Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Principal Component Regression

PCR, or principal component regression, is a simple extension of MLR and PCA. In the first step, the principal components are calculated. The scores of the most important principal components are used as the basis for the multiple linear regression with the target data y.

The most important point in PCR is the proper selection of the eigenvectors to be included. A plot of the eigenvalues usually indicates to the "best" number of eigenvectors.

Advantages of PCR over MLR:

  • Noise remains in the residuals, since the eigenvectors with low eigenvalues represent only parts of the data with low variance.
  • The regression coefficients are more stable. This is due to the fact that the eigenvectors are orthogonal to each other.