Question 1

SCENARIO 14-20-A
You are the CEO of a dairy company. You are planning to expand milk production by purchasing
additional cows, lands and hiring more workers. From the existing 50 farms owned by the company,
you have collected data on total milk production (in liters), the number of milking cows, land size (in
acres) and the number of laborers. The data are shown below and also available in the Excel file
Scenario14-20-DataA.XLSX.
S 
You believe that the number of milking cows $\left( X _ { 1 } \right)$, land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm.
-Referring to Scenario 14-20-A, what is the value of the test statistic to determine whether there
is a significant relationship between total milk production and the entire set of explanatory
variables?

Accepted Answer

The answer of SCENARIO 14-20-A
You are the CEO of a...

Question 2

SCENARIO 14-15
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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per
pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with $Y = \%$ Passing as the dependent variable, $X _ { 1 } =$
Salaries and $X _ { 2 } =$ Spending:

$\begin{array}{lr}
\hline {\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.4276 \
\text { R Square } & 0.1828 \
\text { Adjusted R Square } & 0.1457 \
\text { Standard Error } & 5.7351 \
\text { Observations } & 47 \
\hline
\end{array}$

ANOVA

$\begin{array}{lrrrrrr}
\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \rho \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -72.9916 & 45.9106 & -1.5899 & 0.1190 & -165.5184 & 19.5352 \
\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \
\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & -1.5972 & 2.3455 \
\hline
\end{array}$

-Referring to Scenario 14-15, the null hypothesis $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$ implies that percentage of
students passing the proficiency test is not affected by either of the explanatory variables.

Accepted Answer

A) True 
 B)False

Question 3

SCENARIO 14-18
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 mean total Scholastic
Aptitude Test score (SAT) at the university or college and whether the TOEFL criterion is at least 90
(Toefl90 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and
0 otherwise).
The PHStat output is given below:
Binary Logistic Regression $$\begin{array}{l}
\begin{array} { l r r r r } 
\hline { \text { Predictor } } & \text { Coefficients } & \text { SE Coef } &  { Z } & p \text {-Value } \
\hline \text { Intercept } & - 3.9594 & 1.6741 & - 2.3650 & 0.0180 \
\text { SAT } & 0.0028 & 0.0011 & 2.5459 & 0.0109 \
\text { Toefl90:1 } & 0.1928 & 0.5827 & 0.3309 & 0.7407
\end{array}\\
\begin{array} { l l } 
\text { Deviance } & 101.9826
\end{array}
\end{array}$$
-Referring to Scenario 14-18, which of the following is the correct expression for the estimated model? a) $Y = - 3.9594 + 0.0028 S A T + 0.1928$ Toef 190
b) $\hat { Y } = - 3.9594 + 0.0028 S A T + 0.1928$ Toefl 90
c) $\ln ($ odds ratio $) = - 3.9594 + 0.0028 S A T + 0.1928$ Toefl 90
d) $\ln ($ estimated odds ratio $) = - 3.9594 + 0.0028$ SAT $+ 0.1928$ Toefl 90

Accepted Answer

The answer of SCENARIO 14-18
A logistic regression model was estimated...

Question 4

SCENARIO 14-10
You worked as an intern at We Always Win Car Insurance Company last summer. You notice that
individual car insurance premiums depend very much on the age of the individual and the number of
traffic tickets received by the individual. You performed a regression analysis in EXCEL and
obtained the following partial information: $\begin{array}{l}
\hline{ \text { Regression } \text { Statistics } } \
\hline \text { Multiple R } & 0.8546 \
\text { R Square } & 0.7303 \
\text { Adjusted R Square } & 0.6853 \
\text { Standard Error } & 226.7502 \
\text { Observations } & 15 \
\hline
\end{array}$

$\text { ANOVA }$

$\begin{array} { l r r r r r r } 
\hline & \text { Coefficients } & \text { Standard Error } & { \text { tStat } } & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \
\hline \text { Intercept } & 821.2617 & 161.9391 & 5.0714 & 0.0003 & 326.6124 & 1315.9111 \
\text { Age } & - 1.4061 & 2.5988 & - 0.5411 & 0.5984 & - 9.3444 & 6.5321 \
\text { Tickets } & 243.4401 & 43.2470 & 5.6291 & 0.0001 & 111.3406 & 375.5396 \
\hline
\end{array}$
-Referring to Scenario 14-10, the estimated mean change in insurance premiums for every 2
additional tickets received is _____.

Accepted Answer

The answer of SCENARIO 14-10
You worked as an intern at...

Question 5

SCENARIO 14-13
An econometrician is interested in evaluating the relationship of demand for building materials to
mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is $$Y = 10 + 5 X _ { 1 } + 8 X _ { 2 }$$
where
$$\begin{array} { l } 
\text { where }&\quad X _ { 1 } = \text { mortgage rate in } \% \
&X _ { 2 } = 1 \text { if SF, } 0 \text { if LA } \
&\quad\quad \quad \quad Y = \text { demand in } \$ 100 \text { per capita }
\end{array}$$
-Referring to Scenario 14-13, the predicted demand in Los Angeles when the mortgage rate is
8% is ________.

Accepted Answer

The answer of SCENARIO 14-13
An econometrician is interested in evaluating...

Question 6

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

Accepted Answer

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

Question 7

SCENARIO 14-15
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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per
pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with $Y = \%$ Passing as the dependent variable, $X _ { 1 } =$
Salaries and $X _ { 2 } =$ Spending:

$\begin{array}{lr}
\hline {\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.4276 \
\text { R Square } & 0.1828 \
\text { Adjusted R Square } & 0.1457 \
\text { Standard Error } & 5.7351 \
\text { Observations } & 47 \
\hline
\end{array}$

ANOVA

$\begin{array}{lrrrrrr}
\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \rho \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -72.9916 & 45.9106 & -1.5899 & 0.1190 & -165.5184 & 19.5352 \
\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \
\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & -1.5972 & 2.3455 \
\hline
\end{array}$

-Referring to Scenario 14-15, what are the lower and upper limits of the 95% confidence
interval estimate for the effect of a one thousand dollars increase in instructional spending per
pupil on the mean percentage of students passing the proficiency test?

Accepted Answer

The answer of SCENARIO 14-15
The superintendent of a school district...

Question 8

SCENARIO 14-20-B
You are the CEO of a dairy company. You are planning to expand milk production by purchasing
additional cows, lands and hiring more workers. From the existing 50 farms owned by the company,
you have collected data on total milk production (in liters), the number of milking cows, land size (in
acres) and the number of laborers. The data are shown below and also available in the Excel file
Scenario14-20-DataB.XLSX.
MILK 84686 101876 103248 70508 76072 86615 87508 105195 120351 68658 
You believe that the number of milking cows $\left( X _ { 1 } \right)$, land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm.
-Referring to Scenario 14-20-B, which of the following is the correct null hypothesis to test whether the number of laborers has any effect on the total milk production while holding constant
The effect of the other independent variables? a) $H _ { 0 } : \beta _ { 1 } = 0$
b) $H _ { 0 } : \beta _ { 2 } = 0$
c) $H _ { 0 } : \beta _ { 3 } = 0$
d) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$

Accepted Answer

The answer of SCENARIO 14-20-B
You are the CEO of a...

Question 9

SCENARIO 14-15
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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per
pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with $Y = \%$ Passing as the dependent variable, $X _ { 1 } =$
Salaries and $X _ { 2 } =$ Spending:

$\begin{array}{lr}
\hline {\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.4276 \
\text { R Square } & 0.1828 \
\text { Adjusted R Square } & 0.1457 \
\text { Standard Error } & 5.7351 \
\text { Observations } & 47 \
\hline
\end{array}$

ANOVA

$\begin{array}{lrrrrrr}
\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \rho \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -72.9916 & 45.9106 & -1.5899 & 0.1190 & -165.5184 & 19.5352 \
\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \
\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & -1.5972 & 2.3455 \
\hline
\end{array}$

-Referring to Scenario 14-15, you can conclude definitively that instructional
spending per pupil individually has no impact on the mean percentage of students passing the
proficiency test, taking into account the effect of mean teacher salary, at a 1% level of
significance based solely on but not actually computing the 99% the confidence interval estimate
for $\beta _ { 2 }$ .

Accepted Answer

A) True 
 B)False

Question 10

Multiple regression is the process of using several independent variables to
predict a number of dependent variables.

Accepted Answer

A) True 
 B)False

Question 11

SCENARIO 14-16
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a
car? Data on the following variables for 30 different vehicle models were collected: $Y$ (Accel Time): Acceleration time in sec.
$X _ { I }$ (Engine Size): c.c.
$X _ { 2 }$ (Sedan): 1 if the vehicle model is a sedan and 0 otherwise

The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.

$\begin{array}{lr}
\hline{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.6096 \
\text { R Square } & 0.3716 \
\text { Adjusted R Square } & 0.3251 \
\text { Standard Error } & 1.4629 \
\text { Observations } & 30 \
\hline
\end{array}$

ANOVA

$\begin{array}{lrrrrrr}
\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 7.1052 & 0.6574 & 10.8086 & 0.0000 & 5.7564 & 8.4540 \
\text { Engine Size } & -0.0005 & 0.0001 & -3.6477 & 0.0011 & -0.0008 & -0.0002 \
\text { Sedan } & 0.7264 & 0.5564 & 1.3056 & 0.2027 & -0.4152 & 1.8681 \
\hline
\end{array}$

-Referring to Scenario 14-16, the 0 to 60 miles per hour acceleration time of a
sedan is predicted to be 0.0005 seconds higher than that of a non-sedan with the same engine size.

Accepted Answer

A) True 
 B)False

Question 12

SCENARIO 14-20-A
You are the CEO of a dairy company. You are planning to expand milk production by purchasing
additional cows, lands and hiring more workers. From the existing 50 farms owned by the company,
you have collected data on total milk production (in liters), the number of milking cows, land size (in
acres) and the number of laborers. The data are shown below and also available in the Excel file
Scenario14-20-DataA.XLSX.
S 
You believe that the number of milking cows $\left( X _ { 1 } \right)$, land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm.
-Referring to Scenario 14-20-A, what are the numerator and denominator degrees of freedom,
respectively, for the test statistic to determine whether there is a significant relationship between
total milk production and the entire set of explanatory variables?

Accepted Answer

The answer of SCENARIO 14-20-A
You are the CEO of a...

Question 13

SCENARIO 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 and the number of firms that manufacture automobile parts in and around the city.
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 Scenario 14-9, what is the value of the coefficient of multiple determination?

Accepted Answer

The answer of SCENARIO 14-9
You decide to predict gasoline prices...

Question 14

SCENARIO 14-18
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 mean total Scholastic
Aptitude Test score (SAT) at the university or college and whether the TOEFL criterion is at least 90
(Toefl90 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and
0 otherwise).
The PHStat output is given below:
Binary Logistic Regression $$\begin{array}{l}
\begin{array} { l r r r r } 
\hline { \text { Predictor } } & \text { Coefficients } & \text { SE Coef } &  { Z } & p \text {-Value } \
\hline \text { Intercept } & - 3.9594 & 1.6741 & - 2.3650 & 0.0180 \
\text { SAT } & 0.0028 & 0.0011 & 2.5459 & 0.0109 \
\text { Toefl90:1 } & 0.1928 & 0.5827 & 0.3309 & 0.7407
\end{array}\\
\begin{array} { l l } 
\text { Deviance } & 101.9826
\end{array}
\end{array}$$
-Referring to Scenario 14-18, what should be the decision ('reject' or 'do not reject') on the null
hypothesis when testing whether Toefl90 makes a significant contribution to the model in the
presence of SAT at a 0.05 level of significance?

Accepted Answer

The answer of SCENARIO 14-18
A logistic regression model was estimated...

Exam 14: Introduction to Multiple

Multiple regression is the process of using several independent variables to predict a number of dependent variables.