Deck 14: Introduction to Multiple

Question 1

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

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

Answer 1

A

Question 2

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

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

Answer 2

B

Question 3

SCENARIO 14-2
Referring to Scenario 14-2, for these data, what is the estimated coefficient for performance
Rating, b1?

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

Answer 3

B

Question 4

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

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

Question 5

Question 6

Question 7

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

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

Question 8

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

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

Question 9

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

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

Question 10

SCENARIO 14-3
Referring to Scenario 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
Value of 0.971.What additional percentage of the total variation of consumption has been
Explained by including aggregate prices in the multiple regression?

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

Question 11

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

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

Question 12

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

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

Question 13

Question 14

SCENARIO 14-2
Referring to Scenario 14-2, for these data, what is the value for the regression constant, b0?

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

Question 15

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

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

Question 16

SCENARIO 14-1
Referring to Scenario 14-1, for these data, what is the estimated coefficient for the variable
Representing years an employee has been with the company, b1?

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

Question 17

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

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

Question 18

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

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

Question 19

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

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

Question 20

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

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

Question 21

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

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

Question 22

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, suppose the builder wants to test whether the coefficient on Size is
Significantly different from 0.What is the value of the relevant t-statistic?

A) -0.7630
B) 3.2708
C) 10.8668
D) 60.0864

Question 23

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

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

Question 24

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, which of the following values for the level of significance is the
Smallest for which at most one explanatory variable is significant individually?

A) 0.001
B) 0.010
C) 0.025
D) 0.050

Question 25

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, which of the following values for the level of significance is the
Smallest for which at least one explanatory variable is significant individually?

A) 0.005
B) 0.010
C) 0.025
D) 0.050

Question 26

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, what fraction of the variability in house size is explained by income
And size of family?

A) 17.56%
B) 70.69%
C) 71.89%
D) 84.79%

Question 27

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, which of the following values for the level of significance is the
Smallest for which the regression model as a whole is significant?

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

Question 28

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

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

Question 29

SCENARIO 14-3
Referring to Scenario 14-3, to test whether aggregate price index has a negative impact on
Consumption, the p-value is _______?

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

Question 30

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, which of the following values for the level of significance is the
Smallest for which each explanatory variable is significant individually?

A) 0.001
B) 0.010
C) 0.025
D) 0.050

Question 31

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, when the builder used a simple linear regression model with house
Size (House)as the dependent variable and family size (Size)as the independent variable, he
Obtained an r2 value of 1.25%.What additional percentage of the total variation in house size has
Been explained by including income in the multiple regression?

A) 15.00%
B) 70.64%
C) 71.50%
D) 73.62%

Question 32

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, at the 0.01 level of significance, what conclusion should the builder
Draw regarding the inclusion of Size in the regression model?

A) Size is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B) Size is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C) Size 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) Size 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 33

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, suppose the builder wants to test whether the coefficient on Income is
Significantly different from 0.What is the value of the relevant t-statistic?

A) -0.7630
B) 3.2708
C) 10.8668
D) 60.0864

Question 34

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

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

Question 35

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, which of the independent variables in the model are significant at the
5% level?

A) Income only
B) Size only
C) Income and Size
D) None

Question 36

SCENARIO 14-3
Referring to Scenario 14-3, to test for the significance of the coefficient on gross domestic
Product, the p-value is

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

Question 37

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

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

Question 38

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

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

Question 39

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

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

Question 40

SCENARIO 14-4
14-10 Introduction to Multiple Regression
Referring to Scenario 14-4, at the 0.01 level of significance, what conclusion should the builder
Reach regarding the inclusion of Income in the regression model?

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

Question 41

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

Question 42

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

Question 43

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

Question 44

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, one company in the sample had sales of $20 billion (Sales = 20,000).
This company spent $300 million on capital and $700 million on wages.What is the residual (in
Millions of dollars)for this data point?

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

Question 45

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, suppose the microeconomist wants to test whether the coefficient on
Capital is significantly different from 0.What is the value of the relevant t-statistic?

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

Question 46

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

Question 47

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what is the p-value for Capital?

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

Question 48

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what are the predicted sales (in millions of dollars)for a company
Spending $500 million on capital and $200 million on wages?

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

Question 49

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

Question 50

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, which of the independent variables in the model are significant at the
5% level?

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

Question 51

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what fraction of the variability in sales is explained by spending on
Capital and wages?

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

Question 52

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, which of the following values for α is the smallest for which the
Regression model as a whole is significant?

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

Question 53

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what is the p-value for testing whether Capital has a negative
Influence on corporate sales?

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

Question 54

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what is the p-value for Wages?

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

Question 55

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what is the p-value for testing whether Wages have a negative impact
On corporate sales?

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

Question 56

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what is the p-value for testing whether Wages have a positive impact
On corporate sales?

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

Question 57

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, one company in the sample had sales of $21.439 billion (Sales =
21,439).This company spent $300 million on capital and $700 million on wages.What is the
Residual (in millions of dollars)for this data point?

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

Question 58

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, at the 0.01 level of significance, what conclusion should the
Microeconomist reach regarding the inclusion of Capital in the regression model?

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

Question 59

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what are the predicted sales (in millions of dollars)for a company
Spending $100 million on capital and $100 million on wages?

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

Question 60

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.
Introduction to Multiple Regression 14-17
Referring to Scenario 14-5, what is the p-value for testing whether Capital has a positive
Influence on corporate sales?

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

Question 61

True or False: The total sum of squares (SST)in a regression model will never be greater than the
regression sum of squares (SSR).

Question 62

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

Question 63

True or False: The coefficient of multiple determination measures the proportion of the total
variation in the dependent variable that is explained by the set of independent variables.

Question 64

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 + 5X1 + 8X2
where X1 = mortgage rate in %
X2 = 1 if SF, 0 if LA
Y = demand in $100 per capita
Referring to Scenario 14-13, the predicted demand in Los Angeles when the mortgage rate is
8% is ________.

Question 65

True or False: A regression had the following results: SST = 82.55, SSE = 29.85.It can be said
that 63.84% of the variation in the dependent variable is explained by the independent variables
in the regression.

Question 66

True or False: If you have taken into account all relevant explanatory factors, the residuals
from a multiple regression model should be random.

Question 67

True or False: Consider a regression in which b2 = - 1.5 and the standard error of this
coefficient equals 0.3.To determine whether X2 is a significant explanatory variable, you would
compute an observed t-value of - 5.0.

Question 68

True or False: You have just computed a regression model in which the value of coefficient of
multiple determination is 0.57.To determine if this indicates that the independent variables
explain a significant portion of the variation in the dependent variable, you would perform an F-
test.

Question 69

True or False: A regression had the following results: SST = 102.55, SSE = 82.04.It can be
said that 90.0% of the variation in the dependent variable is explained by the independent
variables in the regression.

Question 70

True or False: A multiple regression is called "multiple" because it has several data points.

Question 71

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 + 5X1 + 8X2
where X1 = mortgage rate in %
X2 = 1 if SF, 0 if LA
Y = demand in $100 per capita
Referring to Scenario 14-13, holding constant the effect of city, each additional increase of 1%
in the mortgage rate would lead to an estimated increase of ________ in the mean demand.

Question 72

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 + 5X1 + 8X2
where X1 = mortgage rate in %
X2 = 1 if SF, 0 if LA
Y = demand in $100 per capita
Referring to Scenario 14-13, the predicted demand in San Francisco when the mortgage rate is
10% is ________.

Question 73

True or False: The slopes in a multiple regression model are called net regression coefficients.

Question 74

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

Question 75

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

Question 76

Question 77

True or False: A multiple regression is called "multiple" because it has several explanatory
variables.

Question 78

True or False: A regression had the following results: SST = 102.55, SSE = 82.04.It can be
said that 20.0% of the variation in the dependent variable is explained by the independent
variables in the regression.

Question 79

True or False: A regression had the following results: SST = 82.55, SSE = 29.85.It can be said
that 73.4% of the variation in the dependent variable is explained by the independent variables in
the regression.

Question 80

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 + 5X1 + 8X2
where X1 = mortgage rate in %
X2 = 1 if SF, 0 if LA
Y = demand in $100 per capita
Referring to Scenario 14-13, the effect of living in San Francisco rather than Los Angeles is to
increase the mean demand by an estimated ________.