You're going to have a hard time convincing me that trigonometry and vectors are a necessary precursor for regression analysis or Bayes' theorem.

If you just type a command into R then you can do regression analysis in R but the most important lesson about regression analysis might be: Don't believe in the results. They often don't replicate.

If you do principle component analysis then you do need to understand what vectors are and what it means when they are orthogonal to each other. I'm not sure that you can understand well what degrees of freedom in a data set are without that background.