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ChristianKl comments on Thinking like a Scientist - Less Wrong
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I was struggling to word the doctor parapgraph in a manner which was succinct but still got the idea across. I think query worded it better.
On math curriculum, that advanced classes build off of calculus is a function of current design. They could recenter courses around statistics and have calculus be an extension of it. Some of the calculus course would need to be reincorporated into the stats courses, but a lot of it wouldn't. You're going to have a hard time convincing me that trigonometry a̶n̶d̶ ̶v̶e̶c̶t̶o̶r̶s̶ are a necessary precursor for regression analysis or Bayes' theorem. The minority of students in physics and engineering that need both calculus and statistics should not dictate how other majors are taught. Fixing the curriculum isn't an easy problem, but they've had more than a century to solve it and there seems to be little movement in this direction.
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.