Question 1

SCENARIO 17-1
A real estate builder wishes to determine how house size (House) is influenced by family income
(Income), family size (Size), and education of the head of household (School). House size is
measured in hundreds of square feet, income is measured in thousands of dollars, and education is in
years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel
output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adjusted R Square } & 0.726 \ \text { Standard Error } & 5.195 \ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \ \text { Residual } & & 1214.2264 & 26.3962 & & \ \text { Total } & 49 & 4820.0000 & & & \end{array}$

$\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$
-Referring to Scenario 17-1, which of the independent variables in the model are significant at the 5% level?
A) Income, Size, School
B) Income, Size
C) Size, School
D) Income, School

Accepted Answer

Income and Size have p-values (0.0003 and 0.0001, respectively) less than 0.05, indicating they are significant at the 5% level. School has a p-value of 0.1383, which is not significant at the 5% level.

Question 2

SCENARIO 17-1
A real estate builder wishes to determine how house size (House) is influenced by family income
(Income), family size (Size), and education of the head of household (School). House size is
measured in hundreds of square feet, income is measured in thousands of dollars, and education is in
years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel
output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adjusted R Square } & 0.726 \ \text { Standard Error } & 5.195 \ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \ \text { Residual } & & 1214.2264 & 26.3962 & & \ \text { Total } & 49 & 4820.0000 & & & \end{array}$

$\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$
-Referring to Scenario 17-1, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, he
Obtained an r2 value of 23.0%. What additional percentage of the total variation in house size has
Been explained by including family size and income in the multiple regression?
A) 2.8%
B) 51.8%
C) 72.6%
D) 74.8%

Accepted Answer

The R² value for the multiple regression is 74.8%. The R² value for the simple regression with only education is 23.0%. The additional percentage of variation explained by including family size and income is 74.8% - 23.0% = 51.8%.

Question 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). Annual data
From 30 years were collected. Which of the following would be the most appropriate analysis to
Perform?
A) Simple linear regression.
B) Multiple linear regression.
C) Exponential smoothing.
D) Autoregressive modeling for trend fitting and forecasting

Accepted Answer

Multiple linear regression is appropriate because the economist is interested in understanding how consumption is influenced by two independent variables: gross domestic product and aggregate price.

Question 4

A Paso Robles wine producer wanted to forecast the cases of Merlot wine sold. The number of cases of merlot wine sold in a 28-year period was collected. Which of the following would be the
Most appropriate analysis to perform?
A) The Marascuilo Procedure.
B) The Tukey-Kramer Procedure.
C) Least-squares forecasting with monthly or quarterly data.
D) Exponential smoothing modeling.

Accepted Answer

Exponential smoothing modeling is appropriate for forecasting time series data, such as the number of cases of wine sold over a period of time, as it helps to smooth out fluctuations and identify trends.

Question 5

Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to
Compare the 4 procedures, and collects the following numbers of patients from their own records:  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Procedure }$
$\begin{array}{l|cccc||c} 
& \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \
\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \
\text { Return } & 11 & 15 & 9 & 11 & 46 \
\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142
\end{array}$

Which of the following tests will be the most appropriate to find out which of the 4 procedures is the most effective?
a) $\chi ^ { 2 }$ test for difference in proportions.
b) $Z$ test for difference in proportions.
c) One-way ANOVA $F$ test for differences among more than two means
d) The Marascuilo procedure.

Accepted Answer

The answer of Four surgical procedures currently are used to...

Question 6

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in
Bushels per acre. Which of the following tests will be the most appropriate to find out if the
Different patches is advantageous in reducing the random error?
A) One-way ANOVA F test for differences among more than two means.
B) Randomized block F test for differences among more than two means.
C) Randomized block F test for block effect.
D) Two-way ANOVA F test for the variety effect.

Accepted Answer

The answer of An agronomist wants to compare the crop...

Question 7

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in
Bushels per acre. Which of the following tests will be the most appropriate to find out if there is
Any difference in crop yield among the 3 varieties?
A) Paired t test
B) One-way ANOVA F test for differences among more than two means.
C) Randomized block F test for differences among more than two means.
D) Two-way ANOVA F test for the variety effect.

Accepted Answer

The randomized block design is appropriate here because each patch of field acts as a block, controlling for variability among patches, while comparing the yields of the three varieties.

Question 8

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 mean of the percentage of students attending class (%
Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in
Dollars (Spending) of 47 schools in the state. She believed that holding everything else constant,
Instructional spending per pupil had a positive but decreasing impact on percentage. Which of
The following would be the most appropriate analysis to perform?
A) Autoregressive modeling.
B) Exponential smoothing.
C) Least-squares forecasting with monthly or quarterly data.
D) Linear regression with log transformation.

Accepted Answer

A linear regression with log transformation would be appropriate to model a positive but decreasing impact, as it can capture diminishing returns or non-linear relationships.

Question 9

SCENARIO 17-1
A real estate builder wishes to determine how house size (House) is influenced by family income
(Income), family size (Size), and education of the head of household (School). House size is
measured in hundreds of square feet, income is measured in thousands of dollars, and education is in
years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel
output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adjusted R Square } & 0.726 \ \text { Standard Error } & 5.195 \ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \ \text { Residual } & & 1214.2264 & 26.3962 & & \ \text { Total } & 49 & 4820.0000 & & & \end{array}$

$\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$
-Referring to Scenario 17-1, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15

Accepted Answer

The p-values for Income and Size are 0.0003 and 0.0001, respectively, both of which are less than 0.01, making them significant at the 0.01 level.

Question 10

SCENARIO 17-1
A real estate builder wishes to determine how house size (House) is influenced by family income
(Income), family size (Size), and education of the head of household (School). House size is
measured in hundreds of square feet, income is measured in thousands of dollars, and education is in
years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel
output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adjusted R Square } & 0.726 \ \text { Standard Error } & 5.195 \ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \ \text { Residual } & & 1214.2264 & 26.3962 & & \ \text { Total } & 49 & 4820.0000 & & & \end{array}$

$\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$
-Referring to Scenario 17-1, what fraction of the variability in house size is explained by income, size of family, and education?
A) 27.0%
B) 33.4%
C) 74.8%
D) 86.5%

Accepted Answer

The R Square value of 0.748 indicates that 74.8% of the variability in house size is explained by the model, which includes income, family size, and education.

Question 11

An investor wanted to forecast the price of a certain stock. He collected the mean daily price for the stock over the past 10 years. Which of the following would be the most appropriate analysis
To perform?
A) The Marascuilo Procedure.
B) The Tukey-Kramer Procedure.
C) Least-squares forecasting with monthly or quarterly data.
D) Autoregressive modeling.

Accepted Answer

Autoregressive modeling is appropriate for time series data like stock prices, as it uses past values to predict future values.

Question 12

A contractor wants to forecast the number of contracts in future quarters, using quarterly data on number of contracts over the last 10 years. Which of the following would be the most
Appropriate analysis to perform?
A) Autoregressive modeling.
B) One-way ANOVA.
C) Least-squares forecasting with monthly or quarterly data.
D) Two-way ANOVA.

Accepted Answer

The answer of A contractor wants to forecast the number...

Question 13

A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to see if the percentage favoring
The incumbent candidate is too erratic. Which of the following would be the most appropriate
Analysis to perform?
A) Multiple linear regression.
B) Exponential smoothing.
C) Construct a p-chart.
D) Perform a Levene's test.

Accepted Answer

A p-chart is used to monitor the proportion of defectives in a process, which in this case can be applied to track the proportion of voters favoring the incumbent over time to see if it is stable or erratic.

Question 14

The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is related to the type of community (urban, rural,
Suburban) in which an applicant resides. Which of the following tests will be the most
Appropriate?
A) $x ^ { 2 }$ test for independence.
B) Two-way ANOVA F test for the type of community effect.
C) Two-way ANOVA F test for interaction effect.
D) Kruskal-Wallis rank Test.

Accepted Answer

The $x ^ { 2 }$ test for independence is the most appropriate test for this scenario because it tests whether there is a relationship between two categorical variables. In this case, the two categorical variables are admissions status and type of community.

Question 15

A Paso Robles wine producer wanted to forecast the cases of Merlot wine sold. The number of cases of merlot wine sold in a 28-year period was collected. Which of the following would be the
Most appropriate analysis to perform?
A) The Marascuilo Procedure.
B) The Tukey-Kramer Procedure.
C) Least-squares forecasting with monthly or quarterly data.
D) Moving averages modeling.

Accepted Answer

The answer of A Paso Robles wine producer wanted to...

Question 16

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts
Hypothesize that when the gem is valued at very high prices, the demand increases with price due
To the status owners believe they gain in obtaining the gem. Data on price and quantity sold were
Collected for a sample of 35 rare gems of this type. Which of the following would be the most
Appropriate analysis to perform?
A) Quadratic regression model.
B) Exponential smoothing.
C) Autoregressive modeling for trend fitting and forecasting.
D) Least-squares forecasting with monthly or quarterly data.

Accepted Answer

A quadratic regression model is appropriate because it can capture the non-linear relationship between price and demand, including the hypothesized increase in demand at very high prices.

Question 17

A manager of a product sales group believes the number of sales made by an employee depends on how many years that employee has been with the company and how he/she scored on a
Business aptitude test. A random sample of 38 employees was selected to collect data on their
Number of sales, number of years with the company and scores on a business aptitude test.
Which of the following would you perform to draw conclusion on the belief?
A) One-way ANOVA.
B) Simple linear regression.
C) Two-way ANOVA
D) Multiple linear regression.

Accepted Answer

Multiple linear regression is appropriate here as it allows for the analysis of the relationship between one dependent variable (number of sales) and multiple independent variables (years with the company and aptitude test scores).

Question 18

SCENARIO 17-1
A real estate builder wishes to determine how house size (House) is influenced by family income
(Income), family size (Size), and education of the head of household (School). House size is
measured in hundreds of square feet, income is measured in thousands of dollars, and education is in
years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel
output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adjusted R Square } & 0.726 \ \text { Standard Error } & 5.195 \ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \ \text { Residual } & & 1214.2264 & 26.3962 & & \ \text { Total } & 49 & 4820.0000 & & & \end{array}$

$\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$
-Referring to Scenario 17-1, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15

Accepted Answer

The smallest level of significance for which every explanatory variable is significant individually is 0.15, as the p-value for "School" is 0.1383, which is less than 0.15 but greater than the other options.

Question 19

Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to
Compare the 4 procedures, and collects the following numbers of patients from their own records:  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Procedure }$
$\begin{array}{l|cccc||c} 
& \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \
\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \
\text { Return } & 11 & 15 & 9 & 11 & 46 \
\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142
\end{array}$

Which of the following tests will be the most appropriate to find out whether the 4 procedures are equally effective?
a) $\chi ^ { 2 }$ test for difference in proportions.
b) $Z$ test for difference in proportions.
c) One-way ANOVA $F$ test for differences among more than two means
d) Kruskal-Wallis rank Test.

Accepted Answer

The answer of Four surgical procedures currently are used to...

Question 20

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in
Bushels per acre. She has found out that the different varieties do have an impact on crop yield.
Which of the following tests will be the most appropriate to find out which variety will produce
The highest yield?
A) One-way ANOVA F test for differences among more than two means.
B) Kruskal-Wallis rank Test.
C) Tukey-Kramer multiple comparisons procedure for one-way ANOVA.
D) Tukey multiple comparisons procedure for randomized block designs.

Accepted Answer

The answer of An agronomist wants to compare the crop...

Quiz 17: Getting Ready to Analyze Data

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) . Annual data From 30 years were collected. Which of the following would be the most appropriate analysis to Perform?

A Paso Robles wine producer wanted to forecast the cases of Merlot wine sold. The number of cases of merlot wine sold in a 28-year period was collected. Which of the following would be the Most appropriate analysis to perform?

An investor wanted to forecast the price of a certain stock. He collected the mean daily price for the stock over the past 10 years. Which of the following would be the most appropriate analysis To perform?

A contractor wants to forecast the number of contracts in future quarters, using quarterly data on number of contracts over the last 10 years. Which of the following would be the most Appropriate analysis to perform?

The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is related to the type of community (urban, rural, Suburban) in which an applicant resides. Which of the following tests will be the most Appropriate?

A Paso Robles wine producer wanted to forecast the cases of Merlot wine sold. The number of cases of merlot wine sold in a 28-year period was collected. Which of the following would be the Most appropriate analysis to perform?