I'd like to know what PCA tells me about how the variables affect each other.
For example, let's say I've three variables Cholesterol, Exercise, Calorie Intake and Sleep. I want to know how Exercise, Sleep and Calorie Intake affect Cholesterol. Will the Cholesterol be lower (or higher) if I eat more calories or if I exercise more? After PCA I get the following:
Standard deviations:  2.0562689 0.4926162 0.2796596 0.1543862 Rotation: PC1 PC2 PC3 PC4 Cholesterol 0.36138659 -0.65658877 0.58202985 0.3154872 Exercise -0.08452251 -0.73016143 -0.59791083 -0.3197231 CalorieI 0.85667061 0.17337266 -0.07623608 -0.4798390 Sleep 0.35828920 0.07548102 -0.54583143 0.7536574 PC1 PC2 PC3 PC4 Standard deviation 2.0563 0.49262 0.2797 0.15439 Proportion of Variance 0.9246 0.05307 0.0171 0.00521 Cumulative Proportion 0.9246 0.97769 0.9948 1.00000
What I understand from this is how each individual component account for the variance in the data. The only thing I can say here is that PC1 and PC2 has a cumulative variance which account for ~98% which I implicitly interpret as PC3 and PC4 having no affect on the data at all. I understand that PC1 and PC2 are enough to explain all the data from the four given variables but does it say anything about how the variables affect each other?