How to use pca results for linear regression I have a data set of 11 variables with allot of observations for each one. I want to make linear regression on the variables with the observed $\vec{y}=\alpha +\beta*\vec{X}$ when X is matrix. I'm trying to reduce my parameters so I activate pca algorithm on X. I get the "loading" data but i don't understand how to use it to get only four (for example) variables to estimate instead of 11.

somebody can help?
In general, I would suggest to use a regularization technique for reducing the dimensionality ofa data set in linear regression cases. Please refer to L1 regularization.

If you want to decrease the number variables using PCA, you should look at the lambda values that describe the variations in the principle components, then, select the a few components with the largest corresponding lambda values (eg the first four). 

Note:


Do a scaling if necessary.
Sometimes the very first component is not very relevant and can be eliminated.