# Math Help - combining confidence intervals

1. ## combining confidence intervals

Suppose I have the regression

$Y=X_1 \beta_1 + X_2 \beta_2 +X_3 \beta_3 + X_4 \beta_4+U$

Where each X is an n-vector and each beta is a scalar. Unde the usual assumptions for OLS, Step by step, how can I construct a 95% CI for $\beta_1+\beta_3$

2. You can use Bonferroni, but that's lame.

It's better to use the $(1,0,1,0)X=X_1+X_3$ as your random variable.
It's normally distributed so compute it's variance and use a t-percentile.