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Multivariate Analyses |

You can generate tables of output from principal component analyses
by setting options in the principal component options dialog
shown in Figure 40.6
or from the **Tables** menu
shown in Figure 40.11.
Select **Principal Components** from the
**Tables** menu to display the principal component tables dialog
shown in Figure 40.16.

Choose **Automatic** to display principal components
with eigenvalues greater than the average eigenvalue.
Selecting **1**, **2**, or **3** gives you 1, 2, or 3 principal components.
**All** gives you all eigenvalues.
Selecting **0** in the principal component options
dialog suppresses the principal component tables.

The **Eigenvalues (COV)** or **Eigenvalues (CORR)** table
includes the eigenvalues of the covariance or correlation
matrix, the difference between successive eigenvalues,
the proportion of variance explained by each eigenvalue,
and the cumulative proportion of variance explained.

Eigenvalues correspond to each of the principal components and
represent a partitioning of the total variation in the sample.
The sum of all eigenvalues is equal to the sum of all variable
variances if the covariance matrix is used or to the number
of variables, *p*, if the correlation matrix is used.

The **Eigenvectors (COV)** or **Eigenvectors (CORR)**
table includes the eigenvectors of the covariance
or correlation matrix.
Eigenvectors correspond to each of the principal components
and are used as the coefficients to form linear combinations
of the **Y** variables (principal components).

Figure 40.17 shows tables of all eigenvalues and eigenvectors for the first two principal components.

**Figure 40.17:** Eigenvalues and Eigenvectors Tables

The **Correlations (Structure)** and **Covariances** tables
include the correlations and covariances, respectively,
between the **Y** variables and principal components.
The correlation and covariance matrices measure the
strength of the linear relationship between the derived
principal components and each of the **Y** variables.
Figure 40.18 shows the correlations and covariances
between the **Y** variables and the first two
principal components.

**Figure 40.18:** Correlations and Covariances Tables

The scoring coefficients are the coefficients
of the **Y** variables used to generate principal components.
The **Std Scoring Coefs** table includes the scoring coefficients
of the standardized **Y** variables, and the **Raw Scoring Coefs**
table includes the scoring coefficients
of the centered **Y** variables.

The regression coefficients are the coefficients
of principal components used to generate estimated **Y** variables.
The **Std Reg Coefs (Pattern)** and **Raw Reg Coefs**
tables include the regression coefficients of principal components
used to generate estimated standardized and centered **Y** variables.
Figure 40.19 shows the regression coefficients
of the principal components for the standardized **Y** variables,
as well as the scoring coefficients of the standardized **Y** variables
for the first two principal components.

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