Chapter 24—Multivariate Statistical Analysis TRUE/FALSE Multivariate statistical analysis permit the researcher to consider the effects of three or more variables at the same time ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 581 The variate is a mathematical way in which a set of variables can be represented with one equation ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 581 The basic types of multivariate techniques are metric methods and nonmetric methods ANS: F The two basic types of mulitvariate techniques are dependence methods and interdependence methods PTS: REF: p 582 NAT: AACSB: Reflective Thinking Multidimensional scaling is a type of interdependence method ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 583 The type of measurement scales used will determine which multivariate statistical techniques are appropriate for the data ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 583 Nominal and ordinal scales are referred to as metric scales ANS: F These are nonmetric scales PTS: REF: p 583 NAT: AACSB: Reflective Thinking In multiple regression, the dependent variable must be continuous and interval-scaled ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 584 Multiple regression analysis includes a single independent variable but several dependent variables ANS: F Multiple regression analysis is an extension of simple regression analysis allowing a metric dependent variable to be predicted by multiple independent variables PTS: REF: p 584 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 9 Mulitvariate dependence techniques are variants of the general linear model (GLM) ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 584 10 Several dummy variables can be included in a regression model ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 585 11 In multiple regression, dummy variables are those that have no effect on the dependent variable ANS: F A dummy variable uses and to code the different levels of a dichotomous variable PTS: REF: p 585 NAT: AACSB: Reflective Thinking 12 In a regression equation, the beta coefficients indicate the effect on the dependent variable of a 1-unit increase in any of the independent variables ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 585 13 Partial correlations measure the variance inflation among independent variables ANS: F Partial correlation is the correlation between two variables after taking into account the fact that they are correlated with other variables too PTS: REF: p 586 NAT: AACSB: Reflective Thinking 14 In multiple regression, the coefficient of multiple determination indicates the percentage of the variation in Y that can be explained by all independent variables ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 586 15 Multicollinearity in regression analysis refers to how strongly interrelated the independent variables in a model are ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 589 16 MANOVA predicts multiple continuous dependent variables with multiple continuous independent variables ANS: F The independent variables are categorical PTS: REF: p 589 NAT: AACSB: Reflective Thinking 17 Discriminant analysis predicts a categorical dependent variable based on a linear combination of independent variables © 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 590 18 To determine whether the discriminant analysis can be used as a good predictor, information provided in the “confusion matrix” is used ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 592 19 The purpose of factor analysis is to summarize the information contained in a large number of variables into as large a number of factors as possible ANS: F Factor analysis is a multivariate interdependence technique that statistically identifies a reduced number of factors from a larger number of measured variables PTS: REF: p 593 NAT: AACSB: Reflective Thinking 20 A factor loading indicates how strongly a measured variable is correlated with a factor ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 594 21 The most common rule for extracting factors in factor analysis is to base the number of factors on the number of eigenvalues greater than 5.0 ANS: F The rule is an eigenvalue greater than 1.0 PTS: REF: p 594 NAT: AACSB: Reflective Thinking 22 Factor rotation is a mathematical way of simplifying factor results ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 594 23 In factor analysis, "communality" is a measure of the percentage of a variable's variation that can be explained by the factors ANS: T PTS: NAT: AACSB: Reflective Thinking REF: p 596 24 In cluster analysis, each cluster should have low internal homogeneity and high external heterogeneity ANS: F The cluster should have high internal (within-cluster) homogeneity and external (between-cluster) heterogeneity PTS: REF: p 597 NAT: AACSB: Reflective Thinking 25 Multidimensional scaling provides a means for placing objects in multidimensional space on the basis of respondents’ judgments of the similarity of objects © 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 599 MULTIPLE CHOICE Which type of analysis involves three or more variables? a univariate statistical analysis b bivariate statistical analysis c multivariate statistical analysis d all of the above ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 581 Which of the following is a mathematical way in which a set of variables can be represented with one equation? a structuralism b variate c ANOVA d synergy ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 581 The two basic groups of multivariate techniques are: a dependence methods and interdependence methods b primary methods and secondary methods c simple methods and complex methods d partial methods and complete methods ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 582 When a multivariate statistical technique is used to predict a dependent variable from several independent variables, the researcher is studying: a dependence b independence c interdependence d segments ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 583 Which of the following is a dependence method of analysis? a structural equations modeling b multiple regression analysis c multiple discriminant analysis d all of the above ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 583 All of the following are examples of dependence methods of analysis EXCEPT: a multiple regression analysis b multiple discriminant analysis © 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 c cluster analysis d multivariate analysis of variance ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 583 Which of the following is an example of an interdependence analysis method? a multidimensional scaling b multiple regression analysis c conjoint analysis d all of the above ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 583 All of the following are examples of interdependence methods of analysis EXCEPT: a factor analysis b cluster analysis c multidimensional scaling d conjoint analysis ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 583 Nominal and ordinal scales are examples of _ scales, while interval and ratio scales are examples of _scales a metric; co-metric b nonmetric; metric c nonmetric; advanced d metric; continuous ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 583 10 If the analysis contains only one dependent variable and that variable is metric, the appropriate statistical analysis is: a multiple discriminant analysis b conjoint analysis c multivariate ANOVA d multiple regression ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 584 11 Which of the following is an appropriate technique when the inputs are metric? a cluster analysis b metric multidimensional scaling c factor analysis d all of the above ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 584 12 Mulitvariate dependence techniques are variants of the _, which is a way of modeling some process based on how different variables cause fluctuations from the average dependent variable a ordinary linear model (OLM) © 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 weighted average model (WAM) c general linear model (GLM) d metric scaling model (MSM) ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 584 13 When a researcher is attempting to predict sales volume by using building permits, amount of advertising, and the income levels of residents, the researcher is using: a univariate analysis b a chi-square analysis c multiple regression analysis d factor analysis ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 584 14 Which analysis is portrayed by the equation: Y = bο + b1X1 + b2X2 + b3X3 + bnXn? a simple regression b multiple regression c chi-square d factor analysis ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 584 15 A variable that is coded as either zero or one and that has two distinct levels is called a(n): a regression variable b dummy variable c MANOVA variable d ANOVA variable ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 585 16 The correlation between two variables after taking into account the fact that they are correlated with other variables too is called: a partial correlation b standardized correlation c raw correlation d variant correlation ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 586 17 If the regression equation is: Y = 98.3 +.35X1 + 22.3X2, the predicted value for Y when X1 = and X2 = is: a 118.45 b 210.85 c 67.23 d 98.3 ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 586 © 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 18 A value of R2 = 0.40 means that _ percent of the variance in the dependent variable is explained by the independent variables a 80 b 64 c 40 d 16 ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 586 19 In the following formula, k stands for: a b c d the number of observations the degrees of freedom of the denominator the number of independent variables the sample size ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 588 20 In the formula for the F-test in multiple regression, n - k - stands for: a b c d the degrees of freedom of the numerator the number of observations the degrees of freedom of the denominator the number of independent variables ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 588 21 Jeff is analyzing data and is concerned over how strongly interrelated the independent variables in his model are Jeff is concerned about: a multicollinearity b MANOVA c degrees of freedom d convergence ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 588 22 Which of the following is computed by most regression programs and provide an indication of how much multicollinearity exists among a set of independent variables? a χ2 b β c collinear coefficient d variance inflation factor (VIF) ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 588 23 Which of the following suggests problems with multicollinearity? © 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 VIF > 5.0 β < 3.0 Power > 0.8 α > 0.8 ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 588 24 If the analysis predicts several continuous dependent variables with several categorical independent variables, the appropriate statistical technique is: a multiple regression b multiple discriminant analysis c conjoint analysis d MANOVA ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 589 25 Which type of analysis attempts to predict a categorical dependent variable? a factor analysis b discriminant analysis c regression analysis d linear analysis ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 590 26 If a bank wants to differentiate between successful and unsuccessful credit risks for home mortgage loans, it should use: a factor analysis b multidimensional scaling c MANOVA d discriminant analysis ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 590 27 In discriminant analysis, a linear combination of independent variables that explains group memberships is known as a(n): a regression equation b discriminant function c discriminant factor d n-way ANOVA ANS: B PTS: NAT: AACSB: Reflective Thinking REF: p 590 28 Which multivariate analysis statistically identifies a reduced number of factors from a larger number of measured variables? a factor analysis b regression c discriminant analysis d logit analysis ANS: A PTS: REF: p 593 © 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 NAT: AACSB: Reflective Thinking 29 Which of the following indicates how strongly a measured variable is correlated with a factor? a factor β b discriminator c factor link d factor loading ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 593 30 A researcher has 57 variables in a large dataset and wishes to summarize the information from them into a reduced set of variables Which multivariate technique should be used? a factor analysis b multidimensional scaling c logit analysis d regression analysis ANS: A PTS: NAT: AACSB: Reflective Thinking REF: p 593 31 A mathematical way of simplifying factor analysis results is: a factor loading b factor reduction c factor rotation d factor analysis ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 594 32 In cluster analysis, the researcher wants clusters to have high within-clusters and high between-cluster a independence; dependence b significance; insignificance c heterogeneity; homogeneity d homogeneity; heterogeneity ANS: D PTS: NAT: AACSB: Reflective Thinking REF: p 597 33 General Mills would like to “see” a picture of how its brands are perceived by consumers compared to competitive brands Which statistical technique can measure brands in multidimensional space on the basis of respondents’ judgements of the similarity of the brands? a structural equations modeling b factor analysis c multidimensional scaling d partial positioning ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 599 COMPLETION Statistical methods that permit the study of three or more variables at the same time are called statistical analysis © 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: multivariate PTS: REF: p 581 NAT: AACSB: Reflective Thinking The two types of multivariate techniques are methods and methods ANS: dependence, interdependence interdependance, dependance PTS: REF: p 582 NAT: AACSB: Reflective Thinking Multivariate techniques that try to group things together are known as methods ANS: interdependence PTS: REF: p 583 NAT: AACSB: Reflective Thinking When an analysis studies the effect of several independent variables on a single dependent variable that is interval-scaled, this is called analysis ANS: multiple regression PTS: REF: p 584 NAT: AACSB: Reflective Thinking Multivariate dependence techniques are variants of the ANS: general linear model GLM PTS: REF: p 584 NAT: AACSB: Reflective Thinking A variable has two distinct levels that are coded as and ANS: dummy PTS: REF: p 585 NAT: AACSB: Reflective Thinking The test used to test statistical significance by comparing variation explained by the regression equation to the residual error variation is the ANS: F-test PTS: REF: p 586 NAT: AACSB: Reflective Thinking in regression analysis refers to how strongly interrelated the independent variables in a model are ANS: Multicollinearity © 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 588 NAT: AACSB: Reflective Thinking predicts several dependent variables by using several independent variables ANS: Multivariate analysis of variance MANOVA PTS: REF: p 589 NAT: AACSB: Reflective Thinking 10 If the researcher wants to classify objects into two mutually exclusive categories, the researcher should use analysis ANS: discriminant PTS: REF: p 590 NAT: AACSB: Reflective Thinking 11 The purpose of analysis is to summarize information in a large number of variables into a smaller number of factors ANS: factor PTS: REF: p 593 NAT: AACSB: Reflective Thinking 12 An indication of how strongly a measured variable is correlated with a factor is given by the ANS: factor loading PTS: REF: p 594 NAT: AACSB: Reflective Thinking 13 A mathematical way of simplifying factor results is ANS: factor rotation PTS: REF: p 594 NAT: AACSB: Reflective Thinking 14 A statistical technique that measures objects in multidimensional space on the basis of respondents’ judgments of the similarity of objects is ANS: multidimensional scaling PTS: REF: p 599 NAT: AACSB: Reflective Thinking 15 A multivariate interdependence technique that classifies individuals or objects into a small number of mutually exclusive and exhaustive groups is ANS: cluster analysis PTS: REF: p 597 NAT: AACSB: Reflective Thinking ESSAY © 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 1 Compare and contrast dependence and interdependence techniques List the statistical techniques for both ANS: When hypotheses involve distinction between independent and dependent variables, dependence techniques are needed Multiple regression analysis, multiple discriminant analysis, multivariate analysis of variance, conjoint analysis, and structural equations modeling are all dependence techniques When researchers examine questions that not distinguish between independent and dependent variables, interdependence techniques are used No one variable or variable subset is to be predicted from or explained by the others The most common interdependence methods are factor analysis, cluster analysis, and multidimensional scaling PTS: REF: pp 582-583 NAT: AACSB: Reflective Thinking| AACSB: Communication List the steps in interpreting a multiple regression model ANS: Multiple regression models can be interpreted using these steps: (1) Examine the model F-test for significance (2) Examine the individual statistical tests for each parameter estimate (3) Examine the model R2 (4) Examine collinearity diagnostics, such as variance inflation factors (VIF) for each variable to detect multicollinearity PTS: REF: p 588 NAT: AACSB: Reflective Thinking| AACSB: Communication Explain how MANOVA models differ from ANOVA models ANS: An ANOVA or MANOVA model represent a form of the general linear model (GLM) ANOVA can be extended beyond one-way ANOVA to predict a dependent variable with multiple categorical independent variables Multivariate analysis of variance (MANOVA) is a multivariate technique that predicts multiple continuous dependent variables with multiple independent variables The independent variables are categorical, although a continuous control variable can be included in the form of a covariate PTS: REF: p 589 NAT: AACSB: Reflective Thinking| AACSB: Communication Explain why and how a business researcher uses factor analysis ANS: © 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 Factor analysis is a prototypical multivariate, interdependence technique It is a technique of statistically identifying a reduced number of factors from a larger number of measured variables The factors themselves are not measured, but instead, they are identified by forming a variate using the measured variables Factors are usually latent constructs like attitude or satisfaction or an index like social class A researcher need not distinguish between independent and dependent variables to conduct factor analysis Factor analysis can be divided into two types: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) Exploratory factor analysis reveals how many factors exist among a set of variables and what variables match up or “load on” which factors A factor loading indicates how strongly correlated a factor is with a measured variable Factor analysis is considered a data reduction technique that allows a researcher to summarize information from many variables into a reduced set of variates or composite variables PTS: REF: p 593 NAT: AACSB: Reflective Thinking| AACSB: Communication Explain how cluster analysis can identify market segments ANS: Cluster analysis is a multivariate approach for identifying objects or individuals that are similar to one another in some respect It classifies individuals or objects into a small number of mutually exclusive and exhaustive groups Objects or individuals are assigned to groups so that there is great similarity within groups and much less similarity between groups The cluster should have high internal (withincluster) homogeneity and external (between-cluster) heterogeneity Cluster analysis facilitates market segmentation by identifying subjects or individuals who have similar needs, lifestyles, or responses to marketing mixes PTS: REF: p 597 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  ... Reflective Thinking The test used to test statistical significance by comparing variation explained by the regression equation to the residual error variation is the ANS: F -test PTS: REF: p... models can be interpreted using these steps: (1) Examine the model F -test for significance (2) Examine the individual statistical tests for each parameter estimate (3) Examine the model R2 (4) Examine... sample size ANS: C PTS: NAT: AACSB: Reflective Thinking REF: p 588 20 In the formula for the F -test in multiple regression, n - k - stands for: a b c d the degrees of freedom of the numerator