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Enables you to create the principal components based on Correlations, Covariances, or Unscaled.
Correlations
Covariance Matrix
 ‒ For the on Correlations option, the eigenvalues are scaled to sum to the number of variables.
 ‒ For the on Covariances options, the eigenvalues are not scaled.
 ‒ For the on Unscaled option, the eigenvalues are divided by the total number of observations.
If you select the Bartlett Test option from the red triangle menu, hypothesis tests (Bartlett Test) are given for each eigenvalue (Jackson, 2003).
Eigenvalues
Eigenvectors
Bartlett Test
 ‒ For the on Correlations option, the ith column of loadings is the ith eigenvector multiplied by the square root of the ith eigenvalue. The i,jth loading is the correlation between the ith variable and the jth principal component.
 ‒ For the on Covariances option, the jth entry in the ith column of loadings is the ith eigenvector multiplied by the square root of the ith eigenvalue and divided by the standard deviation of the jth variable. The i,jth loading is the correlation between the ith variable and the jth principal component.
 ‒ For the on Unscaled option, the jth entry in the ith column of loadings is the ith eigenvector multiplied by the square root of the ith eigenvalue and divided by the standard error of the jth variable. The standard error of the jth variable is the jth diagonal entry of the sum of squares and cross products matrix divided by the number of rows (X’X/n).
Note: When you are analyzing the unscaled data, the i,jth loading is not the correlation between the ith variable and the jth principal component.
Biplot
Scree Plot
Scatterplot 3D Score Plot
The variables show as rays in the plot. These rays, called biplot rays, approximate the variables as a function of the principal components on the axes. If there are only two or three variables, the rays represent the variables exactly. The length of the ray corresponds to the eigenvalue or variance of the principal component.
Cluster Summary
 ‒ For the on Correlations option, the ith principal component is a linear combination of the centered and scaled observations using the entries of the ith eigenvector as coefficients.
 ‒ For the on Covariances options, the ith principal component is a linear combination of the centered observations using the entries of the ith eigenvector as coefficients.
 ‒ For the on Unscaled option, the ith principal component is a linear combination of the raw observations using the entries of the ith eigenvector as coefficients.
The ith principal component is a linear combination of the centered and scaled observations using the entries of the ith eigenvector as coefficients.
In the data table, the principal components are given in columns called Prin<number>. The formulas depend on an additional saved column called Prin Data Matrix. This column contains the difference between the vector of the raw data, given by a Matrix expression, and the vector of means.
 1 For all clusters, do the following:
 a. Compute the principal components for the variables in each cluster.
 b. If the second eigenvalues for all of the clusters are less than one then terminate the algorithm.
 2 Partition the cluster whose second eigenvalue is the largest (and greater than 1) into two new clusters as follows:
 a. Rotate the principal components for the variables in the current cluster using an orthoblique rotation.
 b. Define one cluster to consist of the variables in the current cluster whose squared correlations to the first rotated principal component are higher than their squared correlations to the second principal component.
 c. Define the other cluster to consist of the remaining variables in the original cluster. These are the variables that are more highly correlated with the second principal component.
 d. Compute the principal components of the two new clusters.
 3 Test to see if any variable in the data set should be assigned to a different cluster. For each variable, do the following:
 a. Compute the variable’s squared correlation with the first principal component for each cluster.
 b. Place the variable in the cluster for which its squared correlation is the largest.
 ‒ Cluster is a cluster identifier.
 ‒ Number of Members is the number of variables in the cluster.
 ‒ Most Representative Variable is the cluster variable that has the largest squared correlation with its cluster component.
 ‒ Cluster Proportion of Variance Explained is the squared correlation of the Most Representative Variable with its cluster component.
 ‒ Total Proportion of Variation Explained is the squared correlation of the Most Representative Variable in the cluster with the first principal component for all variables in that cluster.
 ‒ Cluster is the cluster identifier.
 ‒ Members lists the variables included in the cluster.
 ‒ RSquare with Own Cluster is the is the squared correlation of the variable with its cluster component.
 ‒ 1 - RSquare Ratio is the a measure of the relative closeness between the cluster to which a variable belongs and its next closest cluster. It is defined as follows:
Saves columns called Cluster <i> Components to the data table. Each column is given by a formula that expresses the cluster component in terms of the uncentered and unscaled variables.