Relation $\Delta Unemployment$ and $\Delta GDPgrowth$
Well it seems like you are observing somthing consistent with  Okun's Law which reveals empirically negative relationship between Unemployment and GDP.

As Donald Freeman states in the conclusion to his paper titled paper Regional tests of Okun's law


  Okun's law is one of the more enduring stylistic facts of U.S. macroeconomics, having
  withstood numerous tests in the almost four decades since it was first promulgated by
  Arthur Okun.