Chapter 23—Bivariate Statistical Analysis: Measures of Association TRUE/FALSE Price is frequently used as an independent variable in marketing research ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 559 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: REF: p 559 NAT: AACSB: Reflective Thinking Covariance is the extent to which a change in one variable corresponds systematically to a change in another ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 559 If r = -0.88, this indicates a weak relationship between the two variables under study ANS: F This indicates a strong negative relationship PTS: REF: p 559 NAT: AACSB: Reflective Thinking The measure of association used in the textbook is the Pearson product-moment correlation coefficient and its symbol is r ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 559 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: REF: p 559 NAT: AACSB: Reflective Thinking 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: REF: p 559 NAT: AACSB: Reflective Thinking 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: REF: p 561 NAT: AACSB: Reflective Thinking 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: 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: REF: p 564 NAT: AACSB: Reflective Thinking 11 The statistical significance of a correlation can be tested using the t-test ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 564 12 In regression analysis, the equation of a straight line is Y = a + X ANS: T PTS: 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: 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: 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: NAT: AACSB: Reflective Thinking REF: p 566 16 In regression, the standardized Y-intercept term is always ANS: F It is always PTS: 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: 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: 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: 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: 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: 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: 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: 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: NAT: AACSB: Reflective Thinking REF: p 572 25 The explanatory power of regression lies in the slope coefficient ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 572 MULTIPLE CHOICE 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: NAT: AACSB: Reflective Thinking REF: p 559 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: NAT: AACSB: Reflective Thinking REF: p 559 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: NAT: AACSB: Reflective Thinking REF: p 559 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: NAT: AACSB: Reflective Thinking REF: p 559 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: NAT: AACSB: Reflective Thinking REF: p 559 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 ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 559 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: NAT: AACSB: Reflective Thinking REF: p 559 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: NAT: AACSB: Reflective Thinking REF: p 559 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: 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: 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: 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: 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: 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 c +0.50 d +1.00 ANS: D PTS: 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 = c r = -1.00 d r = 100 ANS: B PTS: 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: 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: 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: 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: 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: 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: 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 would be: a -18.6 b 10.2 c 18.6 d © 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: 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: 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: 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: 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: 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: NAT: AACSB: Reflective Thinking REF: p 569 28 The statistical significance of a regression model is determined using which 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 a b c d t-test 2 F-test Z-test ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 570 COMPLETION 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: REF: p 559 NAT: AACSB: Reflective Thinking The Pearson product-moment correlation requires at least data ANS: interval PTS: REF: p 559 NAT: AACSB: Reflective Thinking The extent to which a change in one variable corresponds systematically to a change in another is referred to as ANS: covariance PTS: REF: p 559 NAT: AACSB: Reflective Thinking The Pearson product-moment correlation coefficient ranges between and ANS: -1.0, +1.0 +1.0, -1.0 PTS: REF: p 559 NAT: AACSB: Reflective Thinking The statistical measure of the association between two variables is known as the coefficient ANS: correlation PTS: REF: p 559 NAT: AACSB: Reflective Thinking A correlation coefficient indicates both the of the relationship between two variables and the of this relationship ANS: magnitude, direction PTS: 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: REF: p 561 NAT: AACSB: Reflective Thinking The square of the correlation coefficient is called the ANS: coefficient of determination PTS: REF: p 562 NAT: AACSB: Reflective Thinking If the correlation between two variables is -.55, the coefficient of determination is approximately ANS: + 0.30 PTS: 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: REF: p 562 NAT: AACSB: Reflective Thinking 11 In a correlation matrix, the values in the main diagonal equal ANS: 1.00 PTS: 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 PTS: 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: 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: REF: p 566 NAT: AACSB: Reflective Thinking 15 The test for the statistical significance of the regression model is the test ANS: F PTS: REF: p 570 NAT: AACSB: Reflective Thinking ESSAY 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: REF: p 560 NAT: AACSB: Reflective Thinking| AACSB: Communication 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: REF: p 562 NAT: AACSB: Reflective Thinking| AACSB: Communication 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: 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: REF: p 567 NAT: AACSB: Reflective Thinking| AACSB: Communication 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: 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  ... which 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 a b c d t -test 2 F -test Z -test. .. 15 The test for the statistical significance of the regression model is the test ANS: F PTS: REF: p 570 NAT: AACSB: Reflective Thinking ESSAY Discuss the common procedures for testing... REF: p 572 MULTIPLE CHOICE 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