The idea of selecting the 25 features based on maximum correlation seems to be weak because it should introduce a lot of collinearity. In chapter 6 of the ISLR

The idea of selecting the 25 features based on maximum correlation seems to be weak because it should introduce a lot of collinearity. In chapter 6 of the ISLR book there are many methods to work in high dimension, that is when number of features is bigger than number of samples. For example principal components regression, partial least squares, the lasso, ridge regression, forward stepwise selection and PCL. All of those methods can be used with 10 or so lines of R using the packages and examples described in the ISLR book, lab in chapter 6.