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I am writing up a report on fitting Principal Component Regression (PCR) and Partial Least Squares (PLS) to my data-set.

A similar question: Model assumptions of partial least squares (PLS) regression only covers PLS.

According to Springer texts in Statistics "An Introduction to Statistical Learning with Applications in R" Section 6.3.1:

The principal components regression (PCR) approach involves constructing the firstM principal components, Z1, . . ., ZM, and then using these components as the predictors in a linear regression model that is fit using least squares.

Section 6.3.2:

Like PCR, PLS is a dimension reduction method, which first identifies squares a new set of features Z1, . . ., ZM that are linear combinations of the original features, and then fits a linear model via least squares using these M new features.

For both of the methods it says that the new features are used in the linear regression model.

Question

Does this mean that the new regression model has to satisfy the assumptions of a linear model, mainly:

  1. Independent observations
  2. Normality of errors
  3. Errors having a mean of zero
  4. Errors having constant variance

Are there any other assumptions I would have to take into account when fitting these models?

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