((Multivariate Statistical Analysis Final Exam:: 2026- 2027.))
Multivariate Statistical Analysis Final Exam, Key Concepts
Study online at https://quizlet.com/_igetah
1. Canonical Corre- Canonical correlation analysis assesses the relationships between two sets of
lation Analysis variables by finding linear combinations that are maximally correlated with each
other.
2. Canonical Vari- Canonical variates are linear combinations of variables from two different sets
ates and Correla- that maximize the correlation between those sets. The correlation between these
tions canonical variates is called the canonical correlation, and it measures the strength
of their association.
3. Canonical Variate Canonical variate computation is the process of creating new variables by forming
Computation linear combinations of the original variables in each set. These new variables,
or canonical variates, are calculated so that the correlation between the pairs of
variates from each set is as high as possible in canonical correlation analysis.
4. Eigenvalue Prob- The eigenvalue problem is a mathematical procedure where matrices are analyzed
lem to find values (eigenvalues) and corresponding vectors (eigenvectors) that satisfy
a specific equation. In canonical correlation analysis, solving the eigenvalue prob-
lem helps identify the directions in the data that maximize the correlation between
sets of variables.
5. Discrimination Discrimination and classification encompass methods used to separate groups
and based on combined characteristics and to assign new cases to existing groups.
Classification
6. Multivariate Nor- Multivariate normal classification rules are decision rules based on the assump-
mal Classification tion that populations follow a multivariate normal distribution. They use mean
Rules vectors and covariance matrices to assign observations to the population most
likely to have generated them.
7. Linear Discrimi- Linear Discriminant Analysis (LDA) in Multivariate Statistical Analysis is a technique
nant Analysis in used to separate two or more groups by finding a linear combination of variables
Multivariate Sta- that best distinguishes them. LDA assumes that each group has a multivariate
tistical Analysis
Page 1 of 23 3/31/2026
, ((Multivariate Statistical Analysis Final Exam:: 2026- 2027.))
Multivariate Statistical Analysis Final Exam, Key Concepts
Study online at https://quizlet.com/_igetah
normal distribution with the same covariance matrix, resulting in a linear decision
boundary for classification.
8. Linear Score
A linear score is a value calculated as a weighted sum of the input variables for
each observation. In Linear Discriminant Analysis, this score is used to assign each
observation to the group that gives the highest score.
9. Separation and Statistical methods used to distinguish between two groups based on measure-
Classification for ments from multiple variables, with the goal of assigning new observations to one
Two Populations of the populations as accurately as possible.
10. Bayes Optimal Bayes Optimal Rule is a classification method that assigns an observation to
Rule the group with the highest posterior probability, based on known probability
distributions. It provides the best possible classification results by minimizing the
chance of misclassification.
11. Posterior Class Posterior class probability is the probability that an observation belongs to a
Probability particular class, given its observed features and any prior knowledge. It is cal-
culated using Bayes' theorem and helps determine the most likely class for the
observation.
12. Factor Analysis Factor analysis is a technique that identifies underlying latent variables, known
as factors, which explain patterns of similarities among observed measured vari-
ables.
13. Estimation Meth- Estimation methods for factor loadings are statistical procedures used to quantify
ods for Factor the strength and direction of relationships between observed variables and un-
Loadings derlying factors. Examples include principal factor analysis and maximum likeli-
hood estimation.
14. Maximum Likeli- Maximum Likelihood Factor is a method used in factor analysis to estimate factor
hood Factor loadings by finding values that maximize the likelihood of obtaining the observed
correlation matrix, given a specific factor model. This approach assumes that the
Page 2 of 23 3/31/2026
, ((Multivariate Statistical Analysis Final Exam:: 2026- 2027.))
Multivariate Statistical Analysis Final Exam, Key Concepts
Study online at https://quizlet.com/_igetah
data are normally distributed and provides statistical measures to evaluate the
model fit.
15. Factor Score In- Factor score indeterminacy refers to the problem that, in factor analysis, there
determinacy is no unique solution for estimating individual scores on the underlying factors.
Multiple sets of factor scores could reproduce the observed data equally well,
making the scores impossible to determine exactly.
16. Orthogonal Fac- An orthogonal factor model is a type of factor analysis model where all the
tor Model extracted factors are uncorrelated, meaning they are at right angles (orthogonal)
to each other in multivariate space. This simplifies interpretation because each
factor represents a unique dimension of the data.
17. Assumptions Assumptions in orthogonal factor analysis include linearity of relationships be-
tween variables and factors, independence and orthogonality (total uncorrelat-
edness) among factors, normally distributed errors with a mean of zero and
constant variance, and that the errors are uncorrelated with both each other and
the underlying factors.
18. Orthogonality of Orthogonality of factors means that the common factors in the model are uncorre-
Factors lated with each other, so their relationships are at right angles in multidimensional
space.
19. Zero-Mean Fac- This means that the expected value, or average, of each common factor is zero.
tors This centers the factors, so that they represent only deviations from the mean.
20. Model Specifica- Model specification of an orthogonal factor model involves expressing how ob-
tion of Orthogo- served variables are related to underlying factors under the constraint that all
nal Factor Model factors are uncorrelated (orthogonal) with each other. The observed variables are
modeled as linear combinations of the factors plus unique error terms, and the
factors are assumed to have a variance-covariance matrix that is diagonal with
ones along the diagonal.
Page 3 of 23 3/31/2026
Multivariate Statistical Analysis Final Exam, Key Concepts
Study online at https://quizlet.com/_igetah
1. Canonical Corre- Canonical correlation analysis assesses the relationships between two sets of
lation Analysis variables by finding linear combinations that are maximally correlated with each
other.
2. Canonical Vari- Canonical variates are linear combinations of variables from two different sets
ates and Correla- that maximize the correlation between those sets. The correlation between these
tions canonical variates is called the canonical correlation, and it measures the strength
of their association.
3. Canonical Variate Canonical variate computation is the process of creating new variables by forming
Computation linear combinations of the original variables in each set. These new variables,
or canonical variates, are calculated so that the correlation between the pairs of
variates from each set is as high as possible in canonical correlation analysis.
4. Eigenvalue Prob- The eigenvalue problem is a mathematical procedure where matrices are analyzed
lem to find values (eigenvalues) and corresponding vectors (eigenvectors) that satisfy
a specific equation. In canonical correlation analysis, solving the eigenvalue prob-
lem helps identify the directions in the data that maximize the correlation between
sets of variables.
5. Discrimination Discrimination and classification encompass methods used to separate groups
and based on combined characteristics and to assign new cases to existing groups.
Classification
6. Multivariate Nor- Multivariate normal classification rules are decision rules based on the assump-
mal Classification tion that populations follow a multivariate normal distribution. They use mean
Rules vectors and covariance matrices to assign observations to the population most
likely to have generated them.
7. Linear Discrimi- Linear Discriminant Analysis (LDA) in Multivariate Statistical Analysis is a technique
nant Analysis in used to separate two or more groups by finding a linear combination of variables
Multivariate Sta- that best distinguishes them. LDA assumes that each group has a multivariate
tistical Analysis
Page 1 of 23 3/31/2026
, ((Multivariate Statistical Analysis Final Exam:: 2026- 2027.))
Multivariate Statistical Analysis Final Exam, Key Concepts
Study online at https://quizlet.com/_igetah
normal distribution with the same covariance matrix, resulting in a linear decision
boundary for classification.
8. Linear Score
A linear score is a value calculated as a weighted sum of the input variables for
each observation. In Linear Discriminant Analysis, this score is used to assign each
observation to the group that gives the highest score.
9. Separation and Statistical methods used to distinguish between two groups based on measure-
Classification for ments from multiple variables, with the goal of assigning new observations to one
Two Populations of the populations as accurately as possible.
10. Bayes Optimal Bayes Optimal Rule is a classification method that assigns an observation to
Rule the group with the highest posterior probability, based on known probability
distributions. It provides the best possible classification results by minimizing the
chance of misclassification.
11. Posterior Class Posterior class probability is the probability that an observation belongs to a
Probability particular class, given its observed features and any prior knowledge. It is cal-
culated using Bayes' theorem and helps determine the most likely class for the
observation.
12. Factor Analysis Factor analysis is a technique that identifies underlying latent variables, known
as factors, which explain patterns of similarities among observed measured vari-
ables.
13. Estimation Meth- Estimation methods for factor loadings are statistical procedures used to quantify
ods for Factor the strength and direction of relationships between observed variables and un-
Loadings derlying factors. Examples include principal factor analysis and maximum likeli-
hood estimation.
14. Maximum Likeli- Maximum Likelihood Factor is a method used in factor analysis to estimate factor
hood Factor loadings by finding values that maximize the likelihood of obtaining the observed
correlation matrix, given a specific factor model. This approach assumes that the
Page 2 of 23 3/31/2026
, ((Multivariate Statistical Analysis Final Exam:: 2026- 2027.))
Multivariate Statistical Analysis Final Exam, Key Concepts
Study online at https://quizlet.com/_igetah
data are normally distributed and provides statistical measures to evaluate the
model fit.
15. Factor Score In- Factor score indeterminacy refers to the problem that, in factor analysis, there
determinacy is no unique solution for estimating individual scores on the underlying factors.
Multiple sets of factor scores could reproduce the observed data equally well,
making the scores impossible to determine exactly.
16. Orthogonal Fac- An orthogonal factor model is a type of factor analysis model where all the
tor Model extracted factors are uncorrelated, meaning they are at right angles (orthogonal)
to each other in multivariate space. This simplifies interpretation because each
factor represents a unique dimension of the data.
17. Assumptions Assumptions in orthogonal factor analysis include linearity of relationships be-
tween variables and factors, independence and orthogonality (total uncorrelat-
edness) among factors, normally distributed errors with a mean of zero and
constant variance, and that the errors are uncorrelated with both each other and
the underlying factors.
18. Orthogonality of Orthogonality of factors means that the common factors in the model are uncorre-
Factors lated with each other, so their relationships are at right angles in multidimensional
space.
19. Zero-Mean Fac- This means that the expected value, or average, of each common factor is zero.
tors This centers the factors, so that they represent only deviations from the mean.
20. Model Specifica- Model specification of an orthogonal factor model involves expressing how ob-
tion of Orthogo- served variables are related to underlying factors under the constraint that all
nal Factor Model factors are uncorrelated (orthogonal) with each other. The observed variables are
modeled as linear combinations of the factors plus unique error terms, and the
factors are assumed to have a variance-covariance matrix that is diagonal with
ones along the diagonal.
Page 3 of 23 3/31/2026
