# Interpret the key results for Principal Components Analysis

Complete the following steps to interpret a principal components analysis. Key output includes the eigenvalues, the proportion of variance that the component explains, the coefficients, and several graphs.

## Step 1: Determine the number of principal components

Determine the minimum number of principal components that account for most of the variation in your data, by using the following methods.
Proportion of variance that the components explain
Use the cumulative proportion to determine the amount of variance that the principal components explain. Retain the principal components that explain an acceptable level of variance. The acceptable level depends on your application. For descriptive purposes, you may only need 80% of the variance explained. However, if you want to perform other analyses on the data, you may want to have at least 90% of the variance explained by the principal components.
Eigenvalues
You can use the size of the eigenvalue to determine the number of principal components. Retain the principal components with the largest eigenvalues. For example, using the Kaiser criterion, you use only the principal components with eigenvalues that are greater than 1.
Scree plot
The scree plot orders the eigenvalues from largest to smallest. The ideal pattern is a steep curve, followed by a bend, and then a straight line. Use the components in the steep curve before the first point that starts the line trend. Key Results: Cumulative, Eigenvalue, Scree Plot In these results, the first three principal components have eigenvalues greater than 1. These three components explain 84.1% of the variation in the data. The scree plot shows that the eigenvalues start to form a straight line after the third principal component. If 84.1% is an adequate amount of variation explained in the data, then you should use the first three principal components.

## Step 2: Interpret each principal component in terms of the original variables

To interpret each principal components, examine the magnitude and direction of the coefficients for the original variables. The larger the absolute value of the coefficient, the more important the corresponding variable is in calculating the component. How large the absolute value of a coefficient has to be in order to deem it important is subjective. Use your specialized knowledge to determine at what level the correlation value is important.