Deck 10: Multivariate Methods of Marketing Research I: Factor, cluster, and Discriminant Analyses

Question 1

Statisticians often call the clusters obtained through cluster analysis "latent" because they need to be discerned via analysis and are not directly observable.

Answer 1

True
With cluster analysis,the clusters are formed through analysis and are not defined a priori.

Question 2

Cluster analysis clarifies the underlying structure of multivariate data in a way that makes it the best complement to regression analysis.

Answer 2

False
Factor analysis is the perfect complement because it will reduce a data set to a smaller set of variables that are not highly correlated.

Question 3

Discriminant analysis and factor analysis are examples of interdependence methods.

Answer 3

False
Although factor analysis is an interdependence method,discriminant analysis is a dependence method.

Question 4

Factor analysis can be used for data transformations by identifying covariates that are exactly uncorrelated and make good inputs for dependence methods.

Question 5

In hierarchical cluster analysis,once a group of objects is clustered together,they are together for life,i.e.the program never separates them during the analysis.

Question 6

If the eigenvalue of the first factor on a factor analysis is 5.3,this could be interpreted that this first factor is doing the work of about 5.3 of the original variables.

Question 7

Factor analysis tells us which variables are similar to one another and how they should be grouped.

Question 8

Varimax rotation involves an oblique rotation of the factors.

Question 9

Hierarchical clustering works well if a researcher needs a fixed number of clusters,whereas nonhierarchical clustering is more useful when one needs to compare different clustering solutions.

Question 10

The principal .reason for rotating a factor analysis solution is to increase the amount of "explained" variance in the variables.

Question 11

Varimax rotation in factor analysis will tell researchers the optimal number of factors they should have in a data reduction situation.

Question 12

In dependence models,no variable or variables are designated as being predicted by others,because the researcher is interested in the interrelationships among all of the variables taken together.

Question 13

To use cluster analysis,researchers must choose either a distance metric or a clustering criterion.

Question 14

Variables that have drastically different ranges can be standardized for cluster analysis through use of a z-transform,which gives all of the variables equal ranges.

Question 15

In cluster analysis it is especially dangerous if the ranges of the variables are dramatically different.

Question 16

The principal components methodology used in discriminant analysis determines the values in the linear combination that explains as much variance between correlation matrices as possible.

Question 17

The MinEigen criterion imposed by computer programs retains only those factors with eigenvalues greater than 1.

Question 18

Among the most common uses of cluster analysis in marketing are segmenting customers and products.

Question 19

One of the primary problems with the principal components analysis of factor analysis is that it can take most of the variance to explain the first factor and leave little variance for other factors to explain.

Question 20

Unlike regression analysis,cluster analysis does not have any independent variables.

Question 21

In factor analysis,the object of the initial extraction is to

A) develop weights for each variable
B) find a set of factors that are linear combinations of the variables in the correlation matrix
C) rotate the factors so that they will be uncorrelated with one another
D) rotate the factors so they can become correlated with one another

Question 22

When interpreting a factor analysis,factors with eigenvalues slightly greater than 1

A) should be discarded
B) are suspect
C) should be assigned higher loadings
D) should be rotated again

Question 23

In dependence methods

A) one or more variables is being predicted by a set of dependent variables
B) one or more variables is being predicted by a set of independent variables
C) the interrelationship of a set of variables, taken together, is studied
D) one variable is being predicted by a set of independent variables

Question 24

Both _______________ analyses are classified as data reduction methods because they take a great deal of data and summarize them with a much smaller set of quantities.

A) regression and factor
B) factor and discriminant
C) factor and cluster
D) cluster and discriminant

Question 25

A confusion matrix crosstabulates the distances between discriminant functions to facilitate graphical analysis.

Question 26

A principle component can be defined as

Where the b values

A) explain as much variance in the correlation matrix as possible
B) maximize
C) minimize
D) are orthogonal

Question 27

The very purpose of _______________ is to gauge just how much redundancy there is in a set of variables and to assess which questions or variables best align with others and then to group them together.

A) factor analysis
B) cluster analysis
C) multiple regression
D) discriminant analysis

Question 28

In terms of deciding whether to keep or discard a factor based on its eigenvalue,the typical cutoff value is around

A) 0
B) 1
C) 2
D) 5

Question 29

_______________ tells us which cases,or people,or objects are similar and how they should be grouped.

A) Factor analysis
B) Cluster analysis
C) The principle components method
D) Discriminant analysis

Question 30

In factor analysis,the _______________ looks for the single best factor to explain all of the variables in the data set,then it constructs a second factor that explains as much as what is left over as possible,and then a third,and so on.

A) varimax rotation method
B) principal components method
C) eigenvalue
D) hierarchical clustering solution

Question 31

In factor analysis,the _______________ represents how much variance a factor explains relative to how much it would be expected to explain by chance alone,that is,on the average.

A) principal component
B) factor loading
C) eigenvalue
D) correlation matrix

Question 32

Factor analysis uses three steps in arriving at a solution.The first step is to

A) develop a set of correlations between all combinations of variables
B) sort the data by cases from lowest to highest
C) determine the optimum number of factors to explain the variables
D) rotate the factors

Question 33

A problem in developing a scale is in weighting the variables being combined in the scale._______________ can do this by using the _______________ as the weights.

A) factor analysis, factor loadings
B) cluster analysis, centroid distances
C) multiple regression, coefficients of the regression
D) discriminant analysis, coefficients of the DF

Question 34

A discriminant function is a linear combination of the independent variables that makes the predicted mean for each category as different as possible.This function is of the form

Question 35

Discriminant analysis can only be used for a binary nominal dependent variable.

Question 36

Factor analysis can help determine coefficients in multiple regression,because

A) principle components make useful variables
B) factor loadings make useful coefficients
C) coefficients measure the effect of unit changes in a variable assuming all other variables remain constant
D) all of the above

Question 37

The v's of a DF are estimated so that

is minimized.

Question 38

Although discriminant analysis works well for discriminating among known groups of a dependent variable,it cannot be used reliably for predicting into which of the pre-established groups a new set of items will fall when the group membership of those items is not already known.

Question 39

Factor analysis can be used for all of the following applications in marketing research except

A) data reduction
B) structure identification
C) scaling
D) segmentation

Question 40

All of the following are underlying reasons for the increased use of multivariate analysis techniques except

A) expanding global usage of marketing research
B) marketing problems are rarely completely described by one or two variables
C) dramatic increase in computer speed and advances in software packages
D) improved understanding of statistical concepts among marketing researchers

Question 41

In hierarchical cluster analysis,the _______________ tells researchers what order various clusters join with one another.It begins by assuming each object is in its own cluster and then lets the various objects join up.

A) dissimilarity schedule
B) agglomeration schedule
C) squared Euclidean distance
D) scree plot

Question 42

Suppose a factor analysis results in 8 factors and that the communality for variable 12 is 0.863.The 0.863

A) means about 86.3 percent of the variance of variable 12 is explained by the eight factors
B) means that 86.3 percent of the variance of variable 12 is explained by the factor on which it loads
C) is the factor loading for variable 12
D) explains how much of the variable is error

Question 43

Knowing the value that someone scores on the principle factor after a varimax rotation tells you _______________ their score on other factors.

A) the loading coefficient of
B) the linear combination for
C) nothing about
D) the further rotation required to calculate

Question 44

NOTE: Use the following table from a cluster analysis to answer the following questions.
Agglomeration Schedule for Centroid Hierarchical Cluster Analysis

At the point where 7 clusters remain and the centroid distance is 0.617,the Schlitz beer joins which cluster of beers?

A) Coors and Hamm's
B) Miller Lite and Schlitz Light
C) Stroh's Bohemian and Heileman's Old Style
D) Budweiser and Lowenbrau

Question 45

A z-transformation is done by

A) subtracting the mean from the data point and then dividing by the variable's standard deviation
B) taking the square root of the sum of the squares of the differences between the data points
C) dividing each data point by the variable's mean
D) subtracting the variable's standard error from the value of each data point

Question 46

When researchers want to divide a set of items into a known number of clusters,the clustering technique that should be used is _______________ clustering.

A) k-means
B) principal components
C) varimax
D) hierarchical

Question 47

When analyzing a nominal dependent variable in terms of several interval independent variables,researchers use

A) discriminant analysis
B) the principle components method
C) factor analysis
D) cluster analysis

Question 48

A scree plot gives a simple,but fairly crude,visual representation of

A) how quickly the quality of the factors degrade in terms of incremental variance
B) the hierarchy of the clustering solution
C) which segments correspond to which clusters
D) the factor loadings for each of the factors

Question 49

Loadings of -1 or 1 mean the factors are _______________ with those variables.

A) parallel
B) perpendicular
C) orthogonal
D) uncorrelated

Question 50

In the distance or dissimilarity matrix for a cluster analysis using squared Euclidean distance,the larger the number

A) the more unlike the pair
B) the more alike the pair
C) the tighter the cluster
D) the larger the loading

Question 51

In simple terms,_______________ works on dividing up data points so that those in the same group are close to one another while those in different groups are far away.

A) factor analysis
B) cluster analysis
C) principal components analysis
D) discriminant analysis

Question 52

The first thing the clustering routine does is

A) rotate the data orthogonally
B) calculate the communalities
C) calculate the cluster loadings
D) standardize the raw data

Question 53

After making a decision on how many factors to use in a factor analysis,a varimax rotation is used because it will reorient the original factors so their loadings are near

A) 1
B) -1
C) 1 or -1
D) 1, 0, or -1

Question 54

In examining factor loadings in a factor analysis,a high loading would have a score

A) above 0
B) above 3
C) close to either -1 or 1
D) with an absolute value approaching 5

Question 55

In cluster analysis,if the range of the variables is drastically different,then the

A) standard error will be large
B) cluster program will not be able to arrive at a solution
C) variables with the largest ranges will dominate the solution
D) the distance metric will exceed the level of aggregation

Question 56

The best analysis technique for discovering segments within a market is

A) factor analysis
B) cluster analysis
C) principal components analysis
D) discriminant analysis

Question 57

_______________ refer(s)to how well all the factors in the solution taken together explain each of the variables.

A) The overall eigenvalue
B) The F-test
C) Factor loadings
D) Communalities

Question 58

In the factor analysis output,the proportion refers to

A) the total sum-of-squares error in the factor
B) the portion of the error that remains unexplained by that factor
C) how much incremental variance is accounted for by each successive factor
D) how much of the total variance is explained by all of the factors taken together up to that factor

Question 59

NOTE: Use the following table from a cluster analysis to answer the following questions.
Agglomeration Schedule for Centroid Hierarchical Cluster Analysis

After the first 3 clusters are formed,there are 9 clusters remaining,

A) each containing a single brand
B) 9 clusters with a single brand and 3 clusters with two brands each
C) 3 clusters with a single brand and 3 clusters with two brands each
D) 6 clusters with a single brand and 3 clusters with two brands each

Question 60

NOTE: Use the following table from a cluster analysis to answer the following questions.
Agglomeration Schedule for Centroid Hierarchical Cluster Analysis

If the researcher were to stop after the centroid distance of 0.683,how many clusters would be left with a single brand in it?

A) one
B) two
C) three
D) four

Question 61

NOTE: Use the following table from a cluster analysis to answer the following questions.
Agglomeration Schedule for Centroid Hierarchical Cluster Analysis

If the researcher were to stop after the centroid distance of 0.683 with 6 remaining clusters,identify each cluster and which brands are in it.

Question 62

Discuss the meaning of "eigenvalue" and the use of these within factor analysis.

Question 63

What is a latent class,and how does it apply to segmentation analysis?

Question 64

All of the following of real-world uses of discriminant analysis except

A) distinguishing known groups of a dependent variable
B) determining the underlying structure of a set of variables
C) determining which input variables are most important to prediction
D) classifying new customers

Question 65

Identify the three steps in a factor analysis solution.

Question 66

Discuss the similarities and differences between factor and cluster analyses.

Question 67

What is a discriminant function,and how does it relate to cluster analysis and segmentation?

Question 68

NOTE: Use the following table from a cluster analysis to answer the following questions.
Agglomeration Schedule for Centroid Hierarchical Cluster Analysis

When Heineken joins with a cluster,identify all of the other brands already in the cluster it joins.

Question 69

NOTE: Use the following table from a cluster analysis to answer the following questions.
Agglomeration Schedule for Centroid Hierarchical Cluster Analysis

When Budweiser Light joins with a cluster,identify all of the other brands already in the cluster it joins.

Question 70

A _______________ matrix categorizes correct and incorrect predictions.

A) distance
B) correlation
C) confusion
D) dissimilarity

Question 71

Discuss the possible applications in marketing research for factor analysis.

Question 72

The basic idea of _______________ is to find a linear combination of the independent variables that makes the mean scores across categories of the dependent variable as different as possible.

A) discriminant analysis
B) factor analysis
C) principle components
D) cluster analysis

Question 73

_______________ is a collection of methods that test whether a set of means are the same.

A) Discriminant analysis
B) Analysis of covariance
C) Analysis of variance
D) Regression

Question 74

A discriminant function

A) is a linear combination of independent variables
B) can be written as
C) minimizes .
D) all of the above
E) both a and b

Question 75

NOTE: Use the following table from a cluster analysis to answer the following questions.
Agglomeration Schedule for Centroid Hierarchical Cluster Analysis

When is discriminant analysis appropriate?