If you want to do inference and hypothesis testing. You need to save your degree of freedom. You want 10 observations to 20 observations per predictor. So you

If you want to do inference and hypothesis testing. You need to save your degree of freedom. You want 10 observations to 20 observations per predictor. So you can use PCA to collapse a subset of predictors and keep the predictors you are inferring. This will help the sensitivity of your test. Another thing is when you do linear regression or any modeling where it multicolinearity is a problem. This problem is where predictors are confounder or affect each other. PCA change basis so that new predictors are orthogonal to each other getting rid of multicolinearity problem. A toy example is: student gpa, sat score, math grade, height, hour of study Where student GPA is the response or what you want to predict. If you apply PCA to sat score (x1), math grade(x2), height(x3), and hour of study (x4) then it'll give you new predictors that is a linear combination of those predictors. Some statistic book will refer this to a sort of regression. Anyway you may get new variables as: new_x1 = 0.4sat score + 1.2math grade new_x2 = 0.1* height + 0.5* hour of study These new predictors are orthogonal to each other so they don't suffer from multicolinearity. You can now do linear regression using these predictors. The problem is explanation, something you get grouping like height + hour of study. Actually just look here for example: https://www.whitman.edu/Documents/Academics/Mathematics/2017/Perez.pdf https://www.whitman.edu/Documents/Academics/Mathematics/2017... Under "6.4 Example: Principal Component Analysis and Linear Regression"