1 degree increase in the daily minimum outside temperature results in a decrease in average heating costs by $4.51.
C) all else equal, a 1% increase in the daily minimum outside temperature results in an estimated expected decrease in average heating costs by 4.51%.
D) all else equal, an estimated expected $1 increase in average heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.

Answer 1

all else equal, a 1 degree increase in the daily minimum outside temperature results in an estimated expected decrease in average heating costs by $4.51.

Question 2

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.

$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$

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

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

Answer 2

$2.89 billion

Question 3

TABLE 14-12
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below:
Y = Weight- loss (in pounds)
^X1 ^{= Length of time in weight- loss program (in months)
X}2 ^{= 1 if morning session, 0 if not
X}3 ^{= 1 if afternoon session, 0 if not (Base level = evening session)}
Data for 12 clients on a weight- loss program at the clinic were collected and used to fit the interaction model:
$Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$

Partial output from Microsoft Excel follows:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12 \\\hline\end{array}\end{array}$$

ANOVA
$F = 5.41118 \quad\text { Significance } F = 0.040201$

$\begin{array}{lcccr}\hline & \text {Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text {Length (X1)}& 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text {Morn Ses (X2)}& 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text {Aft Ses (X3)} & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text {Length*Morn Ses} & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text {Length * Aft Ses} & -0.54147 & 3.35988 & -0.161158 & 0.8773 \\\hline\end{array}$


-Referring to Table 14-12, in terms of the þ's in the model, give the average change in weight-loss (Y) for every 1 month increase in time in the program (X1) when attending the afternoon session.

A) $\beta_{1}+\beta_{5}$
B) $\beta_{4}+\beta_{5}$
C) $\beta_{1}+\beta_{4}$
D) $\beta_{1}$

Answer 3

$\beta_{1}+\beta_{5}$

Question 4

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed in college (X₂). The professor randomly selects 6 workers and collects the following information:
$$\begin{array} { c c c r } \hline\text { Employee } & Y ( \$ ) & X _ { 1 } & X _ { 2 } \\\hline 1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$$

-In a multiple regression model, the adjusted r²

A) can sometimes be greater than +1.
B) has to fall between 0 and +1.
C) cannot be negative.
D) can sometimes be negative.

Question 5

TABLE 14-12
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below:
Y = Weight- loss (in pounds)
^X1 ^{= Length of time in weight- loss program (in months)
X}2 ^{= 1 if morning session, 0 if not
X}3 ^{= 1 if afternoon session, 0 if not (Base level = evening session)}
Data for 12 clients on a weight- loss program at the clinic were collected and used to fit the interaction model:
$Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$

Partial output from Microsoft Excel follows:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12 \\\hline\end{array}\end{array}$$

ANOVA
$F = 5.41118 \quad\text { Significance } F = 0.040201$

$\begin{array}{lcccr}\hline & \text {Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text {Length (X1)}& 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text {Morn Ses (X2)}& 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text {Aft Ses (X3)} & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text {Length*Morn Ses} & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text {Length * Aft Ses} & -0.54147 & 3.35988 & -0.161158 & 0.8773 \\\hline\end{array}$


-Referring to Table 14-12, what is the experimental unit for this analysis?

A) a month
B) a morning, afternoon, or evening session
C) a clinic
D) a client on a weight-loss program

Question 6

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
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

Question 7

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$

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

Question 8

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average 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 (X₁), the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the EXCEL outputs of two regression models.
$\begin{array}{ll}\text { Model } 1 \\\text { Regression Statistics } \\\hline \text { R Square }& 0.8080 \\\text { AdjustedR S quare }& 0.7568 \\\text { Observations } &20 \end{array}$

ANOVA
$\begin{array}{lrrccc} & \text { df } &{S S} & M S & F & \text { Signuficance F } \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 E-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} && \text { Standard } & & \text {Lower} & \text {Upper }\\& \text {Coefficients} & \text {Error} & \text { t Stat } & \text {p -value} & 90.0 \% & 90.0 \% \\ \hline \text { Intercept }& 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05& 284.9327 & 557.9227 \\ \text { X{1} (Temperature)} & -4.5098 & 0.8129 & -5.5476 &5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \text {X{2} (Insulation) }& -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \text { X{3} (Windows) }& 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \text { X{4} (Furnace Age)} & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \\\hline\end{array}$

$\begin{array}{ll} \text { Model 2} \\\hline \text {Regression Statistics} \\\hline \text {R Square }& 0.7768\\ \text {Adjusted R Square }&0.7506 \\ \text {Observations }& 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrcc}\hline & \text { d f} & \text { SS } & \text { MS } & \text {SS } & \text {Significance F } \\\hline \text {Regression} & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text {Residual }& 17 & 46807.5222 & 2753.384 & & \\ \text {Total }& 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lcccccc} && \text { Standard } & &\text { Lower} &\text { Upper} \\& \text {Coefficients }&\text { Error }&\text { t Stat }& \text { p -value} &95 \%& 95 \% \\\hline \text {Intercept }& 489.3227 & 43.982611 .1253 &3.17 \mathrm{E}-09& 396.5273 & 582.1180 \\\text { X{1} (Temperature) }& -5.1103 & 0.6951-7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\text { X{2} (Insulation) }& -14.7195 & 4.8864-3.0123 & 0.0078 & -25.0290 & -4.4099 \\\hline\end{array}$


-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 H₀ :?₁ = ?₂ = ?₃ = ?₄ = 0 versus H₁ : At least one ?j ? 0, j = 1, 2,...,4 using Model 1?

A) Reject H₀ and conclude that the 4 independent variables taken as a group have significant linear effects on average heating costs.
B) Do not reject H₀ and conclude that the 4 independent variables taken as a group do not have significant linear effects on average heating costs.
C) Reject H₀ and conclude that the 4 independent variables taken as a group do not have significant linear effects on average heating costs.
D) Do not reject H₀ and conclude that the 4 independent variables have significant individual linear effects on average heating costs.

Question 9

TABLE 14-12
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below:
Y = Weight- loss (in pounds)
^X1 ^{= Length of time in weight- loss program (in months)
X}2 ^{= 1 if morning session, 0 if not
X}3 ^{= 1 if afternoon session, 0 if not (Base level = evening session)}
Data for 12 clients on a weight- loss program at the clinic were collected and used to fit the interaction model:

$Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$

Partial output from Microsoft Excel follows:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12\end{array}\end{array}$$ ANOVA
$F = 5.41118 \quad\text { Significance } F = 0.040201$

$\begin{array}{lcccr}\hline & \text {Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text {Length (X1)}& 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text {Morn Ses (X2)}& 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text {Aft Ses (X3)} & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text {Length*Morn Ses} & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text {Length * Aft Ses} & -0.54147 & 3.35988 & -0.161158 & 0.8773 \\\hline\end{array}$


-Referring to Table 14-12, what null hypothesis would you test to determine whether the slope of the linear relationship between weight-loss (Y) and time in the program (X1) varies according to time of session?

A) $H_{0}: \beta_{2}=\beta_{3}=0$
B) $H_{0}: \beta_{2}=\beta_{3}=\beta_{4}=\beta_{5}=0$
C) $H_{0}: \beta_{4}=\beta_{5}=0$
D) $H_{0}: \beta_{1}=\beta_{2}=\beta_{3}=\beta_{4}=\beta_{5}=0$

Question 10

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed in college (X₂). The professor randomly selects 6 workers and collects the following information:
$$\begin{array} { c c r r } \hline\text { Employee } & Y ( \$ ) & X _ { 1 } & X _ { 2 } \\\hline 1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9 \\\hline\end{array}$$

-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) 25.70
D) 24.87

Question 11

Table 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{ll}\text { Model } 1 \\\text { Regression Statistics } \\\hline \text { R Square }& 0.8080 \\\text { AdjustedR S quare }& 0.7568 \\\text { Observations } &20 \end{array}$

ANOVA
$\begin{array}{lrrccc} & \text { df } &{S S} & M S & F & \text { Signuficance F } \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 E-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} && \text { Standard } & & \text {Lower} & \text {Upper }\\& \text {Coefficients} & \text {Error} & \text { t Stat } & \text {p -value} & 90.0 \% & 90.0 \% \\ \hline \text { Intercept }& 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05& 284.9327 & 557.9227 \\ \text { X{1} (Temperature)} & -4.5098 & 0.8129 & -5.5476 &5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \text {X{2} (Insulation) }& -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \text { X{3} (Windows) }& 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \text { X{4} (Furnace Age)} & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \\\hline\end{array}$

$\begin{array}{ll} \text { Model 2} \\\hline \text {Regression Statistics} \\\hline \text {R Square }& 0.7768\\ \text {Adjusted R Square }&0.7506 \\ \text {Observations }& 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrcc}\hline & \text { d f} & \text { SS } & \text { MS } & \text {SS } & \text {Significance F } \\\hline \text {Regression} & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text {Residual }& 17 & 46807.5222 & 2753.384 & & \\ \text {Total }& 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lcccccc} && \text { Standard } & &\text { Lower} &\text { Upper} \\& \text {Coefficients }&\text { Error }&\text { t Stat }& \text { p -value} &95 \%& 95 \% \\\hline \text {Intercept }& 489.3227 & 43.982611 .1253 &3.17 \mathrm{E}-09& 396.5273 & 582.1180 \\\text { X{1} (Temperature) }& -5.1103 & 0.6951-7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\text { X{2} (Insulation) }& -14.7195 & 4.8864-3.0123 & 0.0078 & -25.0290 & -4.4099 \\\hline\end{array}$



-Referring to Table 14-16, which of the following is a correct statement?

A) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class holding constant the effect of average teacher salary, and instructional spending per pupil.
B) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class, average teacher salary, and instructional spending per pupil after adjusting for the number of predictors and sample size.
C) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class after adjusting for the effect of average teacher salary, and instructional spending per pupil.
D) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class, average teacher salary, and instructional spending per pupil.

Question 12

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

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

Question 13

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average 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 (X₁), the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the EXCEL outputs of two regression models.
$\begin{array}{ll}\text { Model } 1 \\\text { Regression Statistics } \\\hline \text { R Square }& 0.8080 \\\text { AdjustedR S quare }& 0.7568 \\\text { Observations } &20 \end{array}$

ANOVA
$\begin{array}{lrrccc} & \text { df } &{S S} & M S & F & \text { Signuficance F } \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 E-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} && \text { Standard } & & \text {Lower} & \text {Upper }\\& \text {Coefficients} & \text {Error} & \text { t Stat } & \text {p -value} & 90.0 \% & 90.0 \% \\ \hline \text { Intercept }& 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05& 284.9327 & 557.9227 \\ \text { X{1} (Temperature)} & -4.5098 & 0.8129 & -5.5476 &5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \text {X{2} (Insulation) }& -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \text { X{3} (Windows) }& 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \text { X{4} (Furnace Age)} & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \\\hline\end{array}$

$\begin{array}{ll} \text { Model 2} \\\hline \text {Regression Statistics} \\\hline \text {R Square }& 0.7768\\ \text {Adjusted R Square }&0.7506 \\ \text {Observations }& 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrcc}\hline & \text { d f} & \text { SS } & \text { MS } & \text {SS } & \text {Significance F } \\\hline \text {Regression} & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text {Residual }& 17 & 46807.5222 & 2753.384 & & \\ \text {Total }& 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lcccccc} && \text { Standard } & &\text { Lower} &\text { Upper} \\& \text {Coefficients }&\text { Error }&\text { t Stat }& \text { p -value} &95 \%& 95 \% \\\hline \text {Intercept }& 489.3227 & 43.982611 .1253 &3.17 \mathrm{E}-09& 396.5273 & 582.1180 \\\text { X{1} (Temperature) }& -5.1103 & 0.6951-7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\text { X{2} (Insulation) }& -14.7195 & 4.8864-3.0123 & 0.0078 & -25.0290 & -4.4099 \\\hline\end{array}$

-Referring to Table 14-6, what are the degrees of freedom of the partial F test for H0 : þ3 = þ4 = 0 versus H1: At least one þj × 0, j = 3,4?

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

Question 14

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:
$\text { SUMMARY }$


$\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { OUTPUT }$

$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } 50 & \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & 0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


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

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

Question 15

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 (X₁) and how he/she scored on a business aptitude test (X₂). A random sample of 8 employees provides the following:
$$\begin{array} { c r r r } \text { Employee } & Y & X _ { 1 } & X _ { 2 } \\\hline 1 & 100 & 10 & 7 \\2 & 90 & 3 & 10 \\3 & 80 & 8 & 9 \\4 & 70 & 5 & 4 \\5 & 60 & 5 & 8 \\6 & 50 & 7 & 5 \\7 & 40 & 1 & 4 \\8 & 30 & 1 & 1\end{array}$$

-Referring to Table 14-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b₂?

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

Question 16

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed in college (X₂). The professor randomly selects 6 workers and collects the following information:
$$\begin{array} { c c c r } \hline\text { Employee } & Y ( \$ ) & X _ { 1 } & X _ { 2 } \\\hline 1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$$

-Referring to Table 14-2, for these data, what is the estimated coefficient for the number of economics courses taken, b₂?

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

Question 17

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average 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 (X₁), the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the EXCEL outputs of two regression models.
$\begin{array}{ll}\text { Model } 1 \\\text { Regression Statistics } \\\hline \text { R Square }& 0.8080 \\\text { AdjustedR S quare }& 0.7568 \\\text { Observations } &20 \end{array}$

ANOVA
$\begin{array}{lrrccc} & \text { df } &{S S} & M S & F & \text { Signuficance F } \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 E-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} && \text { Standard } & & \text {Lower} & \text {Upper }\\& \text {Coefficients} & \text {Error} & \text { t Stat } & \text {p -value} & 90.0 \% & 90.0 \% \\ \hline \text { Intercept }& 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05& 284.9327 & 557.9227 \\ \text { X{1} (Temperature)} & -4.5098 & 0.8129 & -5.5476 &5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \text {X{2} (Insulation) }& -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \text { X{3} (Windows) }& 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \text { X{4} (Furnace Age)} & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \\\hline\end{array}$

$\begin{array}{ll} \text { Model 2} \\\hline \text {Regression Statistics} \\\hline \text {R Square }& 0.7768\\ \text {Adjusted R Square }&0.7506 \\ \text {Observations }& 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrcc}\hline & \text { d f} & \text { SS } & \text { MS } & \text {SS } & \text {Significance F } \\\hline \text {Regression} & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text {Residual }& 17 & 46807.5222 & 2753.384 & & \\ \text {Total }& 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lcccccc} && \text { Standard } & &\text { Lower} &\text { Upper} \\& \text {Coefficients }&\text { Error }&\text { t Stat }& \text { p -value} &95 \%& 95 \% \\\hline \text {Intercept }& 489.3227 & 43.982611 .1253 &3.17 \mathrm{E}-09& 396.5273 & 582.1180 \\\text { X{1} (Temperature) }& -5.1103 & 0.6951-7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\text { X{2} (Insulation) }& -14.7195 & 4.8864-3.0123 & 0.0078 & -25.0290 & -4.4099 \\\hline\end{array}$

-Referring to Table 14-6, what is your decision and conclusion for the test H₀ : ?₂ = 0 versus H₁ : ?₂ < 0 at the ? = 0.01 level of significance using Model 1?

A) Do not reject H₀ and conclude that the amount of insulation has a negative linear effect on average heating costs.
B) Reject H₀ and conclude that the amount of insulation does not have a linear effect on average heating costs.
C) Reject H₀ and conclude that the amount of insulation has a negative linear effect on average heating costs.
D) Do not reject H₀ and conclude that the amount of insulation has a linear effect on average heating cots.

Question 18

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.
$$\begin{array}{l}\text { SUMMARY OUTPUT }\\\begin{array} { l c } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.991 \\\text { R Square } & 0.982 \\\text { Adjusted R Square}&0.976 \\\text { Standard Error } & 0.299 \\\text { Observations } & 10\end{array}\end{array}$$
ANOVA
$\begin{array}{lcccccc}\hline & d f & S S & \text { MS } & F & \text { Significance } F \\\hline \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\\text { Total } & 9 & 34.0440 & & & &\end{array}$
$$\begin{array} { l c c c c } &\text { Coeffieients } & \text { Standard Error }& t \text { Stut } & p \text {-value } & \\\hline \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\\text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\\text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330\end{array}$$

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

Question 19

TABLE 14-12
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below:
Y = Weight- loss (in pounds)
^X1 ^{= Length of time in weight- loss program (in months)
X}2 ^{= 1 if morning session, 0 if not
X}3 ^{= 1 if afternoon session, 0 if not (Base level = evening session)}
Data for 12 clients on a weight- loss program at the clinic were collected and used to fit the interaction model:
$Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$

Partial output from Microsoft Excel follows:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12 \\\hline\end{array}\end{array}$$

ANOVA
$F = 5.41118 \quad\text { Significance } F = 0.040201$

$\begin{array}{lcccr}\hline & \text {Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text {Length (X1)}& 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text {Morn Ses (X2)}& 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text {Aft Ses (X3)} & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text {Length*Morn Ses} & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text {Length * Aft Ses} & -0.54147 & 3.35988 & -0.161158 & 0.8773 \\\hline\end{array}$


-Referring to Table 14-12, in terms of the þ's in the model, give the average change in weight-loss (Y) for every 1 month increase in time in the program (X1) when attending the morning session.

A) $\beta_{4}+\beta_{5}$
B) $\beta_{1}$
C) $\beta_{1}+\beta_{5}$
D) $\beta_{1}+\beta_{4}$

Question 20

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
$\begin{array}{lc}{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.991 \\\text { R Square } & 0.982 \\\text { Adjusted R Square }& 0.976 \\\text { Standard Error } & 0.299 \\\text { Observations } & 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

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

Question 21

TABLE 14-13
As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is
$Y_{i}=\alpha+\beta_{1} X_{1 i}+\beta_{2} X_{2 i}+\beta_{3} X_{3 i}+\varepsilon$
where Y is the meter price;
^X1 ^{is the number of blocks to the quad;
X}2 ^{is a dummy variable that takes the value 1 if the meter}
is located in downtown and off campus and the value 0 otherwise;
^X3 ^{is a dummy variable that takes the value 1 if the meter}
is located outside of downtown and off campus, and the value 0 otherwise.
The following Excel results are obtained.
$\begin{array}{lc}\hline \text {Regression Statistics } \\\hline \text {Multiple R} & 0.9659 \\ \text {R Square}& 0.9331 \\ \text {Adjusted R Square} & 0.9294 \\ \text {Standard Error }& 0.0327 \\ \text {Observations} & 58 \\\hline\end{array}$

ANOVA
$\begin{array}{lrcccr}\hline & \text { d f } & \text { SS} & \text { M S } & \text { F }& \text { Significance F }\\\hline \text { Regression} & 3 & 0.8094 & 0.2698 & 251.1995 & 1.0964 \mathrm{E}-31 \\ \text { Residual }& 54 & 0.0580 & 0.0010 & & \\ \text { Total} & 57 & 0.8675 & & & \\\hline\end{array}$

$\begin{array}{lcccl}\hline & \text { Coefficients} & \text {Standard Error }& \text {t Stat }& \text { p-value} \\\hline \text {Intercept} & 0.5118 & 0.0136 & 37.4675 & 2.4904 \\\mathrm{X1 } & -0.0045 & 0.0034 & -1.3276 & 0.1898 \\\mathrm{X2 } & -0.2392 & 0.0123 & -19.3942 & 5.3581 \mathrm{E}-26 \\\mathrm{X3 } & -0.0002 & 0.0123 & -0.0214 & 0.9829 \\\hline\end{array}$



-Referring to Table 14-13, predict the meter rate per hour if one parks outside of downtown and off campus 3 blocks from the quad.

A) $0.4981
B) $0.2604
C) - $0.0139
D) $0.2589

Question 22

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

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & 0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


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

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

Question 24

TABLE 14-14
An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is
Y = 10 + 5X₁ + 8X₂
where X₁ = mortgage rate in %
X₂ = 1 if SF, 0 if LA
Y = demand in $100 per capita

-Referring to Table 14-14, the fitted model for predicting demand in Los Angeles is .

A) 10 + 5X₁
B) 10 + 13X₁
C) 18 + 5X₂
D) 15 + 8X₂

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


-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) 1.1
D) 2.8

Question 26

TABLE 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$


-Referring to Table 14-16, which of the following is a correct statement?

A) The daily average of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1% holding constant the effects of all the remaining independent variables.
B) The average percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of the percentage of students attending class increases by 1% holding constant the effects of all the remaining independent variables.
C) The average percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of percentage of students attending class increases by 1%.
D) The daily average of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1%.

Question 27

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

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

Question 28

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

Question 29

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

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

Question 30

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average 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 (X₁), the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the EXCEL outputs of two regression models.
$\begin{array}{ll}\text { Model } 1 \\\text { Regression Statistics } \\\hline \text { R Square }& 0.8080 \\\text { AdjustedR S quare }& 0.7568 \\\text { Observations } &20 \end{array}$

ANOVA
$\begin{array}{lrrccc} & \text { df } &{S S} & M S & F & \text { Signuficance F } \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 E-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} && \text { Standard } & & \text {Lower} & \text {Upper }\\& \text {Coefficients} & \text {Error} & \text { t Stat } & \text {p -value} & 90.0 \% & 90.0 \% \\ \hline \text { Intercept }& 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05& 284.9327 & 557.9227 \\ \text { X{1} (Temperature)} & -4.5098 & 0.8129 & -5.5476 &5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \text {X{2} (Insulation) }& -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \text { X{3} (Windows) }& 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \text { X{4} (Furnace Age)} & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \\\hline\end{array}$

$\begin{array}{ll} \text { Model 2} \\\hline \text {Regression Statistics} \\\hline \text {R Square }& 0.7768\\ \text {Adjusted R Square }&0.7506 \\ \text {Observations }& 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrcc}\hline & \text { d f} & \text { SS } & \text { MS } & \text {SS } & \text {Significance F } \\\hline \text {Regression} & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text {Residual }& 17 & 46807.5222 & 2753.384 & & \\ \text {Total }& 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lcccccc} && \text { Standard } & &\text { Lower} &\text { Upper} \\& \text {Coefficients }&\text { Error }&\text { t Stat }& \text { p -value} &95 \%& 95 \% \\\hline \text {Intercept }& 489.3227 & 43.982611 .1253 &3.17 \mathrm{E}-09& 396.5273 & 582.1180 \\\text { X{1} (Temperature) }& -5.1103 & 0.6951-7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\text { X{2} (Insulation) }& -14.7195 & 4.8864-3.0123 & 0.0078 & -25.0290 & -4.4099 \\\hline\end{array}$


-Referring to Table 14-6, what is the value of the partial F test statistic for H₀ :?₃ = ?₄ = 0 versus H₁ : At least one ?j ?0, j = 3,4?

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

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 && 0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


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

Question 32

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

A) 0.001
B) 0.05
C) 0.01
D) none of the above

Question 33

If a categorical independent variable contains 4 categories, then_____ dummy variable(s) will be needed to uniquely represent these categories.

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

Question 34

An interaction term in a multiple regression model may be used when

A) the coefficient of determination is small.
B) there is a curvilinear relationship between the dependent and independent variables.
C) the relationship between X1 and Y changes for differing values of X2.
D) neither one of 2 independent variables contribute significantly to the regression model.

Question 35

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


-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) 17,277.49
C) 16,520.07
D) 20,455.98

Question 36

TABLE 14-2
A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed in college (X₂). The professor randomly selects 6 workers and collects the following information:
$$\begin{array} { c c r r } \text { Employee } & Y ( \$ ) & X _ { 1 } & X _ { 2 } \\\hline 1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9 \\\hline\end{array}$$

-Referring to Table 14-2, for these data, what is the estimated coefficient for performance rating, b1?

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

Question 37

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$



TABLE 14-3
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

Question 38

TABLE 14-17
The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1
= favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age).

The Minitab output is given below:
Logistic Regression Table
$\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\\text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\\text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\\text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\\text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\\text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\\text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\\text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45\end{array}$

Log-Likelihood = -4.890
Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000

Goodness-of-Fit Tests
$\begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array}$


-Referring to Table 14-17, which of the following is the correct interpretation for the Income slope coefficient?

A) Holding constant the effect of the other variables, the estimated probability of purchasing a lawn service increases by 0.2868 for each increase of one thousand dollars in family income.
B) Holding constant the effect of the other variables, the estimated number of lawn service purchased increases by 0.2868 for each increase of one thousand dollars in family income.
C) Holding constant the effect of the other variables, the estimated average number of lawn service purchased increases by 0.2868 for each increase of one thousand dollars in family income.
D) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of purchasing a lawn service increases by 0.2868 for each increase of one thousand dollars in family income.

Question 39

TABLE 14-17
The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1
= favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age).
The Minitab output is given below:
Logistic Regression Table
$\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\\text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\\text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\\text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\\text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\\text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\\text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\\text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45\end{array}$

Log-Likelihood = -4.890
Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000

Goodness-of-Fit Tests
$\begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array}$



-Referring to Table 14-17, which of the following is the correct interpretation for the Attitude slope coefficient?

A) Holding constant the effect of the other variables, the estimated odds ratio of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude.
B) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude.
C) Holding constant the effect of the other variables, the estimated number of lawn service purchased is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude.
D) Holding constant the effect of the other variables, the estimated probability of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude.

Question 40

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


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

Question 41

TABLE 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$

-Referring to Table 14-16, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

A) $H_{0}: \beta_{2}=0$
B) $H_{0}: \beta_{3}=0$
C) $H_{0}: \beta_{0}=0$
D) $H_{0}: \beta_{1}=0$

Question 42

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


-Referring to Table 14-4, one individual in the sample had an annual income of $10,000, 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) 5.40
B) - 5.40
C) - 8.10
D) 8.10

Question 43

TABLE 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$


-Referring to Table 14-16, which of the following is the correct alternative hypothesis to test whether daily average of the percentage of students attending class has any effect on percentage of students passing the proficiency test?

A) $H_{1}: \beta_{1} \neq 0$
B) $H_{1}: \beta_{0} \neq 0$
C) $H_{1}: \beta_{2} \neq 0$
D) $H_{1}: \beta_{3} \neq 0$

Question 44

TABLE 14-9
You decide to predict gasoline prices in different cities and towns in the United States for your term project. Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on gasoline, and the number of people using public transportation. You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821. Your computed value of standard error of the estimate is 1.9549.

-Referring to Table 14-9, if variables that measure the number of new business starts in the last year and population density of the city were removed from the multiple regression model, which of the following would be true?

A) The coefficient of multiple determination will definitely increase.
B) The coefficient of multiple determination will not increase.
C) The adjusted r² cannot increase.
D) The adjusted r² will definitely increase.

Question 45

TABLE 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$


-Referring to Table 14-16, which of the following is the correct null hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

A) $H_{0}: \beta_{0}=\beta_{1}=\beta_{2}=\beta_{3}=0$
B) $H_{0}: \beta_{1}=\beta_{2}=\beta_{3} \neq 0$
C) $H_{0}: \beta_{1}=\beta_{2}=\beta_{3}=0$
D) $H_{0}: \beta_{0}=\beta_{1}=\beta_{2}=\beta_{3} \neq 0$

Question 46

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

Question 47

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

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

Question 49

The coefficient of multiple determination r²Y.12

A) will have the same sign as b₁.
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) measures the variation around the predicted regression equation.

Question 50

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
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

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

Question 51

TABLE 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$

-Referring to Table 14-16, which of the following is the correct alternative hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

A) $H_{1}: \beta_{1} \neq 0$
B) $H_{1}: \beta_{3} \neq 0$
C) $H_{1}: \beta_{0} \neq 0$
D) $H_{1}: \beta_{2} \neq 0$

Question 52

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$



-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) 0.7258
C) 0.2743
D) 0.5485

Question 53

TABLE 14-11
A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on average total Scholastic Aptitude Test score (SAT) at the university or college, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).

Logistic Regression Table
$\begin{array}{lrrrrrrr} & & & && \text { Odds } & \text { 95: CI } \\\text { Predictor } & {\text { Coef }} & \text { SE Coef } & Z &{\text { P }} & \text { Ratio } & \text { Lower } & \text { Upper } \\\text { Constant } &-27.118&6 .696& -4.05 & 0.000 & & & \\\text { SAT } & 0.015 & 0.004666 & 3.17 & 0.002 & 1.01 & 1.01 & 1.02 \\\text { Toefl550 } & -0.390 & 0.9538 & -0.41 & 0.682 & 0.68 & 0.10 & 4.39 \\\text { Room/Brd } & 2.078 & 0.5076 & 4.09 & 0.000 & 7.99 & 2.95 & 21.60\end{array}$

Log-Likelihood = -21.883
Test that all slopes are zero: G = 62.083, DF = 3, P-Value = 0.000
Goodness-of-Fit Tests

$\begin{array}{lrcr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 143.551 & 76 & 0.000 \\ \text { Deviance } & 43.767 & 76 & 0.999 \\ \text { Hosmer-Lemeshow } & 15.731 & 8 & 0.046\end{array}$


-Referring to Table 14-11, which of the following is the correct interpretation for the Tofel500 slope coefficient?

A) Holding constant the effect of the other variables, the estimated average value of school type is 0.39 lower when the school has a TOEFL criterion that is at least 550.
B) Holding constant the effect of the other variables, the estimated probability of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not.
C) Holding constant the effect of the other variables, the estimated school type decreases by 0.39 when the school has a TOEFL criterion that is at least 550.
D) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of the school being a private school is 0.39 lower for a school that has a TOEFL criterion that is at least 550 than one that does not.

Question 54

TABLE 14-9
You decide to predict gasoline prices in different cities and towns in the United States for your term project. Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on gasoline, and the number of people using public transportation. You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821. Your computed value of standard error of the estimate is 1.9549.

-Referring to Table 14-9, what is the value of the coefficient of multiple determination?

A) 0.2225
B) 0.4576
C) 0.6472
D) 0.5626

Question 55

TABLE 14-12
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below:
Y = Weight- loss (in pounds)
^X1 ^{= Length of time in weight- loss program (in months)
X}2 ^{= 1 if morning session, 0 if not
X}3 ^{= 1 if afternoon session, 0 if not (Base level = evening session)}
Data for 12 clients on a weight- loss program at the clinic were collected and used to fit the interaction model:
$Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$

Partial output from Microsoft Excel follows:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12 \\\hline\end{array}\end{array}$$

ANOVA
$F = 5.41118 \quad\text { Significance } F = 0.040201$

$\begin{array}{lcccr}\hline & \text {Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text {Length (X1)}& 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text {Morn Ses (X2)}& 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text {Aft Ses (X3)} & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text {Length*Morn Ses} & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text {Length * Aft Ses} & -0.54147 & 3.35988 & -0.161158 & 0.8773 \\\hline\end{array}$


-Referring to Table 14-12, which of the following statements is supported by the analysis shown?

A) There is sufficient evidence (at ? = 0.05) to indicate that the relationship between weight-loss (Y) and months in program (X1) depends on session time.
B) There is sufficient evidence (at ? = 0.10) to indicate that the session time (morning, afternoon, evening) affects weight-loss (Y).
C) There is insufficient evidence (at ? = 0.10) to indicate that the relationship between weight-loss (Y) and months in program(X1) depends on session time.
D) There is sufficient evidence (at ? = 0.05) of curvature in the relationship between weight-loss (Y) and months in program(X1).

Question 56

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

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

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


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

Question 58

TABLE 14-11
A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on average total Scholastic Aptitude Test score (SAT) at the university or college, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).
Logistic Regression Table
$\begin{array}{lrrrrrrr} & & & && \text { Odds } & \text { 95: CI } \\\text { Predictor } & {\text { Coef }} & \text { SE Coef } & Z &{\text { P }} & \text { Ratio } & \text { Lower } & \text { Upper } \\\text { Constant } &-27.118&6 .696& -4.05 & 0.000 & & & \\\text { SAT } & 0.015 & 0.004666 & 3.17 & 0.002 & 1.01 & 1.01 & 1.02 \\\text { Toefl550 } & -0.390 & 0.9538 & -0.41 & 0.682 & 0.68 & 0.10 & 4.39 \\\text { Room/Brd } & 2.078 & 0.5076 & 4.09 & 0.000 & 7.99 & 2.95 & 21.60\end{array}$

Log-Likelihood = -21.883
Test that all slopes are zero: G = 62.083, DF = 3, P-Value = 0.000
Goodness-of-Fit Tests

$\begin{array}{lrcr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 143.551 & 76 & 0.000 \\ \text { Deviance } & 43.767 & 76 & 0.999 \\ \text { Hosmer-Lemeshow } & 15.731 & 8 & 0.046\end{array}$

-Referring to Table 14-11, which of the following is the correct interpretation for the SAT slope coefficient?

A) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of the school being a private school increases by 0.015 for each increase of one point in average SAT score.
B) Holding constant the effect of the other variables, the estimated school type increases by 0.015 for each increase of one point in average SAT score.
C) Holding constant the effect of the other variables, the estimated probability of the school being a private school increases by 0.015 for each increase of one point in average SAT score.
D) Holding constant the effect of the other variables, the estimated average value of school type increases by 0.015 for each increase of one point in average SAT score.

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

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

Question 60

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


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

Question 61

TABLE 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$



-Referring to Table 14-16, which of the following is a correct statement?

A) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class after adjusting for the effect of average teacher salary, and instructional spending per pupil.
B) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class, average teacher salary, and instructional spending per pupil after adjusting for the number of predictors and sample size.
C) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class, average teacher salary, and instructional spending per pupil.
D) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class holding constant the effect of average teacher salary, and instructional spending per pupil.

Question 62

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

Question 63

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

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

Question 64

TABLE 14-12
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below:
Y = Weight- loss (in pounds)
^X1 ^{= Length of time in weight- loss program (in months)
X}2 ^{= 1 if morning session, 0 if not
X}3 ^{= 1 if afternoon session, 0 if not (Base level = evening session)}
Data for 12 clients on a weight- loss program at the clinic were collected and used to fit the interaction model:
$Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$
Partial output from Microsoft Excel follows:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12 \\\hline\end{array}\end{array}$$

ANOVA
$F = 5.41118 \quad\text { Significance } F = 0.040201$

$\begin{array}{lcccr}\hline & \text {Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text {Length (X1)}& 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text {Morn Ses (X2)}& 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text {Aft Ses (X3)} & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text {Length*Morn Ses} & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text {Length * Aft Ses} & -0.54147 & 3.35988 & -0.161158 & 0.8773 \\\hline\end{array}$


TABLE 14-17
$\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\\text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\\text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\\text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\\text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\\text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\\text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\\text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45\end{array}$

Log-Likelihood = -4.890
Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000

Goodness-of-Fit Tests
$\begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array}$

Regression Staxistics
$\begin{array}{lc}\hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard E rror } & 12.4147\\\\\text { Observations}& 12\end{array}$

ANOVA
$F = 5.41118 \quad$ Significance $F = 0.040201$

$\begin{array}{lllll}\hline\text { Coefficients }&\text { Standard Error}&\text { tStat}\text { p-value }\\\hline\text { Intercept } & 0.089744 & 14.127 & 0.0060 & 0.9951 \\\text { Length }\left(X_{1}\right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \\\text { Morn Ses }\left(X_{2}\right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \\\text { Aft Ses }\left(X_{3}\right) & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\\text { Length }{ }^{*} \text { Morn S es }& 0.77058 & 3.562 & 0.216334 & 0.8359 \\\text { Length }{ }^{*} \text { Aft Ses }-0.54147 & 3.35988 & -0.161158 & 0.8773 &\end{array}$

-Referring to Table 14-12, in terms of the þ's in the model, give the average change in weight-loss (Y) for every 1 month increase in time in the program (X1) when attending the evening session.

A) þ₄ + þ₅
B) þ₁ + þ₄
C) þ₁ + þ₅
D) þ₁

Question 65

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average 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 (X₁), the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the EXCEL outputs of two regression models.
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$


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

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

Question 66

TABLE 14-13
As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is
$Y_{i}=\alpha+\beta_{1} X_{1 i}+\beta_{2} X_{2 i}+\beta_{3} X_{3 i}+\varepsilon$


where Y is the meter price;
^X1 ^{is the number of blocks to the quad;
X}2 ^{is a dummy variable that takes the value 1 if the meter}
is located in downtown and off campus and the value 0 otherwise;
^X3 ^{is a dummy variable that takes the value 1 if the meter}
is located outside of downtown and off campus, and the value 0 otherwise.
The following Excel results are obtained.
$\begin{array}{lc}\hline \text {Regression Statistics } \\\hline \text {Multiple R} & 0.9659 \\ \text {R Square}& 0.9331 \\ \text {Adjusted R Square} & 0.9294 \\ \text {Standard Error }& 0.0327 \\ \text {Observations} & 58 \\\hline\end{array}$

ANOVA
$\begin{array}{lrcccr}\hline & \text { d f } & \text { SS} & \text { M S } & \text { F }& \text { Significance F }\\\hline \text { Regression} & 3 & 0.8094 & 0.2698 & 251.1995 & 1.0964 \mathrm{E}-31 \\ \text { Residual }& 54 & 0.0580 & 0.0010 & & \\ \text { Total} & 57 & 0.8675 & & & \\\hline\end{array}$

$\begin{array}{lcccl}\hline & \text { Coefficients} & \text {Standard Error }& \text {t Stat }& \text { p-value} \\\hline \text {Intercept} & 0.5118 & 0.0136 & 37.4675 & 2.4904 \\\mathrm{X1 } & -0.0045 & 0.0034 & -1.3276 & 0.1898 \\\mathrm{X2 } & -0.2392 & 0.0123 & -19.3942 & 5.3581 \mathrm{E}-26 \\\mathrm{X3 } & -0.0002 & 0.0123 & -0.0214 & 0.9829 \\\hline\end{array}$


-Referring to Table 14-13, what is the correct interpretation for the estimated coefficient for X₂?

A) All else equal, the estimated average difference in costs between parking on campus, and parking outside of downtown and off campus is - $0.24 per hour.
B) All else equal, the estimated average difference in costs between parking in downtown and off campus, and parking either outside of downtown and off campus or on campus is - $0.24 per hour.
C) All else equal, the estimated average difference in costs between parking in downtown and off campus, and parking outside of downtown and off campus is - $0.24 per hour.
D) All else equal, the estimated average difference in costs between parking in downtown and off campus, and parking on campus is - $0.24 per hour.

Question 67

TABLE 14-15
An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is
Y = 40 - 0.05X₁ + 20X₂ - 0.1X₁X₂
where X₁ = horsepower
X₂ = 1 if 4 cylinders, 0 if 6 cylinders
Y = mileage.

-Referring to Table 14-15, the fitted model for predicting mileages for 4-cylinder cars is .

A) 60 - 0.15X1
B) 40 - 0.10X1
C) 40 - 0.05X1
D) 60 - 0.10X1

Question 68

TABLE 14-17
The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1
= favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age).
The Minitab output is given below:
$\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\\text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\\text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\\text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\\text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\\text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\\text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\\text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45\end{array}$

Log-Likelihood = -4.890
Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000

Goodness-of-Fit Tests
$\begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array}$


-Referring to Table 14-17, which of the following is the correct expression for the estimated model?

A) ln(odds ratio) = - 70.49 + 0.2868 Income + 1.0647 LawnSize - 12.744 Attitude - 0.200 Teenager + 1.0792 Age
B) Y = - 70.49 + 0.2868 Income + 1.0647 LawnSize - 12.744 Attitude - 0.200 Teenager + 1.0792 Age
C) ln(estimated odds ratio) = - 70.49 + 0.2868 Income + 1.0647 LawnSize - 12.744 Attitude - 0.200 Teenager + 1.0792 Age
D) Y^{^} = - 70.49 + 0.2868 Income + 1.0647 LawnSize - 12.744 Attitude - 0.200 Teenager + 1.0792 Age

Question 69

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 (X₁) and how he/she scored on a business aptitude test (X₂). A random sample of 8 employees provides the following:
$$\begin{array} { c r r r } \text { Employee } & Y & X _ { 1 } & X _ { 2 } \\\hline 1 & 100 & 10 & 7 \\2 & 90 & 3 & 10 \\3 & 80 & 8 & 9 \\4 & 70 & 5 & 4 \\5 & 60 & 5 & 8 \\6 & 50 & 7 & 5 \\7 & 40 & 1 & 4 \\8 & 30 & 1 & 1\end{array}$$

-Referring to Table 14-1, for these data, what is the value for the regression constant, b0?

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

Question 70

TABLE 14-11
A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on average total Scholastic Aptitude Test score (SAT) at the university or college, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).
The Minitab output is given below:
Logistic Regression Table
$\begin{array}{lrrrrrrr} & & & && \text { Odds } & \text { 95: CI } \\\text { Predictor } & {\text { Coef }} & \text { SE Coef } & Z &{\text { P }} & \text { Ratio } & \text { Lower } & \text { Upper } \\\text { Constant } &-27.118&6 .696& -4.05 & 0.000 & & & \\\text { SAT } & 0.015 & 0.004666 & 3.17 & 0.002 & 1.01 & 1.01 & 1.02 \\\text { Toefl550 } & -0.390 & 0.9538 & -0.41 & 0.682 & 0.68 & 0.10 & 4.39 \\\text { Room/Brd } & 2.078 & 0.5076 & 4.09 & 0.000 & 7.99 & 2.95 & 21.60\end{array}$

Log-Likelihood = -21.883
Test that all slopes are zero: G = 62.083, DF = 3, P-Value = 0.000
Goodness-of-Fit Tests

$\begin{array}{lrcr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 143.551 & 76 & 0.000 \\ \text { Deviance } & 43.767 & 76 & 0.999 \\ \text { Hosmer-Lemeshow } & 15.731 & 8 & 0.046\end{array}$

-Referring to Table 14-11, which of the following is the correct expression for the estimated model?

A) ln (estimated odds ratio) = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
B) Y = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
C) Y^{^} = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd
D) ln (odds ratio) = - 27.118 + 0.015 SAT - 0.390 Toefl550 + 2.078 Room/Brd

Question 71

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

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

Question 72

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.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l r } \hline \text { Multiple R } & 0.830 \\\text { R Square } & 0.689 \\\text { Adjusted R Square } & 0.662 \\\text { Standard Error } & 17501.643 \\\text { Observations } & 26\end{array}\end{array}$$

ANOVA
$\begin{array}{lcrrrr}\hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\\hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\\text {Residual }& 23 & 7045072780 & 306307512 & & \\\text {Total }& 25 & 22624849820 & & & \\\hline\end{array}$

$$\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\\text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\\text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\\text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\\hline\end{array}$$


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

Question 73

TABLE 14-16
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and
X₃ = Spending:
$\begin{array}{lr}\hline\text {Regression Statistics } \\\hline \text {Multiple R }& 0.7930 \\\text {R Square} & 0.6288 \\\text {Adjusted R Square} & 0.6029 \\\text {Standard Error }& 10.4570 \\\text {Observations }& 47 \\\hline\end{array}$


ANOVA
$\begin{array}{lccccc}\hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\\hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\\text { Residual} & 43 & 4702.02 & 109.35 & & \\\text { Total }& 46 & 12667.11 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\\hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\\%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\\text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$


-Referring to Table 14-16, which of the following is the correct null hypothesis to test whether daily average of the percentage of students attending class has any effect on percentage of students passing the proficiency test?

A) $H_{0}: \beta_{1}=0$
B) $H_{0}: \beta_{3}=0$
C) $H_{0}: \beta_{0}=0$
D) $H_{0}: \beta_{2}=0$

Question 74

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


-Referring to Table 14-4, which of the independent variables in the model are significant at the 2% level?

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

Question 75

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.
$\text {SUMMARY OUTPUT}$

$\begin{array}{lc}\hline \text { Regression Statistics } \\\hline \text {Multiple R} & 0.991 \\ \text {R Square }& 0.982 \\ \text {Adjusted R Square }& 0.976 \\ \text {Standard Error }& 0.299 \\ \text {Observations }& 10 \\\hline\end{array}$

ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\\hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\\hline\end{array}$


$\begin{array}{lcccr}\hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\\hline\end{array}$


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

A) 0.001
B) 0.05
C) 0.01
D) none of the above

Question 76

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


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

A) 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.
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 significant in explaining house size and should 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 less than 0.01.

Question 77

TABLE 14-13
As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is
$Y_{i}=\alpha+\beta_{1} X_{1 i}+\beta_{2} X_{2 i}+\beta_{3} X_{3 i}+\varepsilon$

where Y is the meter price;
^X1 ^{is the number of blocks to the quad;
X}2 ^{is a dummy variable that takes the value 1 if the meter}
is located in downtown and off campus and the value 0 otherwise;
^X3 ^{is a dummy variable that takes the value 1 if the meter}
is located outside of downtown and off campus, and the value 0 otherwise.
The following Excel results are obtained.
$\begin{array}{lc}\hline \text {Regression Statistics } \\\hline \text {Multiple R} & 0.9659 \\ \text {R Square}& 0.9331 \\ \text {Adjusted R Square} & 0.9294 \\ \text {Standard Error }& 0.0327 \\ \text {Observations} & 58 \\\hline\end{array}$

ANOVA
$\begin{array}{lrcccr}\hline & \text { d f } & \text { SS} & \text { M S } & \text { F }& \text { Significance F }\\\hline \text { Regression} & 3 & 0.8094 & 0.2698 & 251.1995 & 1.0964 \mathrm{E}-31 \\ \text { Residual }& 54 & 0.0580 & 0.0010 & & \\ \text { Total} & 57 & 0.8675 & & & \\\hline\end{array}$

$\begin{array}{lcccl}\hline & \text { Coefficients} & \text {Standard Error }& \text {t Stat }& \text { p-value} \\\hline \text {Intercept} & 0.5118 & 0.0136 & 37.4675 & 2.4904 \\\mathrm{X1 } & -0.0045 & 0.0034 & -1.3276 & 0.1898 \\\mathrm{X2 } & -0.2392 & 0.0123 & -19.3942 & 5.3581 \mathrm{E}-26 \\\mathrm{X3 } & -0.0002 & 0.0123 & -0.0214 & 0.9829 \\\hline\end{array}$


-Referring to Table 14-13, if one is already outside of downtown and off campus but decides to park 3 more blocks from the quad, the estimated average parking meter rate will

A) decrease by 0.4979.
B) decrease by 0.0139.
C) decrease by 0.0135.
D) decrease by 0.0045.

Question 78

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

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

Question 79

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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$


-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 not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
C) School is significant in explaining house size and should be included in the model because its p-value is more 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 80

TABLE 14-14
An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is
Y = 10 + 5X₁ + 8X₂
where X₁ = mortgage rate in %
X₂ = 1 if SF, 0 if LA
Y = demand in $100 per capita

-Referring to Table 14-14, the fitted model for predicting demand in San Francisco is .

A) 10 + 13X1
B) 18 + 5X1
C) 10 + 5X1
D) 15 + 8X2