 Chebyshev test for a regression coefficient

An unbiased coefficient estimator with known variance $v$ gives a conservative level-$\alpha$ test of a zero coefficient by rejecting when its absolute value is at least $\sqrt{v/\alpha }$. Chebyshev's inequality bounds the null rejection probability by $\alpha$. This test needs the variance assumptions but no Gaussian error distribution; a normal-reference test requires additional distributional justification.