Can someone help me interpret the results of my principal component analysis? I have three variables: LAPOP05_10, LAPOP1_10, and LAPOP1_20. I have run a principal component analysis (PCA), and have obtained the following results:
Importance of components:
                         PC1     PC2     PC3
Standard deviation     1.649 0.51274 0.13824
Proportion of Variance 0.906 0.08763 0.00637
Cumulative Proportion  0.906 0.99363 1.00000

PC1 will explain about 91% of the variance in the data, and PCA2 will explain about 9%. Here is my loading plot:
I am new to PCA, and am not understanding how to interpret these results. Is this saying that the LAPOP05_10 explains the majority of the PC1 data? Any help would be much appreciated!


Usually, PCA is useful for dimensionality reduction. In your case, you have only 3 and it doesn't make sense.
Anyway, if it is only a toy example e you would like to understand how to interpret the results, the first component is negatively associated with all three features while the second is negatively associated with LAPOP05_10 and positively associated with the other two features.
The interpretation of loadings becomes useful if you can assign a sort of label to the components. For example, if one component is associated with economic features, you may use that component for regression as a feature that represents the economic aspects.
