# Quiz 19: Factor Analysis

Business

Q 1Q 1

Which statement is not true about principal components analysis (PCA)?
A) The total variance in the data is considered.
B) PCA is recommended when the primary concern is to determine the minimum number of factors that will account for maximum variance in the data for use in subsequent multivariate analysis.
C) The factors are estimated based only on the common variance.
D) The diagonal of the correlation matrix consist of unities.

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Multiple Choice

C

Q 2Q 2

F represents in the factor model X

_{i }= A_{i1 }F_{1 }+ A_{i2 }F_{2}+ A_{i3 }F_{3 }+ ... + A_{im }F_{m }+ V_{i}U_{i}. A) the common factor B) the number of common factors C) a unique factor variable D) the number of variablesFree

Multiple Choice

A

Q 3Q 3

It is recommended that the factors extracted should account for at least of the variance.
A) 50 %
B) 60%
C) 65%
D) 70%

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Multiple Choice

B

Q 4Q 4

If the variables are standardized, the factor model may be presented as .
A) X

_{i }= A_{i1 }F_{1 }+ A_{i2 }F_{2 }+ A_{i3 }F_{3 }+ ... + A_{im }F_{m }+ V_{i}U_{i}B) F_{i }= W_{i1 }X_{1 }+ W_{i2 }X_{2 }+ W_{i3 }X_{3 }+ ... + W_{im }X_{m }+ V_{i}U_{i}C) X_{i }= W_{i1 }F_{1 }+ W_{i2 }F_{2 }+ W_{i3 }F_{3 }+ ... + W_{im }F_{m }+ V_{i}U_{i}D)^{X}i^{= }^{A}i1^{F}1^{+ }^{A}i2^{F}2^{+ }^{A}i3^{F}3 + ... +^{A}im^{F}mFree

Multiple Choice

Q 5Q 5

A _ is a plot of the original variables using the factor loadings as coordinates.
A) scree plot
B) scattergram
C) factor loading plot
D) territorial map

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Multiple Choice

Q 6Q 6

The first step in conducting factor analysis is .
A) determine the method of factor analysis
B) construct the correlation matrix
C) formulate the problem
D) determine the number of factors

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Multiple Choice

Q 7Q 7

Factor analysis may not be appropriate in all of the following situations except .
A) a small value for Bartlett's test of sphericity is found
B) the variables are not correlated
C) small values of the KMO statistic are found
D) the variables are correlated

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Multiple Choice

Q 8Q 8

are simple correlations between the variables and the factors.
A) Factor scores
B) Correlation loadings
C) Factor loadings
D) Both A and B are correct

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Multiple Choice

Q 9Q 9

Communality is .
A) the amount of variance a variable shares with all the other variables being considered
B) the percentage of the total variance attributed to each factor
C) the proportion of variance explained by the common factors
D) both A and C are correct

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Multiple Choice

Q 10Q 10

The amount of variance a variable shares with all other variables included in the factor analysis is referred to as .
A) percentage of variance
B) total variance
C) shared variance
D) communality

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Multiple Choice

Q 11Q 11

Which of the following is a way to interpret factors?
A) based on the variables that load high on a factor
B) by plotting the variables using the factor loadings as coordinates
C) both A and B
D) none of the above

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Multiple Choice

Q 12Q 12

is an index that compares the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficient.
A) Wilks' lambda
B) KMO measure of sampling adequacy
C) Bartlett's test of sphericity
D) Mahalanobis ratio

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Multiple Choice

Q 13Q 13

Factor analysis can be used in which of the following circumstances?
A) to identify a new, smaller set of uncorrelated variables to replace the original set of correlated variables in subsequent multivariate analysis
B) to identify underlying dimensions, or factors, that explain the correlations among a set of variables
C) to identify a smaller set of salient variables from a larger set for use in subsequent multivariate analysis
D) All are correct circumstances.

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Multiple Choice

Q 14Q 14

is a class of procedures primarily used for data reduction and summarization.
A) Factor analysis
B) Discriminant analysis
C) Conjoint analysis
D) Regression analysis

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Multiple Choice

Q 15Q 15

If the goal of factor analysis is to reduce the original set of variables to a smaller set of composite variables for use in subsequent multivariate analysis, it is useful to _.
A) compute factor scores for each respondent
B) compute discriminant scores for each respondent
C) select surrogate variables
D) both A and B are correct

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Multiple Choice

Q 16Q 16

The factor scores for the ith factor may be estimated as follows: .
A) X

_{i }= W_{i1 }F_{1 }+ W_{i2 }F_{2 }+ W_{i3 }F_{3 }+ ... + W_{im}_{ }F_{m}B) F_{i }= W_{i1 }X_{1 }+ W_{i2 }X_{2 }+ W_{i3 }Y_{3 }+ ... + W_{ik}_{ }Y_{k}C) F_{i }= W_{i1 }X_{1 }+ W_{i2 }X_{2 }+ W_{i3 }X_{3 }+ ... + W_{ik}_{ }X_{k}D) X_{i }= A_{i1 }F_{1 }+ A_{i2 }F_{2 }+ A_{i3 }F_{3 }+ ... + A_{im}_{ }F_{m}Free

Multiple Choice

Q 17Q 17

A principal components analysis was run and the following eigenvalue results were obtained: 2.731, 2.218, .442, .341, .183, and .085. How many factors would you retain using the eigenvalues to determine the number of factors?
A) one
B) two
C) four
D) six

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Multiple Choice

Q 18Q 18

Which of the following statements is not true about factor rotation?
A) Different methods of rotation may result in the identification of different factors.
B) Through rotation, the factor matrix is transformed into a simpler one that is easier to interpret.
C) Rotation affects the communalities and the percentage of total variance explained.
D) Preferably, each factor should have a nonzero, or significant, loadings or coefficients for only some of the variables.

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Multiple Choice

Q 19Q 19

Which method of analysis does not classify variables as dependent or independent?
A) discriminant analysis
B) regression analysis
C) analysis of variance
D) factor analysis

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Multiple Choice

Q 20Q 20

Which is not a method of factor analysis?
A) common factor analysis
B) omega method
C) unweighted least squares
D) principal components analysis

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Multiple Choice

Q 21Q 21

should be used when factors in the population are likely to be strongly correlated.
A) Orthogonal rotation
B) Oblique rotation
C) The varimax procedure
D) None of the above

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Multiple Choice

Q 22Q 22

Which statement is not correct concerning factor scores?
A) In common factor analysis, estimates of factor scores are obtained, and there is no guarantee that factors will be uncorrelated with each other.
B) In principal components analysis it is possible to compute exact factor scores that are uncorrelated.
C) Factor scores can be used instead of the original variables in subsequent multivariate analysis.
D) All statements are correct.

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Multiple Choice

Q 23Q 23

When selecting surrogate variables from variables with similarly high loadings, the choice should be based on _ .
A) theoretical considerations
B) measurement considerations
C) the variable with the highest loading on a factor
D) Both A and B are correct

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Multiple Choice

Q 24Q 24

is the last step in factor analysis.
A) Rotate the factors
B) Interpret the factors
C) Determine the number of factors
D) Determine the model fit

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Multiple Choice

Q 25Q 25

A is a lower triangle matrix showing the simple correlations, r, between all possible pairs of variables included in the analysis.
A) factor matrix
B) classification matrix
C) total correlation matrix
D) correlation matrix

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Multiple Choice

Q 26Q 26

is an approach to factor analysis that estimates the factors based only on the common variance.
A) Principal components analysis
B) Unweighted least squares
C) Omega method
D) Common factor analysis

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Multiple Choice

Q 27Q 27

Factor analysis is a(n) in that the entire set of interdependent relationships is examined.
A) varimax procedure
B) orthogonal procedure
C) KMO measure of sampling adequacy
D) interdependence technique

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Multiple Choice

Q 28Q 28

Sometimes, because of prior knowledge, the researcher knows how many factors to expect and thus can specify the number of factors to be extracted beforehand. This is referred to as .
A) determination based on significance tests
B) determination based on split- half reliability
C) a priori determination
D) determination based on scree plot

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Multiple Choice

Q 29Q 29

The represents the total variance explained by each factor.
A) residual
B) eigenvalue
C) communality
D) percentage of variance

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Multiple Choice

Q 30Q 30

m represents in the factor model, X

_{i }= A_{i1 }F_{1 }+ A_{i2 }F_{2 }+ A_{i3 }F_{3 }+ ... + A_{im }F_{m }+ V_{i}U_{i}. A) the number of common factors B) the mth standardized variable C) the common factors D) the number of variablesFree

Multiple Choice

Q 31Q 31

As a rough guideline, there should be at least times as many observations (sample size) as there are variables.
A) two or three
B) three or four
C) four or five
D) five or six

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Multiple Choice

Q 32Q 32

is an approach to factor analysis that considers the total variance in the data.
A) Common factor analysis
B) Unweighted least squares
C) Omega method
D) Principal components analysis

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Multiple Choice

Q 33Q 33

Which of the following applications is appropriate for using factor analysis?
A) to understand the media consumption habits of the target market
B) to determine if variation in market share can be accounted for by the size of the sales force and advertising expenditures
C) to identify the characteristics of price- sensitive consumers
D) Both A and C are correct.

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Multiple Choice

Q 34Q 34

The percentage of the total variance attributed to each factor analysis model is called the percentage of variance.

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True False

Q 35Q 35

It is possible to compute as many principal components as there are variables; in doing so, parsimony is gained.

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True False

Q 36Q 36

When using eigenvalues to determine the number of factors, only factors with eigenvalues greater than .05 are retained.

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True False

Q 37Q 37

Generally, the number of factors determined by a scree plot will be one or a few less than that determined by the eigenvalue criterion.

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True False

Q 38Q 38

The differences between the observed correlations (as given in the input correlation matrix) and the reproduced correlations (as estimated from the factor matrix) can be examined to determine model fit.

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True False

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True False

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True False

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True False

Q 42Q 42

The various methods of factor analysis are differentiated by the approach used to derive the weights or factor score coefficients.

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True False

Q 43Q 43

Factor scores should be computed if the goal of factor analysis is to use the results in subsequent multivariate analysis.

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True False

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True False

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True False

Q 46Q 46

Selecting surrogate variables works well if one factor loading for a variable is clearly higher than all other factor loadings.

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True False

Q 47Q 47

Only in the case of principal components analysis is it possible to compute exact factor scores.

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True False

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True False

Q 49Q 49

Residuals are the differences between the observed correlations, as given in the input correlation matrix, and the reproduced correlations, as estimated from the factor matrix.

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True False

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True False

Q 51Q 51

The test statistic for sphericity is based on a chi- square transformation of the determinant of the correlation matrix. A large value of the test statistic will favor the acceptance of the null hypothesis.

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True False

Q 52Q 52

A factor is an underlying dimension that explains the correlations among a set of variables.

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True False

Q 53Q 53

In order to use factor analysis, it is important that the variables be appropriately measured on an ordinal or nominal scale.

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True False

Q 54Q 54

The unrotated factor matrix seldom results in factors that can be interpreted because the factors are correlated with many variables.

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True False

Q 55Q 55

The equation X

_{i }= A_{i1 }F_{1 }+ A_{i2 }F_{2 }_{+ }A_{i3 }F_{3 }+ ... + A_{im }F_{m }_{+ }V_{i}U_{i }, represents the common factors expressed as linear combinations of the observed variables.Free

True False

Q 56Q 56

If interpreting factors using the rotated factor matrix, a negative coefficient for a negative variable (prevention of tooth decay is not important) would lead to a positive interpretation (prevention of tooth decay is important).

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True False

Q 57Q 57

Interpretation is facilitated by identifying the variables that have small loadings on the same factor.

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True False

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True False

Q 59Q 59

Factor analysis is somewhat similar to discriminant analysis in that each variable is expressed as a linear combination of underlying factors.

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True False

Q 60Q 60

The variables to be included in the factor analysis should be specified based on past research, theory, and the judgment of the researcher.

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True False

Q 61Q 61

Factors can be estimated so that their factor scores are not correlated and the first factor accounts for the highest variance in the data, the second factor the second highest and so on.

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True False

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True False

Q 63Q 63

Principal components analysis is appropriate when the primary concern is to identify the underlying dimensions and the common variance is of interest.

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True False

Q 64Q 64

Percentage of variance accounted for, scree plot, and a priori determination are all procedures for determining the number of factors.

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True False

Q 65Q 65

When selecting variables to serve as surrogate variables, you should look for the variable with the highest loading on a factor.

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True False

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Q 68Q 68

Describe principal components analysis and common factor analysis and the differences between the two methods of factor analysis.

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Q 69Q 69

Discuss the process of selecting surrogate variables. Also discuss how the researcher should decide on which variable to choose in complex situations.

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