Chapter 23—Bivariate Statistical Analysis: Measures of Association
TRUE/FALSE
1. Price is frequently used as an independent variable in marketing research.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
2. Measure of association is a general term that refers to causality.
ANS: F
Measure of association is a general term that refers to a number of bivariate statistical techniques used
to measure the strength of a relationship between two variables, and causality is not always
hypothesized or determined.
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
3. Covariance is the extent to which a change in one variable corresponds systematically to a change in
another.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
4. If r = -0.88, this indicates a weak relationship between the two variables under study.
ANS: F
This indicates a strong negative relationship.
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
5. The measure of association used in the textbook is the Pearson product-moment correlation coefficient
and its symbol is r.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
6. A Spearman correlation is more appropriate for interval and ratio data than is the Pearson productmoment correlation.
ANS: F
A Spearman correlation is more appropriate for ordinal level data.
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
7. The correlation coefficient, r, indicates the magnitude of the linear relationships but not the direction
of that relationship.
ANS: F
A correlation coefficient indicates both the magnitude of the linear relationship and the direction of
that relationship.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
8. Correlation always means that a causal relationship exists between the two variables under study.
ANS: F
Systematic covariation does not in and of itself establish causality. The relationship would also need
to be nonspurious and that any hypothesized “cause” would have to occur before any subsequent
effect.
PTS: 1
REF: p. 561
NAT: AACSB: Reflective Thinking
9. The square of the correlation coefficient indicates the part of the total variance of Y that can be
accounted for by X.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 563
10. In a correlation matrix, the main diagonal contains correlations of zero.
ANS: F
The main diagonal consists of correlations of 1.00 because it is the correlation of a variable with itself.
PTS: 1
REF: p. 564
NAT: AACSB: Reflective Thinking
11. The statistical significance of a correlation can be tested using the t-test.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 564
12. In regression analysis, the equation of a straight line is Y = a + X.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 564
13. In a regression equation, the slope of the line, , is the change in X that is due to a corresponding
change of one unit of Y.
ANS: F
In a regression equation, the slope of the line, , is the change in Y that is due to a corresponding
change of one unit of X.
PTS: 1
REF: p. 566
NAT: AACSB: Reflective Thinking
14. In most business research, the estimate of  in a regression equation is most important.
ANS: F
The estimate of  is most important because the explanatory power of regression rests with this
parameter because this is where the direction and strength of the relationship between the independent
and dependent variable is explained.
PTS: 1
REF: p. 566
NAT: AACSB: Reflective Thinking
15. In simple regression, raw parameter estimates reflect the measurement scale range.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 566
16. In regression, the standardized Y-intercept term is always 1.
ANS: F
It is always 0.
PTS: 1
REF: p. 566
NAT: AACSB: Reflective Thinking
17. If the purpose of the regression analysis is forecasting, then standardized regression estimates must be
used.
ANS: F
Raw parameter estimates must be used for forecasting.
PTS: 1
REF: p. 567
NAT: AACSB: Reflective Thinking
18. One way to determine the relationship between X and Y is to simply visually draw the best-fit straight
line through the points in the figure.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 567
19. The ordinary least-squares method of regression analysis is based on the logic of how much better a
regression line can predict values of Y compared to simply using the mean as a prediction.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 569
20. The least-squares regression line minimizes the sum of the squared deviations of the actual values
from the predicted values in the regression line.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 569
21. The statistical significance of a regression model is determined by a 2 test.
ANS: F
An F-test provides the statistical significance of a regression model.
PTS: 1
REF: p. 570
NAT: AACSB: Reflective Thinking
22. The coefficient of determination reflects the proportion of variance that can be explained by the
regression line.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 572
23. A rule of thumb for R2 is that it must be greater than 0.80 for a regression model to be significant.
ANS: F
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
Guidelines for R2 values are neither simple nor straightforward. Additionally, R2 does not provide a
test of significance, but rather reflects the proportion of variance explained by the regression line.
PTS: 1
REF: p. 572
NAT: AACSB: Reflective Thinking
24. The first step in interpreting simple regression output is to interpret the overall significance of the
model.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 572
25. The explanatory power of regression lies in the slope coefficient.
ANS: T
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 572
MULTIPLE CHOICE
1. When the on-time performance of airlines is used to predict the number of customer complaints in a
regression equation, on-time performance is the _____ variable and the number of customer
complaints is the _____ variable.
a. independent; dependent
b. dependent; dependent
c. dependent; independent
d. independent; predictor
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
2. A bivariate statistical technique that is used to measure the strength of the relationship between two
variables is called the:
a. one-group t-test
b. two-group t-test
c. measure of association
d. correlation matrix
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
3. The extent to which a change in one variable corresponds systematically to a change in another is
called:
a. spurious association
b. significance
c. covariance
d. standardized coefficient
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
4. The Pearson product-moment correlation requires what type of scale for the data?
a. nominal
b. interval
c. ordinal
d. all of the above
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
5. The Pearson product-moment correlation coefficient ranges between:
a. zero and +1.0
b. -1.0 and zero
c. -1.0 and +1.0
d. -2.0 and +2.0
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
6. If there is no relationship between two variables, the correlation coefficient between them would be:
a. +1.0
b. -1.0
c. +0.50
d. 0
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
7. If the correlation between two variables is - 0.75, this means that:
a. there is a weak positive relationship between the variables
b. there is a strong inverse relationship between the variables
c. there is a weak negative relationship between the variables
d. there is a strong positive relationship between the variables
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
8. When the correlation between two variables is +0.92, this means that as one variable _____ , the other
variable _____.
a. decreases; increases
b. increases; decreases
c. increases; increases
d. decreases; stays the same
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 559
9. The _____ is a measure obtained by squaring the correlation coefficient.
a. t-statistic
b. coefficient of determination (R2)
c. F-ratio
d. Pearson coefficient
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 562
10. Which of the following represents the proportion of the total variance of a variable accounted for by
another value of another variable?
a. product-moment correlation
b. correlation coefficient
c. F-test
d. coefficient of determination
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 562
11. If the correlation coefficient is - 0.62, the coefficient of determination is approximately:
a. + 0.38
b. + 0.62
c. - 0.38
d. - 0.23
ANS: A
PTS: 1
REF: p. 562
NAT: AACSB: Reflective Thinking| AACSB: Analytic
12. If the correlation between X and Y is -0.72, approximately what percentage of the variance in Y can be
explained by X?
a. 52 percent
b. 72 percent
c. 85 percent
d. 28 percent
ANS: A
PTS: 1
REF: p. 562
NAT: AACSB: Reflective Thinking| AACSB: Analytic
13. Which of the following is the standard form for reporting observed correlations among multiple
variables?
a. correlation matrix
b. contingency table
c. Pearson grid
d. inverse table
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 562
14. In a correlation matrix, the correlations in the main diagonal are all equal to:
a. -1.00
b. 0
c. +0.50
d. +1.00
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 564
15. If the t-test is used to test the significance of a correlation coefficient, the null hypothesis is:
a. r = +1.00
b. r = 0
c. r = -1.00
d. r = 100
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 564
16. In regression analysis, the symbol X is commonly used for the _____ variable, and the symbol Y is
commonly used for the _____ variable.
a. dependent; moderating
b. independent; dependent
c. dependent; independent
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
d. independent; moderating
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 564
17. In regression analysis, the dependent variable is also called the _____ variable.
a. predictor
b. exogenous
c. criterion
d. internal
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 564
18. In the regression equation, Y = a + X, Y is the:
a. dependent variable
b. slope
c. independent variable
d. Y-intercept
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 564
19. In the regression equation, Y = a + X ,  is the:
a. y-intercept
b. independent variable
c. slope of the regression line
d. dependent variable
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 566
20. In the regression equation, Y = a + X, a is the symbol for the:
a. slope of the regression line
b. Y-intercept of the regression line
c. dependent variable
d. independent variable
ANS: B
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 566
21. If the regression equation is: Y = 24.35 - 14.2 X , then 24.35 is the _____ , while -14.2 is the _____.
a. slope; y-intercept
b. independent variable; slope
c. dependent variable; y-intercept
d. Y-intercept; slope
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 567
22. If the regression equation is: Y = -4.2 + 3.6 X , then the expected score for Y when X is 4 would be:
a. -18.6
b. 10.2
c. 18.6
d. 4
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
ANS: B
PTS: 1
REF: p. 567
NAT: AACSB: Reflective Thinking|AACSB: Analytic
23. Which of the following provides a common metric allowing regression results to be compared to one
another no matter what the original scale range may have been?
a. standardized regression coefficient ()
b. 2
c. coefficient of determination (R2)
d. raw parameter estimates
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 567
24. Which of the following is most appropriate if the purpose of the regression analysis is forecasting?
a. standardized regression coefficient ()
b. Y-intercept 
c. coefficient of determination (R2)
d. raw parameter estimates
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 567
25. Lance is studying the relationship between sales training of the sales force and customer satisfaction
and loyalty. When researchers like Lance are focused on explanation rather than prediction, then
which of the following is most appropriate when using simple regression?
a. standardized regression coefficient ()
b. Y-intercept 
c. 2
d. raw parameter estimates
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 567
26. All of the following are simple regression estimation techniques EXCEPT:
a. chi-square estimation
b. maximum likelihood
c. visual estimation
d. ordinary least squares (OLS)
ANS: A
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 567
27. Which regression estimation technique is based on the logic of how much better a regression line can
predict values of Y compared to simply using the mean as a prediction for all observations no matter
what the value of X may be?
a. visual estimation
b. maximum likelihood
c. coefficient of determination
d. ordinary least squares (OLS)
ANS: D
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 569
28. The statistical significance of a regression model is determined using which test?
a. t-test
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
b. 2
c. F-test
d. Z-test
ANS: C
PTS: 1
NAT: AACSB: Reflective Thinking
REF: p. 570
COMPLETION
1. If the number of coupons given out at shopping malls is used to predict the number of tickets that will
be sold to a country and western band's performance at a local club, the number of coupons is the
____________________ variable.
ANS: independent
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
2. The Pearson product-moment correlation requires at least ____________________ data.
ANS: interval
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
3. The extent to which a change in one variable corresponds systematically to a change in another is
referred to as ____________________.
ANS: covariance
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
4. The Pearson product-moment correlation coefficient ranges between ____________________ and
____________________.
ANS:
-1.0, +1.0
+1.0, -1.0
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
5. The statistical measure of the association between two variables is known as the
____________________ coefficient.
ANS: correlation
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
6. A correlation coefficient indicates both the ____________________ of the relationship between two
variables and the ____________________ of this relationship.
ANS: magnitude, direction
PTS: 1
REF: p. 559
NAT: AACSB: Reflective Thinking
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
7. Covariation in which the association between variables is in the opposite direction indicates a(n)
____________________.
ANS:
negative relationship
inverse relationship
PTS: 1
REF: p. 561
NAT: AACSB: Reflective Thinking
8. The square of the correlation coefficient is called the ____________________.
ANS: coefficient of determination
PTS: 1
REF: p. 562
NAT: AACSB: Reflective Thinking
9. If the correlation between two variables is -.55, the coefficient of determination is approximately
____________________.
ANS: + 0.30
PTS: 1
REF: p. 562
NAT: AACSB: Reflective Thinking
10. The standard format for reporting the correlations between several variables is called the
____________________.
ANS: correlation matrix
PTS: 1
REF: p. 562
NAT: AACSB: Reflective Thinking
11. In a correlation matrix, the values in the main diagonal equal ____________________.
ANS: 1.00
PTS: 1
REF: p. 563
NAT: AACSB: Reflective Thinking
12. In testing for the significance of a correlation, the null hypothesis is that the correlation is equal to
____________________.
ANS:
zero
0
PTS: 1
REF: p. 564
NAT: AACSB: Reflective Thinking
13. The regression parameter that represents the height of the regression line relative to horizontal is
____________________.
ANS:
alpha

PTS: 1
REF: p. 566
NAT: AACSB: Reflective Thinking
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
14. In a regression equation, the slope of the regression line is denoted by the symbol
____________________.
ANS:
beta

PTS: 1
REF: p. 566
NAT: AACSB: Reflective Thinking
15. The test for the statistical significance of the regression model is the ____________________ test.
ANS: F
PTS: 1
REF: p. 570
NAT: AACSB: Reflective Thinking
ESSAY
1. Discuss the common procedures for testing association for data that are nominal, ordinal, and
interval/ratio.
ANS:
For nominal data, the statistical choice is cross-tabulation with 2 test. For ordinal data, the statistical
choice is the Spearman rank correlation or cross-tabulation with 2 test. For interval/ratio data, the
statistical choice is Pearson’s r or simple regression.
PTS: 1
REF: p. 560
NAT: AACSB: Reflective Thinking| AACSB: Communication
2. Compare and contrast correlation, covariance, and causation.
ANS:
Concomitant variation is one condition needed to establish a causal relationship between two
variables. When two variables covary, they display concomitant variation. This systematic
covariation does not in and of itself establish causality. The relationship would also need to be
nonspurious and that any hypothesized “cause” would have to occur before any subsequent effect.
PTS: 1
REF: p. 562
NAT: AACSB: Reflective Thinking| AACSB: Communication
3. Explain how regression differs from correlation.
ANS:
Regression analysis is a technique for measuring the linear association between a dependent and an
independent variable. Although simple regression and correlation are mathematically equivalent in
most respects, regression is a dependence technique where correlation is an interdependence technique.
A dependence technique draws a distinction between dependent and independent variables. An
interdependence technique does not make this distinction and simply is concerned with how variables
relate to one another.
PTS: 1
REF: p. 564
NAT: AACSB: Reflective Thinking| AACSB: Communication
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.
4. Discuss the pros and cons of raw regression estimates and standardized regression estimates and
discuss when each is appropriate.
ANS:
Regression parameter estimates can be presented in either raw or standardized form. One potential
problem with raw parameter estimates is due to the fact that they reflect the measurement scale
range. However, if the purpose of the regression analysis is forecasting, then raw parameter estimates
must be used. This is another way of saying that the researcher’s primary interest is prediction. A
standardized regression coefficient () provides a common metric allowing regression results to be
compared to one another no matter what the original scale range may have been. Standardized
regression estimates should be used when the researcher is testing explanatory hypotheses (i.e., when
the purpose of the research is more explanation than prediction).
PTS: 1
REF: p. 567
NAT: AACSB: Reflective Thinking| AACSB: Communication
5. Discuss the steps in interpreting a simple regression output.
ANS:
Interpreting simple regression output is a simple two-step process:
(1) Interpret the overall significance of the model. The output will include the “model F” and a
significance value. When the model F is significant (low p-value), the independent variable explains a
significant portion of the variation in the dependent variable. The coefficient of determination, or R2,
can be interpreted. This is the percentage of total variation in the dependent variable accounted for by
the independent variable.
(2) The individual parameter coefficient is interpreted. The t-value associated with the slope
coefficient can be interpreted.
PTS: 1
REF: pp. 572-573
NAT: AACSB: Reflective Thinking| AACSB: Communication
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in
whole or in part.