Principal Component Regression -- Clearly Explained and Implemented

Principal Component Regression (PCR) is a regression technique that serves the same goal as standard linear regression -- model the relationship between a target variable and the predictor variables. The difference is that PCR uses the principal components as the predictor variables for regression analysis instead of the original features. The idea is that the smaller number of principal components represents most of the variability in the data and (presumptively) the relationship with the target variable. Therefore, instead of using all the original features for regression, we only utilize a subset of the principal components. Although the assumption of a relationship with the target variable does not always hold, it is often a reasonable enough approximation to yield good results.