Use the eigenvalue results to determine the number of principal components.

One way to determine the number of principal components is based on the size of eigenvalues. In the eigenanalysis of the correlation matrix, the eigenvalues of the correlation matrix equal the variances of the principal components. According to the Kaiser criterion, retain principal components with eigenvalues greater than 1.

You can also decide on the number of principal components based on the amount of explained variance. For example, you may retain components that cumulatively explain 90% of the variance. Another technique is to analyze a scree plot. Use any one or combination of these techniques to determine the number of principal components.

For the loan applicant data:

·    The first principal component has variance 3.5476 (equal to the largest eigenvalue) and accounts for 0.443 (44.3%) of the total variation in the data.

·    The second principal component (variance 2.1320) accounts for 0.266 (26.6%) of the total data variation.

·    The third principal component (variance 1.0447) accounts for 0.131 (13.1%) of the total data variation.

The first three principal components with variances equal to the eigenvalues greater than 1 represent 0.841 (84.1%) of the total variability, suggesting that 3 principal components adequately explain the variation in the data.