I add one more type of regression to the "tecator meat data" in this case is the "Ridge Regression".
Ridge Regression use all the predictors, but penalizes their values in order they can not get high values.
We can see that it not get such as best fitting as the PCR or PLS in the case of spectroscopy data, but it is quite common to use it in other data for Machine Learning Application. Ridge Regression is a type of Regularization where we have two types L1 and L2.
In the plot you can see also the RMSE for the validation set: