7.3.2 Variance and Standard Errors of ols estimators We need the standard errors for two main purposes: (1) to establish confidence intervals for the true parameter values (2)to test statistical hypotheses. u-N(0, 02)bN(Bl, var(b)) b n( b,N(B,, var(b,)) var(b= X2∑x3+x3∑x21-2x2X∑x2x 2(7.23) n ∑x2∑x-(∑x2x3)2 seb1)=√ar(b1) (724) var(b2)= (7.25) 2t-3t (b2) (7.26 var( (b3) (7.27) C∑x2)∑x3)-C∑x2 (b3)= var(b3) (728)7.3.2 Variance and Standard Errors of OLS Estimators We need the standard errors for two main purposes: (1) to establish confidence intervals for the true parameter values (2) to test statistical hypotheses. 1. ui ~N(0, σ 2 ) →b1～N（B1 , var(b1 )） b2～N（B2 , var(b2 )） b3～N（B3 , var(b3 )） var(b1 )= · (7.23) se(b1 )= (7.24) var(b2 )= · (7.25) se(b2 )= (7.26) var(b3 )= · (7.27) se(b3 )= (7.28)       − + − +      2t 3t 2 2 3t 2 2t 2 3 2t 3t 2 2t 2 3 2 3t 2 2 x x ( x x ) X x X x 2X X x x n 1 2 σ var(b ) 1 2 2t 3t 2 3t 2 2t 2 3t ( x )( x ) ( x x ) x     − 2 σ var(b ) 2 2 2t 3t 2 3t 2 2t 2 2t ( x )( x ) ( x x ) x     − var(b ) 3 2 σ