Question 1

Instruction 13-3
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
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.991 \ \text { R Square } & 0.982 \ \text { Adj. R Square } & 0.976 \ \text { Std. Error } & 0.299 \ \text { Observations } & 10 \end{array}$
ANOVA
$\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Signiff } \ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \ \text { Residual } & 7 & 0.6277 & 0.0897 & & \ \text { Total } & 9 & 34.0440 & & & \ & & & & & \ & \text { Coeff } & \text { StaError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } & \ \text { Intercept } & - 1.6335 & 0.5674 & - 0.152 & 0.8837 & \ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 & \ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 & \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 13-3,the p-value for the aggregated price index is

Accepted Answer

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

Question 2

Instruction 13-4
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 metres,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:
 OUTPUT
SUMMARY
Regression Statistics
$ \begin{array}{ll}\text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adj. R Square } & 0.726 \ \text { Std. Error } & 5.195 \ \text { Observations } & 50\end{array} $
ANOVA
$\begin{array}{llllll} 
& d f & \text { SS } & \text { MS } & \text { F } & \text { Siguif } \boldsymbol{F} \
\text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & & \
\text { Total } & 49 & 4820.0000 & & &
\end{array}$

$\begin{array}{lllll} 
& \text { Coeff } & \text { SttError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \
\text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \
\text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \
\text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \
\text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383
\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 13-4,which of the following values for the level of significance is the smallest for which all explanatory variables are significant individually?

Accepted Answer

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

Question 3

Instruction 13-14 The Head of the Accounting Department wanted to see if she could predict the average grade of students using the number of course units (credits)and total university entrance exam scores of each.She takes a sample of students and generates the following Microsoft Excel output: SUMMARY Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.916 \ \text { R Square } & 0.839 \ \text { Adj. R Square } & 0.732 \ \text { Std. Error } & 0.24685 \ \text { Observations } & 6 \end{array}$ ANOVA $\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Signif } \boldsymbol { F } \ \text { Regression } & 2 & 0.95219 & 0.47610 & 7.813 & 0.0646 \ \text { Residual } & 3 & 0.18281 & 0.06094 & & \ \text { Total } & 5 & 1.13500 & & & \ & & & & & \ & \text { Coeff } & \text { StdError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } & \ \text { Intercept } & 4.593897 & 1.13374542 & 4.052 & 0.0271 & \ \text { GDP } & - 0.247270 & 0.06268485 & - 3.945 & 0.0290 & \ \text { Price } & 0.001443 & 0.00101241 & 1.425 & 0.2494 & \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-14,the value of the coefficient of multiple determination,r²_Y_.12,is ________.

Accepted Answer

The answer of Instruction 13-14
The Head of the Accounting Department...

Question 4

Instruction 13-4
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 metres,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:
 OUTPUT
SUMMARY
Regression Statistics
$ \begin{array}{ll}\text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adj. R Square } & 0.726 \ \text { Std. Error } & 5.195 \ \text { Observations } & 50\end{array} $
ANOVA
$\begin{array}{llllll} 
& d f & \text { SS } & \text { MS } & F & \text { Siguif } F \
\text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & & \
\text { Total } & 49 & 4820.0000 & & &
\end{array}$

$\begin{array}{lllll} 
& \text { Coeff } & \text { StdError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \
\text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \
\text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \
\text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \
\text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383
\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 13-4,suppose the builder wants to test whether the coefficient on School is significantly different from 0.What is the value of the relevant t-statistic?

Accepted Answer

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

Question 5

Instruction 13-1
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 (XS1U1B11S1U1B0)and how he/she scored on a business aptitude test (XS1U1B12S1U1B0).A random sample of 8 employees provides the following:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Employee } & \text { Y } & \text { XI } & \text { X2 } \
\hline 1 & 100 & 10 & 7 \
\hline 2 & 90 & 3 & 10 \
\hline 3 & 80 & 8 & 9 \
\hline 4 & 70 & 5 & 4 \
\hline 5 & 60 & 5 & 8 \
\hline 6 & 50 & 7 & 5 \
\hline 7 & 40 & 1 & 4 \
\hline 8 & 30 & 1 & 1 \
\hline
\end{array}$$
-Referring to Instruction 13-1,for these data,what is the estimated coefficient for the variable representing scores on the aptitude test,b2?

Accepted Answer

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

Question 6

The purpose of the partial F test in multiple regression is to determine the predictive power of a model including all the X variables.

Accepted Answer

A) True 
 B)False

Question 7

Instruction 13-15
A financial analyst wanted to examine the relationship between salary (in $1,000)and 4 variables: age (XS1U1B11S1U1B0 = Age),experience in the field (XS1U1B12S1U1B0 = Exper),number of degrees (XS1U1B13S1U1B0 = Degrees),and number of previous jobs in the field (XS1U1B14S1U1B0 = Prevjobs).He took a sample of 20 employees and obtained the following Microsoft Excel output:
 SUMMARY
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.992 \ \text { R Square } & 0.984 \ \text { Adj. R Square } & 0.979 \ \text { Std. Error } & 2.26743 \ \text { Observations } & 20 \end{array}$
ANOVA
$\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Signif } \boldsymbol { F } \ \text { Regression } & 4 & 4609.83164 & 1152.45791 & 224.160 & 0.0001 \ \text { Residual } & 15 & 77.11836 & 5.14122 & & \ \text { Total } & 19 & 4686.95000 & & & \end{array}$
$\begin{array} { l l l l l } & \text { Coeff } & \text { StdError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } \ \text { Intercept } & - 9.611198 & 2.77988638 & - 3.457 & 0.0035 \ \text { Age } & 1.327695 & 0.11491930 & 11.553 & 0.0001 \ \text { Exper } & - 0.106705 & 0.14265559 & - 0.748 & 0.4660 \ \text { Degrees } & 7.311332 & 0.80324187 & 9.102 & 0.0001 \ \text { Prevjobs } & - 0.504168 & 0.44771573 & - 1.126 & 0.2778 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 13-15,the critical value of an F test on the entire regression for a level of significance of 0.01 is ________.

Accepted Answer

The answer of Instruction 13-15
A financial analyst wanted to examine...

Question 8

Instruction 13-14 The Head of the Accounting Department wanted to see if she could predict the average grade of students using the number of course units (credits)and total university entrance exam scores of each.She takes a sample of students and generates the following Microsoft Excel output: SUMMARY Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.916 \ \text { R Square } & 0.839 \ \text { Adj. R Square } & 0.732 \ \text { Std. Error } & 0.24685 \ \text { Observations } & 6 \end{array}$ ANOVA $\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Signif } \boldsymbol { F } \ \text { Regression } & 2 & 0.95219 & 0.47610 & 7.813 & 0.0646 \ \text { Residual } & 3 & 0.18281 & 0.06094 & & \ \text { Total } & 5 & 1.13500 & & & \ & & & & & \ & \text { Coeff } & \text { StdError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } & \ \text { Intercept } & 4.593897 & 1.13374542 & 4.052 & 0.0271 & \ \text { GDP } & - 0.247270 & 0.06268485 & - 3.945 & 0.0290 & \ \text { Price } & 0.001443 & 0.00101241 & 1.425 & 0.2494 & \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-14,the value of the adjusted coefficient of multiple determination,r²adj,is ________.

Accepted Answer

The answer of Instruction 13-14
The Head of the Accounting Department...

Question 9

Instruction 13-6
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 Celsius (XS1U1B11S1U1B0),the amount of insulation in cm (XS1U1B12S1U1B0),the number of windows in the house (XS1U1B13S1U1B0),and the age of the furnace in years (XS1U1B14S1U1B0).Given below are the Microsoft Excel outputs of two regression models.
 $\begin{array}{lr}
{\text { Model 1 }} \
\hline {\text { Regression Statistics }} \
\hline \text { R Square } & 0.8080 \
\text { Adjusted R Square } & 0.7568 \
\text { Observations } & 20 \
\hline
\end{array}$
ANOVA
$\begin{array}{lrrrrrr}
\hline & d f & & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 \mathrm{E}-05 \
\text { Residual } & 15 & 40262.3259 & 2684.155 & & \
\text { Total } & 19 & 209765.75 & & & \
\hline
\end{array}$

$\begin{array}{lrrrrrrr}
\hline & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {\text { P-value }} & \text { Lower 90.0\% } & \text { Upper 90.0\% } \
\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05 & 284.9327 & 557.9227 \
\mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \
\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \
\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \
\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702
\end{array}$ $\begin{array}{l}
\text { Model } 2\
\begin{array}{lr}
\hline {\text { Regression Statistics }} \
\hline \text { R Square } & 0.7768 \
\text { Adjusted R } & \
\text { Square } & 0.7506 \
\text { Observations } & 20 \
\hline
\end{array}
\end{array}$
ANOVA
$\begin{array}{lrrrrrr} 
& d f & &{\text { SS }} & M S & F & \text { Significance } F \
\hline \text { Regression } & & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \
\text { Residual } & 17 & 46807.5222 & 2753.384 & & \
\text { Total } & 19 & 209765.75 & & & \
\hline
\end{array}$

$\begin{array}{lrrrrrrr} 
& \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 3.17 \mathrm{E}-09 & 396.5273 & 582.1180 \
\mathrm{X}_{1} \text { (Temperature) } & -5.1103 & 0.6951 & -7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \
\mathrm{X}_{2} \text { (Insulation) } & -14.7195 & 4.8864 & -3.0123 & 0.0078 & -25.0290 & -4.4099
\end{array}$
-Referring to Instruction 13-6,what is the value of the partial F test statistic for H0: ?3 = ?4 = 0 vs.H1: At least one ?j ? 0,j = 3,4?

Accepted Answer

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

Question 10

Instruction 13-2
A lecturer in industrial relations believes that an individual's wage rate at a factory (Y)depends on his performance rating (XS1U1B11S1U1B0)and the number of economics courses the employee successfully completed at university (XS1U1B12S1U1B0).The lecturer randomly selects six workers and collects the following information:
 $\begin{array}{clll}
\underline{\text { Employee }} & \underline{Y(\$)} & \underline{X}_{1} &\underline{X}_{2}\
1 & 10 & 3 & 0 \
2 & 12 & 1 & 5 \
3 & 15 & 8 & 1 \
4 & 17 & 5 & 8 \
5 & 20 & 7 & 12 \
6 & 25 & 10 & 9
\end{array}$
-Referring to Instruction 13-2,an employee who took 12 economics courses scores 10 on the performance rating.What is her estimated expected wage rate?

Accepted Answer

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

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

Instruction 13-9
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect 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 kilograms)
XS1U1B11 S1U1B0= Length of time in weight-loss program (in months)
XS1U1B12S1U1B0 = 1 if morning session,0 if not
XS1U1B13S1U1B0 = 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 = β0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B11S1U1B0XS1U1B12S1U1B0 + βS1U1B15S1U1B0XS1U1B11S1U1B0XS1U1B13S1U1B0 + ε
Partial output from Microsoft Excel follows:
 Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.73514 \ \text { R Square } & 0.540438 \ \text { Adjusted R Square } & 0.157469 \ \text { Standard Error } & 12.4147 \ \text { Observations } & 12 \end{array}$
ANOVA
$\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \ & & & & \ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$
-In a multiple regression model,the adjusted r2

Accepted Answer

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

Question 13

A regression equation is computed on a sample of 40 cases and includes two predictor variables.The degrees of freedom for the partial F statistic are ________.

Accepted Answer

The answer of A regression equation is computed on a...

Question 14

Instruction 13-4
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 metres,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:
 OUTPUT
SUMMARY
Regression Statistics
$ \begin{array}{ll}\text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adj. R Square } & 0.726 \ \text { Std. Error } & 5.195 \ \text { Observations } & 50\end{array} $
ANOVA
$\begin{array}{llllll} 
& d f & \text { SS } & \text { MS } & \text { F } & \text { Siguif } \boldsymbol{F} \
\text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & & \
\text { Total } & 49 & 4820.0000 & & &
\end{array}$

$\begin{array}{lllll} 
& \text { Coeff } & \text { SttError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \
\text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \
\text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \
\text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \
\text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383
\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 13-4,which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?

Accepted Answer

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

Question 15

Instruction 13-8
You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premium depends very much on the age of the individual,the number of traffic tickets received by the individual,and the population density of the city in which the individual lives.You performed a regression analysis in Microsoft Excel and obtained the following information:
 $\begin{array}{l}
\text { Regression Analysis }\
\begin{array}{lr}
\hline {\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.63 \
\text { R Square } & 0.40 \
\text { Adjusted R Square } & 0.23 \
\text { Standard Error } & 50.00 \
\text { Observations } & 15.00
\end{array}
\end{array}$
ANOVA
$\begin{array}{lrrrrrr} 
& d f & & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 3 & & 5994.24 & 2.40 & 0.12 \
\text { Residual } & 11 & 27496.82 & & & \
\text { Total } & & 45479.54 & & &
\end{array}$

$\begin{array}{lrrrrrrr} 
& \text { Coefficients } & \text { Standard } & t \text { Stat } & \text { P-value } & \text { Lower 99.0\% } & \text { Upper 99.0\% } \
\hline \text { Intercept } & {\text { Error }} & & & & & \
\text { AGE } & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \
\text { TICKETS } & -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \
\text { DENSITY } & 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \
& -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91
\end{array}$
-Referring to Instruction 13-8,to test the significance of the multiple regression model,what are the degrees of freedom?

Accepted Answer

The answer of Instruction 13-8
You worked as an intern at...

Question 16

Instruction 13-4
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 metres,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:
 OUTPUT
SUMMARY
Regression Statistics
$ \begin{array}{ll}\text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adj. R Square } & 0.726 \ \text { Std. Error } & 5.195 \ \text { Observations } & 50\end{array} $
ANOVA
$\begin{array}{llllll} 
& d f & \text { SS } & \text { MS } & F & \text { Siguif } F \
\text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & & \
\text { Total } & 49 & 4820.0000 & & &
\end{array}$

$\begin{array}{lllll} 
& \text { Coeff } & \text { StdError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \
\text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \
\text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \
\text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \
\text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383
\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 13-4,at the 0.01 level of significance,what conclusion should the builder draw regarding the inclusion of Income in the regression model?

Accepted Answer

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

Question 17

Instruction 13-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.The Microsoft Excel output below shows results of this multiple regression.
 SUMMARY
Regression Statistics
\begin{tabular} { l r }  Multiple $\mathrm { R }$ & $0.830$ \ \hline Square & $0.689$ \end{tabular}
R Square $\quad 0.689$
Adj. R Square $\quad 0.662$
Std. Error $\quad 17501.643$
Observations 26
ANOVA
$\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Siguif } \boldsymbol { F } \ \text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \ \text { Residual } & 23 & 7045072780 & 306307512 & & \ \text { Total } & 25 & 22624849820 & & & \end{array}$
$\begin{array} { l l l l l } & \text { Coeff } & \text { StdError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-value } \ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 13-5,at the 0.01 level of significance,what conclusion should the microeconomist draw regarding the inclusion of Capital in the regression model?

Accepted Answer

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

Question 18

From the coefficient of multiple determination,you cannot detect the strength of the relationship between Y and any individual independent variable.

Accepted Answer

A) True 
 B)False

Question 19

Instruction 13-2
A lecturer in industrial relations believes that an individual's wage rate at a factory (Y)depends on his performance rating (XS1U1B11S1U1B0)and the number of economics courses the employee successfully completed at university (XS1U1B12S1U1B0).The lecturer randomly selects six workers and collects the following information:
 $\begin{array}{clll}
\underline{\text { Employee }} & \underline{Y(\$)} & \underline{X}_{1} &\underline{X}_{2}\
1 & 10 & 3 & 0 \
2 & 12 & 1 & 5 \
3 & 15 & 8 & 1 \
4 & 17 & 5 & 8 \
5 & 20 & 7 & 12 \
6 & 25 & 10 & 9
\end{array}$
-Referring to Instruction 13-2,for these data,what is the estimated coefficient for the number of economics courses taken,b2?

Accepted Answer

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

Question 20

Instruction 13-13
The education department's regional executive officer wanted to predict the percentage of students passing a Grade 6 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,
XS1U1B11S1U1B0 = % Attendance,XS1U1B12 S1U1B0= Salaries and XS1U1B13 S1U1B0= Spending:
 $\begin{array}{lr}
\hline {\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.7930 \
\text { R Square } & 0.6288 \
\text { Adjusted R } & 0.6029 \
\text { Square } & \
\text { Standard } & 10.4570 \
\text { Error } & \
\text { Observations } & 47
\end{array}$
ANOVA
$\begin{array}{lrrrrr} 
& \text { df }  &{\text { SS }} & \text { MS } & F&\text { Significance F } \

\hline \text { Regression } & 3 & 7965.08 & 2655.03 & 24.2802 & 0.0000 \
\text { Residual } & 43 & 4702.02 & 109.35 & & \
\text { Total } & 46 & 12667.11 & & &
\end{array}$

$\begin{array}{lrrrrrr} 
& \text { Coefficients } & \begin{array}{c}
\text { Standard } \
\text { Error }
\end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \
\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \
\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \
\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153
\end{array}$
-Referring to Instruction 13-13,there is sufficient evidence that at least one of the explanatory variables is related to the percentage of students passing the proficiency test.

Accepted Answer

A) True 
 B)False

Exam 13: Introduction to Multiple Regression

The purpose of the partial F test in multiple regression is to determine the predictive power of a model including all the X variables.

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

A regression equation is computed on a sample of 40 cases and includes two predictor variables.The degrees of freedom for the partial F statistic are ________.

From the coefficient of multiple determination,you cannot detect the strength of the relationship between Y and any individual independent variable.