▁know ▁whether ▁its ▁estimated ▁coefficient ▁diff ers ▁significantly ▁from ▁zero — that ▁is , ▁whether ▁this ▁particular ▁explan atory ▁variable ▁in ▁fact ▁has ▁explan atory ▁power ▁in ▁predict ing ▁the ▁response ▁variable . ▁Here ▁the ▁null ▁hypothesis ▁is ▁that ▁the ▁true ▁coefficient ▁is ▁zero . ▁This ▁hypothesis ▁is ▁tested ▁by ▁computing ▁the ▁coefficient ' s ▁t - stat istic , ▁as ▁the ▁ratio ▁of ▁the ▁coefficient ▁estimate ▁to ▁its ▁standard ▁error . ▁If ▁the ▁t - stat istic ▁is ▁larger ▁than ▁a ▁pred et erm ined ▁value , ▁the ▁null ▁hypothesis ▁is ▁rejected ▁and ▁the ▁variable ▁is ▁found ▁to ▁have ▁explan atory ▁power , ▁with ▁its ▁coefficient ▁significantly ▁different ▁from ▁zero . ▁Otherwise , ▁the ▁null ▁hypothesis ▁of ▁a ▁zero ▁value ▁of ▁the ▁true ▁coefficient ▁is ▁accepted . ▁ ▁In ▁addition , ▁the ▁Ch ow ▁test ▁is ▁used ▁to ▁test ▁whether ▁two ▁subs amples ▁both ▁have ▁the ▁same ▁underlying ▁true ▁coefficient ▁values . ▁The ▁sum ▁of ▁squ ared ▁resid uals ▁of ▁re gress ions ▁on ▁each ▁of ▁the ▁subsets ▁and ▁on ▁the ▁combined ▁data ▁set ▁are ▁compared ▁by ▁computing ▁an ▁F - stat istic ; ▁if ▁this ▁exceed s ▁a ▁critical ▁value , ▁the ▁null ▁hypothesis ▁of ▁no ▁difference ▁between ▁the ▁two ▁subsets ▁is ▁rejected ; ▁otherwise , ▁it ▁is ▁accepted . ▁▁ ▁Example ▁with ▁real ▁data ▁▁▁ ▁The ▁following ▁data ▁set ▁gives ▁average ▁height s ▁and ▁weights ▁for ▁American ▁women ▁aged ▁ 3 0 – 3 9 ▁( source : ▁The ▁World ▁Al man ac ▁and ▁Book ▁of ▁Fact s , ▁