Chapter 17: Bivariate Correlation and Regression
Multiple Choice
1. If you are studying the impact of training on salesperson performance as indicated
on an exam taken by salespersons at the end of training, salesperson sales would
be the ____________ variable, and the salesperson exam score would be the
_____________ variable.
a. criterion, predictor
b. covariate, independent
c. independent, predictor
d. dependent, independent
e. none of the above
2. Which of the following techniques requires at that both variables are ratio or
interval data?
a. bivariate regression
b. ANOVA
c. t test
d. Pearson’s product-moment correlation
e. All are appropriate.
3. The percentage of total variation in the dependent variable that is described by the
independent variable is expressed by_________.
a. coefficient of determination
b. correlation coefficient
c. coefficient of covariation
d. regression coefficient
e. none of the above
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4. In a regression equation, sales would typically be the ______________ variable.
a. independent
b. coefficient
c. dependent
d. none of the above
5. ____________ is the mathematical technique for fitting a line that best describes
the relationship between two variables.
a. Pearson’s product-moment correlation
b. Least squares procedure
c. Chi-square test
d. Significance test
e. none of the above
6. Y
*
*
* *
* *
X
Given this plot, which of the following provides the best description?
a. perfect linear association
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b. strong exponential association
c. strong parabolic association
d. no association
e. strong curvilinear association
7. A regression equation that estimates the number of hours of study that impact a
test score would most likely produce what type of relationship?
a. positive
b. negative
c. curvilinear
d. none of the above
8. Research on fear appeal in advertising suggests that a moderate amount of fear is
most effective at achieving persuasion. That is, using not enough fear or too
much fear in advertising will not be effective. This is an example of what type of
relationship that regression might find?
a. positive linear
b. negative linear
c. curvilinear
d. no relationship
e. none of the above
9. Which of the following is the appropriate technique for correlation analysis,
which involves metric (interval or ratio) data?
a. Spearman’s rank-order correlation
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b. Jensen’s analysis of covariance
c. Kendall’s coefficient of concordance
d. Pearson’s product-moment correlation
e. none of the above
10. What are the possible values in correlation analysis?
a. 0 to 1
b. -1 to +1
c. -1 to 0
d. -.99 to + .99
e. none of the above
11. When two variables are not correlated at all, the correlation coefficient would be
_______.
a. -1
b. 0
c. 1
d. -2
e. none of the above
12. The explained variation by the regression is referred to as the:
a. total variation.
b. bivariate.
c. sum of squares due to regression .
d. none of the above
13. If a marketer wants to correlate an ordinal ranking of TV sets with the nominal
scale variable gender, the marketer would have to use_____________.
a. ANOVA
b. Pearson’s product-moment correlation
c. z-test
d. chi-square test
e. none of the above
14. Which test statistic is used to test the significance of the results of a regression
analysis?
a. F
b. t
c. Z
d. chi-square
e. none of the above
15. In regression, the higher the _________ value, the more likely the relationship
between variables is significant.
a. F
b. p
c. Z
d. none of the above
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16. Bivariate regression can not demonstrate:
a. when the two variables are linear.
b. when the two variables are strongly inversely related.
c. when the two variables are strongly positively related.
d. when the two variables are causally related.
17. A correlation analysis between sales and sales training scores results in R = +.98.
Which of the following best interprets the relationship between sales and sales
training?
a. 98% of the salespeople taking the test have higher sales.
b. The correlation between sales and sales training is very weak and
insignificant.
c. The correlation between sales and sales training is strong and positive,
indicating that higher sales training scores are closely associated with
higher sales and vice-versa.
d. 98% of the variation in sales is explained by variations in sales training
scores.
e. none of the above
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18.
Y
*
*
* *
*
*
*
X
Given this plot, which of the following provides the best description?
a. strong inverse linear association
b. strong exponential association
c. strong parabolic association
d. no association
e. strong curvilinear association
19. When the value of one variable increases at exactly the same rate as another
variable decreases, this is said to be a ___________________relationship.
a. strong positive linear
b. positive linear
c. perfect negative linear
d. parabolic
e. none of the above
20. In a regression output in SPSS, R2 represents:
a. the independent variable.
b. the dependent variable.
c. the estimated slope of the regression line.
d. the coefficient of determination.
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Ans: D
Difficulty: Medium
Response: See page 522
Ref: Bivariate Regression
Learning Objective 17.3: To become aware of the coefficient of determination R^2.
21. An R2 of .05 would indicate:
a. a significant relationship between X and Y.
b. a negative relationship between X and Y.
c. a very small relationship between X and Y.
d. none of the above
22. In a regression equation, which symbol represents the dependent variable?
a. Y
b. X
c. e
d. r
e. none of the above
23. Which of the following is not included in the equation for the coefficient of
determination?
a. explained variation
b. total variation
c. estimated variation
d. unexplained variation
24. ___________ are statistical methods of analyzing the relationship between two
variables.
a. Bivariate techniques
b. Univariate techniques
c. Multivariate techniques
d. None of the above
25. The dependent variable is also called the __________________.
a. Measure
b. Criterion
c. Principle
d. Standard
26. _______________ refers to analysis is one of strength of the linear relationship
between two variables when one is considered the independent variable and the
other the dependent variable
a. Multivariate regression
b. Univariate regression
c. Bivariate regression
d. None of the above
27. What is the variation not explained by the regression?
a. Dependent variation
b. Error sum of squares
c. Neither A nor B
d. Both A and B
True/False
28. Dependent variables are also known as predictor variables.
29. Bivariate statistical techniques are often used to establish cause and effect
relationships between two or more variables.
30. The coefficient of determination is used in correlation analysis.
32. A perfect correlation indicates that two variables are causally related.
33. A R = -.95 is always weaker than +.95, because positive relationships are more
significant than negative relationships.
34. In bivariate regression, both the independent and dependent variables are
measured in the form of nominal and/or ordinal data.
35. The variation explained by the regression equation is called SSR or sum of
squares due to the regression, and the variation not explained by the regression is
called SSE or the error sum of squares.
36. The least squares estimation procedure often results in a perfectly straight line.
37. The R2 statistic ranges from -1 to 1.
38. A scatter plot compares actual data to a predicted relationship between 2
variables.
39. Bivariate regression looks at the relationship between many variables.
40. An R2 of 0 indicates no relationship between variables.
41. Ordinal data cannot be analyzed using regression analysis.
42. In regression, the unexplained variation is referred to as error sum of squares
(SSE).
43. One way to study the relationship between the dependent and independent
variable is to plot the data in a scatter diagram.
44. In the equation for regression analysis, the letter X represents the independent
variable.
45. The correct formula for the analysis of variance used to test the significance of
results is F = MSR / MSE.
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Response: See page 525
Ref: Bivariate Analysis of Association
Learning Objective 17.2: To understand bivariate regression analysis.
Essay Questions
46. Some of the results of a regression analysis are as follows:
SSE = 52,500 SST = 485,200
Compute the Coefficient of Determination (R2) and interpret.
47. Interpret the correlation coefficient for the following data:
Sales Sales Training Score
45,000 98
34,500 74
23,750 57
51,450 99
41,000 85
The resulting correlation coefficient is +.98 and the probability of insignificance
is 3%.
48. Draw a graph depicting a strong but inverse correlation between X(Sales) and
number of times the sales force did not reach its quota. Interpret the relationship.
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sales force did not reach its quota increases, sales decrease. The resulting graph
will be linear and down sloping to the right (negative slope).
Difficulty: Medium
Response: See page 526-527
Ref: Correlation Analysis
Learning Objective 17.1: To comprehend the nature of correlation analysis.
Given the Correlation Matrix below, answer questions 49-51:
AGE
EDUCATION
AGE
1.00
.000
400
-.10
.221
400
INCOME
-.65
.000
400
.62
.000
400
EDUCATION
-.10
.221
400
1.00
.000
400
Assume that respondents answered the questions with ratio scale responses.
49. Which of the relationships in the matrix is the strongest?
50. How would you interpret the relationship between Education and Age?
51. How many pairs of responses were in this correlation analysis? ________