How does the correlation statistic parameter affect the cost of index scan?
The details you want will not be found in the documentation, but rather in the source code.  In particular, src/backend/optimizer/path/costsize.c in the function cost_index.

It computes min_IO_cost based on the assumption the table is correlated, max_IO_cost based on the assumption it is uncorrelated, and then interpolates between them based on the correlation.