Why does a 16bit LFSR pass all Diehard tests?

I made a implementation of an LFSR in Hardware. It was based on the LFSR from the wikipedia page. It has the same output.

It pass all the tests for dieharder, however, if I plot the pairs I get this not very random lines in 2D

2D plot of the LFSR

So, how can I have a strong statistical test that could prove this PRGN is not ideal?