The following SPL query calculates the Pearson coefficient of two fields named x and y.

index=*
| fields x y
| eval n=1 | eval xx=x*x | eval xy=x*y | eval yy=y*y
| addcoltotals | tail 1
| eval rho_xy=(xy/n-x/n*y/n)/(sqrt(xx/n-(x/n)*(x/n))*sqrt(yy/n-(y/n)*(y/n)))
| fields rho_xy