Question 1

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

Accepted Answer

The purpose of extraction is to extract a smaller set of factors that are linear combinations of the variables in the correlation matrix.

Question 2

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

Accepted Answer

Factors with eigenvalues below 1 should be discarded,those slightly above one considered suspect,and those greater than 1 retained.

Question 3

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

Accepted Answer

With dependence methods one or more dependent variables is predicted by a set of independent variables.It is interdependence methods that study the interrelationship of a set of variables taken together.

Question 4

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

Accepted Answer

The data reduction methods are factor analysis and cluster analysis.

Question 5

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

Accepted Answer

A confusion matrix categorizes correct and incorrect predictions by crosstabulating the dependent variable category that the discriminant function predicts a subject will be in with the category that the subject is actually in.

Question 6

A principle component can be defined as
$$z = b _ { 1 } X _ { 1 } + b _ { 2 } X _ { 2 } + \ldots + b _ { m } X _ { m }$$
Where the b values
A) explain as much variance in the correlation matrix as possible
B) maximize 
C) 
D) are orthogonal

Accepted Answer

z is the linear combination,called a principal component.The principal components methodology determines values for {b₁,b₂,…,b_m} that explain as much variance in the correlation matrix as possible.

Question 7

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

Accepted Answer

Factor analysis is excellent for reducing a large number of variables,or questions on a survey,to a smaller set of constructs or variables.

Question 8

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

Accepted Answer

Typically,1 is used as the cutoff,below which factors are discarded.How much greater than 1 an eigenvalue should be for a factor to be deemed acceptable is subject to the experimenter's judgment and needs.

Question 9

_______________ 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

Accepted Answer

Cluster analysis tells which cases are similar and how they can be grouped.

Question 10

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

Accepted Answer

This is the purpose of the principal components analysis and is the first step in running a factor analysis.

Question 11

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

Accepted Answer

By definition,the eigenvalue represents how much of the total variance is explained by a factor relative to the average.

Question 12

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

Accepted Answer

The steps are:1.develop a set of correlations between all combinations of variables
2.extract an initial set of factors
3.rotate the initial factors

Question 13

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

Accepted Answer

Factor analysis is an excellent method for determining the weights for a scale.

Question 14

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
 $$D F = v _ { 1 } X _ { 1 } + \mathcal { V } _ { 2 } X _ { 2 } + \ldots + \mathcal { V } _ { m } X _ { m }$$

Accepted Answer

This is the definition of a discriminant function.

Question 15

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

Accepted Answer

It can be used for any k number of categories in nominal data.

Question 16

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

Accepted Answer

Coefficients in multiple regression measure the effects of unit changes in a variable assuming all other variables remain constant,and factor analysis can provide uncorrelated factors.

Question 17

The v's of a DF are estimated so that
 $F = \frac { S S _ { \text {between } } } { S S _ { \text {within } } }$ 
is minimized.

Accepted Answer

The v's of a DF are estimated so that
 $F = \frac { S S _ { \text {between } } } { S S _ { \text {within } } }$ is maximized.

Question 18

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.

Accepted Answer

One of the uses of discriminant analysis is classification/prediction.That is,given a new set of items (e.g.,customers,products,firms)whose group membership is not known,into which of the pre-established groups are they likely to fall?

Question 19

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

Accepted Answer

Segmentation is an application for cluster analysis,not factor analysis.

Question 20

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

Accepted Answer

Although more marketing research is used globally,it is not an underlying reason for increased usage of multivariate techniques.

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

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

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

In dependence methods

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

A principle component can be defined as $z = b _ { 1 } X _ { 1 } + b _ { 2 } X _ { 2 } + \ldots + b _ { m } X _ { m }$ Where the b values

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.

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

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

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.

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.

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

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 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 $D F = v _ { 1 } X _ { 1 } + \mathcal { V } _ { 2 } X _ { 2 } + \ldots + \mathcal { V } _ { m } X _ { m }$

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

Factor analysis can help determine coefficients in multiple regression,because

The v's of a DF are estimated so that $F = \frac { S S _ { \text {between } } } { S S _ { \text {within } } }$ is minimized.

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.

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

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

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

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

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

In dependence methods

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

A principle component can be defined as z=b1X1+b2X2+…+bmXmz = b _ { 1 } X _ { 1 } + b _ { 2 } X _ { 2 } + \ldots + b _ { m } X _ { m }z=b1​X1​+b2​X2​+…+bm​Xm​ Where the b values

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.

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

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

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.

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.

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

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.

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

Factor analysis can help determine coefficients in multiple regression,because

The v's of a DF are estimated so that F=SSbetween SSwithin F = \frac { S S _ { \text {between } } } { S S _ { \text {within } } }F=SSwithin ​SSbetween ​​ is minimized.

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.

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

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

A principle component can be defined as $z = b _ { 1 } X _ { 1 } + b _ { 2 } X _ { 2 } + \ldots + b _ { m } X _ { m }$ Where the b values

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.

The v's of a DF are estimated so that $F = \frac { S S _ { \text {between } } } { S S _ { \text {within } } }$ is minimized.