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Chapter 12

Examining Relationships in Quantitative Research

Multiple Choice Questions

1. When knowledge about the behavior of one variable allows you to predict the behavior of another variable, this is another way of studying the _____ of the relationship.

A. presence

B. direction

C. strength of association

D. type

E. dispersion

Answer: A

Difficulty: Easy

Page: 312

2. While studying the relationship between advertising and sales growth, a researcher determines that the relationship is sometimes weak and at other times moderate. This variation from one situation to another is the variation in the _____ of the relationship between advertising and sales growth.

A. strength of association

B. presence

C. type

D. direction

E. dispersion

Answer: A

Difficulty: Medium

Page: 312

3. If a consistent and systematic relationship is not present between two variables:

A. a strong association is evident.

B. there is a moderate relationship.

C. an insubstantial relationship exists.

D. there is no relationship.

E. there is a weak association.

Answer: D

Difficulty: Medium

Page: 312

4. A _____ relationship is one between two variables whereby the strength and/or direction of their relationship changes over the range of both variables.

A. linear

B. curvilinear

C. constant

D. proportional

E. collinear

Answer: B

Difficulty: Easy

Page: 312

5. Which of the following is true of relationships between variables?

A. A curvilinear relationship is much simpler to work with than a linear relationship.

B. Marketers are often interested in describing the relationship between variables they think influence purchases of their products.

C. A negative relationship exists between two variables if low levels of one variable are associated with low levels of another.

D. The strength of association is determined by the size of the correlation coefficient, with smaller coefficients indicating a stronger association.

E. The null hypothesis for the Pearson correlation coefficient states that there is a strong association between two variables.

Answer: B

Difficulty: Medium

Page: 313

6. In a certain town, when the ownership of automobiles went up, the number of service stations also went up. This illustrates the concept of:

A. codependence.

B. co-alteration.

C. covariation.

D. coexistence.

E. convergence.

Answer: C

Difficulty: Medium

Page: 313

7. A researcher plots a scatter diagram of two variables. The dots on the plot are scattered roughly as a circle. This indicates that the relationship (covariation) between the two variables is:

A. linear, positive.

B. linear, negative.

C. circular, positive.

D. circular, negative.

E. very close to zero.

Answer: E

Difficulty: Medium

Page: 313

8. Which of the following statements is true of the correlation analysis?

A. The null hypothesis for the Pearson correlation coefficient states that there is always a strong association between two variables.

B. The Pearson correlation coefficient measures the degree of linear association which ranges from 0 to 1.0.

C. The larger the correlation coefficient, the weaker the association between two variables.

D. The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.

E. The Pearson correlation coefficient measures the degree of linear association between three variables.

Answer: D

Difficulty: Medium

Page: 316

9. In calculating the Pearson correlation coefficient, we assume that:

A. when the correlation coefficient is weak, there is a consistent, systematic relationship between the two variables.

B. the relationship we are trying to measure is curvilinear.

C. the variables we want to analyze have a binomially distributed population.

D. the variables have been measured using interval- or ratio-scaled measures.

E. when the correlation coefficient is strong and significant, the two variables are associated in a curvilinear fashion.

Answer: D

Difficulty: Medium

Page: 317

10. When the correlation coefficient is weak, the researcher must consider two possibilities:

A. there simply is no consistent, systematic relationship between the two items in the population and the association exists, but it is not linear and must be investigated further.

B. there is a consistent, systematic relationship between the two items in the population, but it is not linear and must be investigated further.

C. there simply is no consistent, systematic relationship between the two items in the population and the association exists, but it is linear and must be investigated further.

D. there simply is no consistent, systematic relationship between the two items in the population and the association exists, but it is linear and does not need to be investigated further.

E. there is a consistent, systematic relationship between the two items in the population, but it is linear and must be investigated further.

Answer: A

Difficulty: Medium

Page: 319

11. The coefficient of determination:

A. describes the variation in the dependent variable described by the control variable.

B. tells you the percent of the total variation in the independent variable explained by the dependent variable.

C. ranges from -1.0 to +1.0.

D. ranges from .00 to 1.0.

E. is a stronger measure than the Pearson correlation coefficient.

Answer: D

Difficulty: Medium

Page: 319

12. If the coefficient of correlation between two variables is -0.6, their coefficient of determination will be:

A. -0.6.

B. 0.4.

C. 0.36.

D. -0.36.

E. 0.6.

Answer: C

Difficulty: Medium

Page: 319

13. Which of the following is the recommended statistic when two variables have been measured using ordinal scales?

A. Goodman and Kruskals lambda

B. Spearman rank order correlation coefficient

C. Pearson correlation coefficient

D. Non-parametric hypothesis coefficient

E. Goodman and Kruskals gamma

Answer: B

Difficulty: Medium

Page: 320

14. _____ is a statistical technique that uses information about the relationship between an independent or predictor variable and a dependent variable to make predictions.

A. Non-parametric hypothesis coefficient

B. Covariation

C. Beta coefficient analysis

D. Bivariate regression analysis

E. Multiple regression analysis

Answer: D

Difficulty: Medium

Page: 322

15. How many predictor variables are there in a bivariate regression analysis?

A. 0

B. 1

C. 2

D. 3

E. 4

Answer: B

Difficulty: Medium

Page: 322

16. In bivariate regression analysis, the procedure used to determine the best-fitting line is called the:

A. least squares procedure.

B. squared error procedure.

C. sum of errors procedure.

D. least error procedure.

E. minimum error procedure.

Answer: A

Difficulty: Medium

Page: 323

17. With regard to the least squares procedure, any data point that does not fall on the regression line is the result of:

A. specific variance.

B. nonresidual variance.

C. unexplained variance.

D. sum of the squared errors.

E. multicollinearity.

Answer: C

Difficulty: Easy

Page: 323

18. Which of the following is true of the fundamentals of regression analysis?

A. A fundamental basis of regression analysis is the assumption of a circular relationship between the independent and dependent variables.

B. The betas are the regression coefficients.

C. The differences between actual and predicted values of the dependent variable are known as the regression coefficients and are represented by b.

D. The regression coefficient is calculated by squaring errors of each dependent variable.

E. If a regression coefficient is small, the variable is a better predictor of the dependent variable.

Answer: B

Difficulty: Medium

Page: 323

19. The statistical procedure that results in predictions with the lowest sum of squared differences between actual and predicted values in a regression equation is called:

A. SPSS.

B. unexplained variance.

C. ordinary least squares.

D. the slope.

E. regression coefficient.

Answer: C

Difficulty: Medium

Page: 324

20. Once the statistical significance of the regression coefficients is determined, which of the following questions would be answered?

A. How strong is the relationship between the independent and dependent variables?

B. Is there a relationship between the independent and dependent variables?

C. Is the regression coefficient significant?

D. Is the slope of the regression line significant?

E. Is the error term of the equation significant?

Answer: B

Difficulty: Medium

Page: 326

21. If a researcher is interested in measuring the effect of two independent variables on a dependent variable, he/she should use:

A. the Pearson correlation coefficient.

B. the Spearman correlation coefficient.

C. bivariate regression analysis.

D. multiple regression analysis.

E. simple regression.

Answer: D

Difficulty: Medium

Page: 327

22. Which of the following is true of a beta coefficient?

A. The beta coefficient ranges from 1.00 to 3.00, and is a positive correlation coefficient.

B. The beta coefficient is an estimated correlation coefficient.

C. The beta coefficient is an F-ratio that has been recalculated to have a mean of 1 and a standard deviation of 0.

D. A positive beta means as the size of an independent variable decreases, then the size of the dependent variable increases.

E. A beta coefficient shows the change in the dependent variable for each unit change in the independent variable.

Answer: E

Difficulty: Medium

Page: 327

23. Which of the following statements is true of statistical significance?

A. Many times not all the independent variables in a regression equation will be statistically significant.

B. If a regression coefficient is not statistically significant, the value of the dependent variable changes with the value of the statistically insignificant independent variable changes.

C. The statistical significance of each coefficient must be examined before the regression coefficients have been estimated.

D. If the F statistic is statistically significant, it means the chances of the regression model for a sample producing a large coefficient of determination are acceptably high.

E. If a regression coefficient is statistically significant, that means the independent variable does not have a relationship with the dependent variable.

Answer: A

Difficulty: Medium

Page: 328

24. The pattern of covariation around the regression line which is not constant around the regression line, and varies in some way when the values change from small to medium and large is known as _____.

A. multiple regression.

B. homoskedasticity

C. heteroskedasticity

D. normal distribution

E. constant association

Answer: C

Difficulty: Medium

Page: 329

25. Multicollinearity is a(n):

A. statistical procedure that estimates regression equation coefficients which produce the lowest sum of squared differences between the actual and predicted values of the dependent variable.

B. statistical technique which analyzes the linear relationship between a dependent variable and multiple independent variables by estimating coefficients for the equation for a straight line.

C. estimated regression coefficient which has been recalculated to have a mean of zero and a standard deviation of 1.

D. statistic which compares the amount of variation in the dependent measure explained or associated with the independent variables to the unexplained or error variance.

E. situation in which several independent variables are highly correlated with each other.

Answer: E

Difficulty: Medium

Page: 332

True/ False Questions

26. To measure whether a relationship exists, we rely on the concept of statistical significance.

Answer: True

Difficulty: Easy

Page: 312

27. The strength of association is determined by the size of the correlation coefficient.

Answer: True

Difficulty: Medium

Page: 312

28. When two variables have a curvilinear relationship, the formula that best describes the linkage is very simple.

Answer: False

Difficulty: Medium

Page: 313

29. Covariation refers to the degree of association between two variables.

Answer: True

Difficulty: Easy

Page: 313

30. A scatter plot wherein the dots form an ellipse can be described as a positive relationship.

Answer: True

Difficulty: Medium

Page: 313

31. A positive relationship between X and Y means that increases in X are associated with decreases in Y.

Answer: False

Difficulty: Medium

Page: 313

32. Scatter diagrams are a visual way to describe the relationship between two variables and the covariation they share.

Answer: True

Difficulty: Medium

Page: 316

33. If the correlation coefficient is between 0.0 and 0.2, then there is a good chance the null hypothesis will be rejected.

Answer: False

Difficulty: Medium

Page: 316

34. Use of the Pearson correlation coefficient assumes the variables have a normally distributed population.

Answer: True

Difficulty: Medium

Page: 317

35. The coefficient of determination is calculated by taking the square root of the correlation coefficient.

Answer: False

Difficulty: Medium

Page: 319

36. It is possible for a correlation to be statistically significant and still lack substantive significance.

Answer: True

Difficulty: Medium

Page: 319

37. Independent variables are also called predictor variables.

Answer: True

Difficulty: Easy

Page: 322

38. The use of a simple regression model assumes that the error terms associated with making predictions are dependently distributed.

Answer: False

Difficulty: Medium

Page: 322

39. Regression analysis assumes there is a straight line relationship between the independent and dependent variables.

Answer: True

Difficulty: Easy

Page: 322

40. The least squares procedure determines the best-fitting line by maximizing the vertical distances of all the data points from the line.

Answer: False

Difficulty: Medium

Page: 323

41. In a regression analysis, the horizontal distance between the estimated regression line and the actual data points is the unexplained variance called error.

Answer: False

Difficulty: Medium

Page: 323

42. In multiple regression, the value of beta coefficient can never be greater than 1.

Answer: True

Difficulty: Easy

Page: 327

43. Multiple regression analysis is an extension of bivariate regression.

Answer: True

Difficulty: Easy

Page: 327

44. A problem area for marketing researchers in multiple regression is when the independent variables are highly correlated among themselves.

Answer: True

Difficulty: Easy

Page: 332

45. When the correlations between independent variables in regression are high enough to cause problems, one approach is to create summated scales consisting of the independent variables that are highly correlated.

Answer: True

Difficulty: Easy

Page: 332

Essay Questions

46. Discuss the relationship between the Pearson correlation coefficient and the coefficient of determination.

Answer: The Pearson correlation coefficient is a statistical measure of the strength of a linear relationship between two metric variables. The coefficient of determination is obtained by squaring the correlation coefficient. It is a measure of the amount of variation in one variable accounted for by the other variable.

Difficulty: Medium

Page: 316-319

47. What are the several assumptions made while calculating the Pearson correlation coefficient?

Answer: In calculating the Pearson correlation coefficient, we are making several assumptions. First, we assume the two variables have been measured using interval- or ratio-scaled measures. If this is not the case, there are other types of correlation coefficients that can be computed which match the type of data on hand. A second assumption is that the relationship we are trying to measure is linear. That is, a straight line describes the relationship between the variables of interest. Use of the Pearson correlation coefficient also assumes the variables you want to analyze have a normally distributed population.

Difficulty: Medium

Page: 317

48. Discuss multiple regression analysis.

Answer: In most problems faced by managers, there are several independent variables that need to be examined for their influence on a dependent variable. Multiple regression analysis is the appropriate technique to use for these situations. The technique is an extension of bivariate regression. Multiple independent variables are entered into the regression equation, and for each variable a separate regression coefficient is calculated that describes its relationship with the dependent variable. The coefficients enable the marketing researcher to examine the relative influence of each independent variable on the dependent variable. The relationship between each independent variable and the dependent measure is still linear. Now, however, with the addition of multiple independent variables, we have to think of multiple independent variables instead of just a single one. The easiest way to analyze the relationships is to examine the regression coefficient for each independent variable, which represents the average amount of change expected in the dependent variable given a unit change in the value of the independent variable being examined.

Difficulty: Medium

Page: 327

49. Outline the procedure that should be followed in evaluating the results of a regression analysis.

Answer: The appropriate procedure to follow in evaluating the results of a regression analysis is:

1. Assess the statistical significance of the overall regression model using the F statistic and its associated probability.

2. Evaluate the obtained coefficient of determination to see how large it is.

3. Examine the individual regression coefficients and their t statistics to see which are statistically significant.

4. Look at the beta coefficients to assess relative influence.

Difficulty: Medium

Page: 328

50. Discuss the concept of multicollinearity.

Answer: Multicollinearity is a situation in which several independent variables are highly correlated with each other. This characteristic can result in difficulty in estimating separate or independent regression coefficients for the correlated variables. Since multicollinearity can create problems in using regression, analysts must always examine the logic of the signs and significance levels of the regression betas when independent variables are highly correlated. If a hypothesized relationship is the opposite of what is anticipated, one must look at a simple bivariate correlation of the two variables.

Difficulty: Medium

Page: 332

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