Introduction In the first post in this series, we outlined the motivation and theory behind principal component analysis (PCA), which takes points $x_1, \ldots, x_N$ in a high dimensional space to points in a lower dimensional space while preserving as much of the original variance as possible. In this follow-up post, we apply principal components regression (PCR), an algorithm which includes PCA as a subroutine, to a small dataset to demonstrate the ideas in practice. Prerequisites To understan...