I have several OLS models with robust s.e.'s that predict an outcome variable Y
$Y=B_0 + B_1X_1 + B_2X_2$
$Y=B_0 +B_1X_1 + B_2X_2 +B_3X_3$
I am interested in giving an average effect for $B_1$ across Models 1-3 with an accompanied 95% CI.
Can I just take the average of $B_1$'s across Models 1-3 and the average of standard errors to construct my confidence interval? What is this called?