Multivariate regression collinearity

In the previous chapter, it was commented on that the ordinary least-sqnares approach applied to multivariate data (multivariate linear regression, MLR) suffered from serious uncertainty problems when the independent variables were collinear. Principal components regression (PCR) can solve the collin-earity problem and provide additional benefits of factor-based regression methods, such as noise filtering. Recall that PCR compresses the original X-block e.g. matrix of absorbances) into a new block of scores T, containing fewer variables (the so-called factors, latent variables, or principal components), and then regression is performed between T and the property of... 

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