Deck 13: Linear Regression and Correlation

Question 1

The following correlations were computed as part of a multiple regression analysis that used
Education, job, and age to predict income.
Which is the dependent variable?

A) Income
B) Age
C) Education
D) Job

Answer 1

Income

Question 2

i. Multiple regression analysis examines the relationship of several dependent variables on the
Independent variable.
ii. A multiple regression equation defines the relationship between the dependent variable and the
Independent variables in the form of an equation.
iii. Autocorrelation often happens when data has been collected over periods of time.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Answer 2

(ii) and (iii) are correct statements but not (i).

Question 3

i. Multiple regression is used when two or more independent variables are used to predict a value
Of a single dependent variable.
ii. The values of b1, b2 and b3 in a multiple regression equation are called the net regression
Coefficients. They indicate the change in the predicted value for a unit change in one X when the
Other X variables are held constant.
iii. Autocorrelation often happens when data has been collected over periods of time.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Answer 3

(i), (ii), and (iii) are all correct statements.

Question 4

i. The values of b1, b2 and b3 in a multiple regression equation are called the net regression
Coefficients. They indicate the change in the predicted value for a unit change in one X when the
Other X variables are held constant.
ii. Multiple regression analysis examines the relationship of several dependent variables on the
Independent variable.
iii. A multiple regression equation defines the relationship between the dependent variable and the
Independent variables in the form of an equation.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 5

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, percent of population in the community holding a bachelor's
Degree as their highest level of education attained, and percent of population holding a High
School Diploma as their highest level of education attained.
Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment
Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%).
How many dependent variables are there in this regression?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 6

The information below is from the multiple regression analysis computer output for 28 teams in
Major League Baseball. The model is designed to predict wins using attendance, payroll, batting
Average, home runs, stolen bases, errors, and team ERA.
Predict the number of wins for a team with:
BATAVG = 0.260 HOMERUNS = 150 ERA = 3
STOLENBASE = 100 ERROR = 100
PAYROLL = 25(million)
ATTENDANCE = 3(million)

A) 77
B) 102
C) 187
D) 210
E) 186 Multiple Choice Difficulty: Hard Learning

Question 7

i. If an inverse relationship exists between the dependent variable and independent variables, the
Regression coefficients for the independent variables are positive.
ii. Given a multiple linear equation Y' = 5.1 + 2.2X1 - 3.5X2, assuming other things are held constant,
An increase of one unit in the second independent variable will cause a -3.5 unit change in Y.
iii. When the variance of the differences between the actual and the predicted values of the
Dependent variable are approximately the same, the variables are said to exhibit homoscedasticity.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 8

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, and percent of population in the community holding a
Bachelor's degree as their highest level of education attained.
Determine the regression equation.

A) Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%)
B) Poor (%) = -3.88 + 0.798 Single-Families (%) + 0.625 Unemployment Rate (%) - 0.170 Bachelor's Degree (%)
C) Poor (%) = 3.88 + 0.798 Single-Families (%) + 0.625 Unemployment Rate (%) - 0.170 Bachelor's Degree (%)
D) Poor (%) = -3.88 - 0.798 Single-Families (%) - 0.625 Unemployment Rate (%) - 0.170 Bachelor's Degree (%)
E) Poor (%) = 3.88 + 0.798 Single-Families (%) + 0.625 Unemployment Rate (%) + 0.170 Bachelor's Degree (%)

Question 9

How is the Y intercept in the multiple regression equation represented?

A) b1
B) x1
C) b2
D) x2
E) a

Question 10

i. A multiple regression equation defines the relationship between the dependent variable and the
Independent variables in the form of an equation.
ii. Autocorrelation often happens when data has been collected over periods of time.
iii. Homoscedasticity occurs when the variance of the residuals (Y - Y') is different for different
Values of Y'.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 11

A manager at a local bank analyzed the relationship between monthly salary and three independent
Variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 =
Clerical, 1 = technical). The following ANOVA summarizes the regression results:
In the regression model, which of the following are dummy variables?

A) Intercept
B) Service
C) Service and gender
D) Gender and job
E) Service, gender, and job

Question 12

i. Autocorrelation often happens when data has been collected over periods of time.
ii. Homoscedasticity occurs when the variance of the residuals (Y - Y') is different for different values
Of Y'.
iii. Violating the need for successive observations of the dependent variable to be uncorrelated is
Called autocorrelation.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 13

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, percent of population in the community holding a bachelor's
Degree as their highest level of education attained, and percent of population holding a High
School Diploma as their highest level of education attained.
Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment
Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%).-
What is the estimated percentage of poor persons living below the poverty line in a community with
5% of the community as single-families, a 5% unemployment rate, only 5% holding a Bachelor's
Degree and 25% having High School as their highest attained educational level?

A) 2.375
B) -2.375
C) 11.845
D) -11.845

Question 14

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, percent of population in the community holding a bachelor's
Degree as their highest level of education attained, and percent of population holding a High
School Diploma as their highest level of education attained.
Determine the regression equation.

A) Poor (%) = -3.81 - 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%)
B) Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) + 0.170 Bachelor's Degree (%) + 0.003 High School (%)
C) Poor (%) = 3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%)
D) Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%)
E) Poor (%) = 3.81 + 0.798 Single-Families (%) - 0.624 Unemployment Rate (%) + 0.170 Bachelor's Degree (%) - 0.003 High School (%)

Question 15

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, percent of population in the community holding a bachelor's
Degree as their highest level of education attained, and percent of population holding a High
School Diploma as their highest level of education attained.
Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment
Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%)
Interpret the numbers 3.81 and 0.798.

A) As the % of Single Families in an Ontario community increases, the % of poor families increase as well, with a maximum of 3.81% of the population being poor.
B) As the % of Single Families in an Ontario community increases, the % of poor families decrease.
C) There are 3.81% poor families and 0.798 Single-Families in Ontario communities.
D) 3.81 is the y-intercept. When all of the dependent variables have a value of zero, we can expect that 3.81% of the community to be poor. 0.789 indicates that for an extra 0.789% of
Poor families in a community, we can expect that the % of single families will increase by
1%)
E) When all of the independent variables have a value of zero, we can expect that -3.81% of the community to be poor, i.e. 0%. The 0.798 indicates that for each extra % of single

Question 16

i. The values of b1, b2 and b3 in a multiple regression equation are called the net regression
Coefficients. They indicate the change in the predicted value for a unit change in one X when the
Other X variables are held constant.
ii. A multiple regression equation defines the relationship between the dependent variable and the
Independent variables in the form of an equation.
iii. If an inverse relationship exists between the dependent variable and independent variables, the
Regression coefficients for the independent variables are positive.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 17

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, percent of population in the community holding a bachelor's
Degree as their highest level of education attained, and percent of population holding a High
School Diploma as their highest level of education attained.
Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment
Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%)
Which single event would have the strongest effect in reducing the % poor in Ontario?

A) Decreasing the % of single families by 5%.
B) Decreasing the Unemployment rate by 5%.
C) Increasing the % of persons with a Bachelor's Degree by 10%.
D) Decreasing the % of persons with a High School Diploma by 40%.
E) Increasing the % of persons with a Bachelor's Degree by 15%.

Question 18

Multiple regression analysis is applied when analyzing the relationship between

A) an independent variable and several dependent variables.
B) a dependent variable and several independent variables.
C) several dependent variables and several independent variables.
D) several regression equations and a single sample.

Question 19

i. Violating the need for successive observations of the dependent variable to be uncorrelated is
Called autocorrelation.
ii. If an inverse relationship exists between the dependent variable and independent variables, the
Regression coefficients for the independent variables are negative.
iii. Given a multiple linear equation Y' = 5.1 + 2.2X1 - 3.5X2, assuming other things are held constant,
An increase in one unit of the second independent variable will cause a -3.5 unit change in Y.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 20

i. Multiple regression is used when two or more independent variables are used to predict a value
Of a single dependent variable.
ii. The values of b1, b2, and b3 in a multiple regression equation are called the net regression
Coefficients. They indicate the change in the predicted value for a unit change in one X when the
Other X variables are held constant.
iii. Multiple regression analysis examines the relationship of several dependent variables on the
Independent variable.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 21

In regression analysis, the dferr = ________.

A) the sample size -1
B) the sample size - k -1
C) the number of dependent variables
D) the number of independent variables
E) the sample size - k

Question 22

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.09X5 + 26.8X6.
Explain the meaning of b4.

A) For each additional living child, their satisfaction index is expected to increase by 42 points.
B) For each additional $1,000 of annual income, their satisfaction index is expected to increase by 0.028 points.
C) For each additional $10,000 in assets, their satisfaction index is expected to increase by 0.12 points.
D) For each additional $10,000 in assets, their satisfaction index is expected to increase by 1.2 points.
E) For each additional $10,000 in assets, their satisfaction index is expected to increase by 12 points.

Question 23

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.09X5 + 26.8X6.
Explain the meaning of b5.

A) For each additional 10 points on the health status index, their satisfaction index is expected to increase by 9 points.
B) For each additional 10 points on the health status index, their satisfaction index is expected to increase by 0.09 points.
C) For each additional 10 points on the health status index, their satisfaction index is expected to increase by 0.9 points.
D) For each additional 10 points on the health status index, their satisfaction index is expected to drop by 0.09 points.
E) For each additional 10 points on the health status index, their satisfaction index is expected to decrease by 9 points.

Question 24

In a regression analysis, three independent variables are used in the equation based on a sample of
Forty observations. What are the degrees of freedom associated with the F-statistic?

A) 3 and 39
B) 4 and 40
C) 3 and 36
D) 2 and 39

Question 25

For a unit change in the first independent variable with other things being held constant, what
Change can be expected in the dependent variable in the multiple regression equation Y' = 5.2 +
6)3X1 - 7.1X2?

A) -7.1
B) +6.3
C) +5.2
D) +4.4

Question 26

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6.
What is the estimated index of satisfaction for a person who first married at 25, has an annual
Income of $26,500, has two children, has assets of $156,000, has in index of health status of 141,
And has 2.5 social activities per week?

A) 389.1
B) 421.6
C) 366.0
D) 601.6
E) 769.8

Question 27

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.09X5 + 26.8X6.
Explain the meaning of b6.

A) For each additional social activity per week, their satisfaction index is expected to increase by 26.8 points.
B) For each additional social activity per week, their satisfaction index is expected to increase by 2.68 points.
C) For each additional 10 points on the health status index, their satisfaction index is expected to increase by 0.9 points.
D) For each additional $10,000 in assets, their satisfaction index is expected to increase by 12 points.
E) For each additional living child, their satisfaction index is expected to increase by 42 points.

Question 28

The information below is from the multiple regression analysis computer output for 28 teams in
Major League Baseball. The model is designed to predict wins using attendance, payroll, batting
Average, home runs, stolen bases, errors, and team ERA.
The multiple correlation coefficient is:

A) 0.900
B) 0.930
C) 0.656
D) 0.867
E) 0.949

Question 29

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6.
What is the estimated index of satisfaction for a person who first married at 25, has an annual
Income of $60,000, has two children, has assets of $350,000, has in index of health status of 141,
And has 2 social activities per week?

A) 777.7
B) 796.6
C) 617.9
D) 601.6
E) 769.8

Question 30

In regression analysis, the dfreg = ________.

A) the sample size - 1
B) the sample size - k - 1
C) the number of dependent variables
D) the number of independent variables
E) the sample size - k

Question 31

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6.
What is the estimated index of satisfaction for a person who first married at 25, has an annual
Income of $100,000, has two children, has assets of $500,000, has in index of health status of 141,
And has 3.5 social activities per week?

A) 777.7
B) 796.6
C) 849.3
D) 601.6
E) 769.8

Question 32

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.09X5 + 26.8X6.
Explain the meaning of b2.

A) For each additional $1,000 of annual income, their satisfaction index is expected to increase by 0.28 points.
B) For each additional $1,000 of annual income, their satisfaction index is expected to increase by 2.8 points.
C) For each additional $1,000 of annual income, their satisfaction index is expected to increase by 28 points.
D) For each additional living child, their satisfaction index is expected to increase by 42 points.
E) For each additional living child, their satisfaction index is expected to increase by 4.2 points.

Question 33

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6.
What is the estimated index of satisfaction for a person who first married at 25, has an annual
Income of $46,000, has two children, has assets of $350,000, has in index of health status of 141,
And has 2.5 social activities per week?

A) 368.3
B) 421.6
C) 366.0
D) 627.3
E) 769.8

Question 34

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.09X5 + 26.8X6.
Explain the meaning of b3.

A) For each additional living child, their satisfaction index is expected to increase by 4.2 points.
B) For each additional living child, their satisfaction index is expected to increase by 42 points.
C) For each additional living child, their satisfaction index is expected to increase by 0.42 points.
D) For each additional $1,000 of annual income, their satisfaction index is expected to increase by 0.028 points.
E) For each additional $1,000 of annual income, their satisfaction index is expected to increase by 2.8 points.

Question 35

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6.
What is the estimated index of satisfaction for a person who first married at 25, has an annual
Income of $100,000, has two children, has assets of $500,000, has in index of health status of 141,
And has 3 social activities per week?

A) 777.7
B) 835.9
C) 588.6
D) 601.6
E) 769.8

Question 36

If the correlation between two variables, X and Y, is +0.67, what is the regression coefficient for
These two variables?

A) +0.67
B) > 0
C) < 0
D) = 0

Question 37

If there are four independent variables in a multiple regression equation, there are also four

A) Y-intercepts.
B) regression coefficients.
C) dependent variables.
D) constant terms.

Question 38

What are the degrees of freedom associated with the regression sum of squares?

A) Number of independent variables
B) 1
C) F-ratio
D) (n - 2)

Question 39

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6.
What is the estimated index of satisfaction for a person who first married at 25, has an annual
Income of $100,000, has two children, has assets of $500,000, has in index of health status of 141,
And has 2 social activities per week?

A) 777.7
B) 796.6
C) 588.6
D) 601.6
E) 809.1

Question 40

A sample of General Mills employees was studied to determine their degree of satisfaction with
Their present life. A special index, called the index of satisfaction, was used to measure satisfaction.
Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of
Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the
Average number of social activities per week (X6). Suppose the multiple regression equation is:
Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6
What is the estimated index of satisfaction for a person who first married at 25, has an annual
Income of $46,000, has two children, has assets of $200,000, has in index of health status of 141,
And has 2.5 social activities per week?

A) 368.3
B) 447.3
C) 366.0
D) 601.6
E) 769.8

Question 41

If the coefficient of multiple determination is 0.81, what percent of variation is not explained?

A) 19%
B) 90%
C) 66%
D) 81%

Question 42

What is the measurement of explained variation?

A) Coefficient of multiple determination
B) Coefficient of multiple nondetermination
C) Regression coefficient
D) Correlation matrix

Question 43

i. The multiple standard error of estimate for two independent variables measures the variation
About a regression plane.
ii. A multiple coefficient of determination equalling -0.76 is definitely possible.
iii. Multiple R2 measures the proportion of explained variation relative to total variation.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 44

i. Multiple R2 measures the proportion of explained variation.
ii. 90% of total variation in the dependent variable is explained by the independent variable for a
Multiple R2= 0.90.
iii. The multiple standard error of estimate measures the variation about the regression plane when
Two independent variables are considered.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 45

i. The multiple standard error of estimate measures the variation about the regression plane when
Two independent variables are considered.
ii. A coefficient of multiple determination equalling -0.76 is definitely possible.
iii. The number of degrees of freedom associated with the regression sum of squares in the
Regression equation model equals the number of independent variables.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 46

i. The multiple standard error of estimate measures the variation about the regression plane when
Two independent variables are considered.
ii. The multiple coefficient of determination, R2, reports the proportion of the variation in Y that is not
Explained by the variation in the set of independent variables.
iii. The coefficient of multiple determination reports the strength of the association between the
Dependent variable and the set of independent variables.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 47

If a multiple regression analysis is based on ten independent variables collected from a sample of
125 observations, what will be the value of the denominator in the calculation of the multiple
Standard error of estimate?

A) 125
B) 10
C) 114
D) 115

Question 48

i. 90% of total variation in the dependent variable is explained by the independent variable for a
Multiple R2= 0.90.
ii. The multiple standard error of estimate measures the variation about the regression plane when
Two independent variables are considered.
iii. The multiple coefficient of determination, R2, reports the proportion of the variation in Y that is
Not explained by the variation in the set of independent variables.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 49

The coefficient of determination measures the proportion of

A) explained variation relative to total variation.
B) variation due to the relationship among variables.
C) error variation relative to total variation.
D) variation due to regression.

Question 50

Which test statistic do we apply to test the null hypothesis that the multiple regression coefficients
Are all zero?

A) z
B) t
C) F
D) SPSS-X

Question 51

i. The multiple coefficient of determination, R2, reports the proportion of the variation in Y that is not
Explained by the variation in the set of independent variables.
ii. The coefficient of multiple determination reports the strength of the association between the
Dependent variable and the set of independent variables.
iii. The multiple standard error of estimate for two independent variables measures the variation
About a regression plane.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 52

How is the degree of association between the set of independent variables and the dependent
Variable is measured?

A) Confidence intervals
B) Autocorrelation
C) Coefficient of multiple determination
D) Standard error of estimate

Question 53

A manager at a local bank analyzed the relationship between monthly salary and three independent
Variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 =
Clerical, 1 = technical). The following ANOVA summarizes the regression results:
Based on the ANOVA, the multiple coefficient of determination is

A) 5.957%.
B) 59.3%.
C) 40.7%.
D) cannot be computed.

Question 54

The information below is from the multiple regression analysis computer output for 28 teams in
Major League Baseball. The model is designed to predict wins using attendance, payroll, batting
Average, home runs, stolen bases, errors, and team ERA.
The standard error of estimate is:

A) 4.467
B) 5.698
C) 5.864
D) 19.977
E) 15.917

Question 55

What does the multiple standard error of estimate measure?

A) Change in Y' for a change in X1.
B) Variation of the data points between Y and Y'.
C) Variation due to the relationship between the dependent and independent variables.
D) Amount of explained variation.

Question 56

i. A coefficient of multiple determination equalling -0.76 is definitely possible.
ii. Multiple R2 measures the proportion of explained variation relative to total variation.
iii. The number of degrees of freedom associated with the regression sum of squares in the
Regression equation model equals the number of independent variables.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 57

What happens as the scatter of data values about the regression plane increases?

A) Standard error of estimate increases.
B) R2 decreases.
C) (1 - R2) decreases.
D) Residual sum of squares decreases.
E) (1 - R2), residual sum of squares and standard error of estimate all increase, and R2 decreases.

Question 58

i. The multiple coefficient of determination, R2, reports the proportion of the variation in Y that is
Explained by the variation in the set of independent variables.
ii. The coefficient of multiple determination reports the strength of the association between the
Dependent variable and the set of independent variables.
iii. A coefficient of multiple determination equalling -0.76 is definitely possible.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 59

What is the range of values for multiple R?

A) -100% to -100% inclusive
B) -100% to 0% inclusive
C) 0% to +100% inclusive
D) Unlimited range

Question 60

i. The coefficient of multiple determination reports the strength of the association between the
Dependent variable and the set of independent variables.
ii. The multiple standard error of estimate for two independent variables measures the variation
About a regression plane.
iii. A multiple coefficient of determination equalling -0.76 is definitely possible.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 61

What can we conclude if the net regression coefficients in the population are not significantly
Different from zero?

A) Strong relationship exists among the variables.
B) No relationship exists between the dependent variable and the independent variables.
C) Independent variables are good predictors.
D) Good forecasts are possible.

Question 62

The information below is from the multiple regression analysis computer output for 28 teams in
Major League Baseball. The model is designed to predict wins using attendance, payroll, batting
Average, home runs, stolen bases, errors, and team ERA.
The critical value of F to be used in the global test of the model is: (5% level of significance)

A) 2.51
B) 2.58
C) 3.70
D) 5.57
E) 3.39

Question 63

The information below is from the multiple regression analysis computer output for 28 teams in
Major League Baseball. The model is designed to predict wins using attendance, payroll, batting
Average, home runs, stolen bases, errors, and team ERA.
The number of degrees of freedom to be used in determining the critical value of t to be used in a
Hypothesis test of the regression coefficients is:

A) 27
B) 26
C) 22
D) 21
E) 20

Question 64

The best example of an alternate hypothesis for a global test of a multiple regression model is:

A) H1: β1 = β2 = β3 = β4.
B) H1: β1 ≠ β2 ≠ β3 ≠ β4.
C) H1: Not all the β's are 0.
D) if F is less than 20.00 then fail to reject.

Question 65

i. If the null hypothesis β4 = 0 is not rejected, then the independent variable X4 has a strong effect in
Predicting the dependent variable.
ii. A dummy variable is added to the regression equation to control for error.
iii. A variable whose possible outcomes are coded as a "1" or a "0" is called a strong independent
Variable.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 66

The best example of a null hypothesis for testing an individual regression coefficient is:

A) H0: β1 = β2 = β3 = β4.
B) H0: μ1 = μ2 = μ3 = μ4.
C) H0: β1 = 0.
D) if F is greater than 20.00 then reject.

Question 67

What test investigates whether all the independent variables have zero net regression coefficients?

A) Multicollinearity
B) Autocorrelation
C) Global
D) Pearson

Question 68

i. A variable whose possible outcomes are coded as a "1" or a "0" is called a dummy variable.
ii. If the null hypothesis β4 = 0 is not rejected, then the independent variable X4 has no effect in
Predicting the dependent variable.
iii. A dummy variable is added to the regression equation to control for error.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 69

Hypotheses concerning individual regression coefficients are tested using which statistic?

A) t-statistic
B) z-statistic
C) χ2 (chi-square statistic)
D) H

Question 70

The information below is from the multiple regression analysis computer output for 28 teams in
Major League Baseball. The model is designed to predict wins using attendance, payroll, batting
Average, home runs, stolen bases, errors, and team ERA.
The t-value computed for testing the coefficient "Batg. Avg." is:

A) 112.991.
B) 2.086.
C) 7.438.
D) 2.832.
E) -1.593.

Question 71

The best example of a null hypothesis for a global test of a multiple regression model is:

A) H0: β1 = β2 = β3 = β4.
B) H0: μ1 = μ2 = μ3 = μ4.
C) H0: β1 = 0.
D) if F is greater than 20.00 then reject.

Question 72

i. A variable whose possible outcomes are coded as a "1" or a "0" is called a dummy variable.
ii. A dummy variable is added to the regression equation to control for error.
iii. If the null hypothesis β4 = 0 is not rejected, then the independent variable X4 has no effect in
Predicting the dependent variable.

A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question 73

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, and designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, percent of population in the community holding a bachelor's
Degree as their highest level of education attained, and percent of population holding a High
School Diploma as their highest level of education attained. Using the output below, determine
Which variable Angela should consider deleting.

A) It doesn't matter which she uses, the results are virtually the same in any case.
B) Angela should delete the high school information, because the P-value is over 0.05.
C) Angela should delete the bachelor's degree information, because the P-value is close to 0.05.
D) Angela should delete the unemployment rate information because the P-value is 0.00.
E) Angela should exclude the single-family and unemployment information because the P- value values are 0.

Question 74

Which of the following is a characteristic of the F-distribution?

A) Normally distributed
B) Positively skewed
C) Negatively skewed
D) Equal to the t-distribution

Question 75

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities.
She collected data on 60 communities from Statistics Canada. She selected the percentage of poor
Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by
Statistics Canada as a measure of poverty for a community, as the dependent variable. The
Independent variables selected are percent of single families in each community, the
Unemployment rate in each community, percent of population in the community holding a bachelor's
Degree as their highest level of education attained, and percent of population holding a High
School Diploma as their highest level of education attained. Using the outputs below for this data
Set, determine whether Angela should use the model with the high school data included, or the
Data without the high school data, and why.

A) It doesn't matter which she uses, the results are virtually the same in either case.
B) Angela should use the data that includes the high school information, because more information is always better than less information.
C) Angela should use the data that includes the high school information, because the calculated F value is lower.
D) Angela should include the high school data because the P-value is 0.977, close to 1.
E) Angela should exclude the high school data because the adjusted R-squared value is a little higher than in the data that includes the high school information.

Question 76

A manager at a local bank analyzed the relationship between monthly salary and three independent
Variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 =
Clerical, 1 = technical). The following ANOVA summarizes the regression results:
Based on the ANOVA and a 0.05 significance level, the global null hypothesis test of the multiple
Regression model.

A) will be rejected and conclude that monthly salary is related to all of the independent variables.
B) will be rejected and conclude that monthly salary is related to at least one of the independent variables.
C) will not be rejected.
D) will show a high multiple coefficient of determination.

Question 77

In multiple regression, a dummy variable can be included in a multiple regression model as

A) an additional quantitative variable.
B) a nominal variable with three or more values.
C) a nominal variable with only two values.
D) a new regression coefficient.

Question 78

A manager at a local bank analyzed the relationship between monthly salary and three independent
Variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 =
Clerical, 1 = technical). The following ANOVA summarizes the regression results:
Based on the hypothesis tests for the individual regression coefficients,

A) all the regression coefficients are not equal to zero.
B) "job" is the only significant variable in the model.
C) only months of service and gender are significantly related to monthly salary.
D) "service" is the only significant variable in the model.

Question 79

The information below is from the multiple regression analysis computer output for 28 teams in
Major League Baseball. The model is designed to predict wins using attendance, payroll, batting
Average, home runs, stolen bases, errors, and team ERA.
The computed F for the global test is:

A) 7.802
B) 25.695
C) 15.790
D) 26.981
E) 114.779

Question 80

A manager at a local bank analyzed the relationship between monthly salary and three independent
Variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 =
Clerical, 1 = technical). The following ANOVA summarizes the regression results:
The results for the variable gender show that,

A) males average $222.78 more than females in monthly salary.
B) females average $222.78 more than males in monthly salary.
C) gender is not related to monthly salary.
D) gender and months of service are correlated.