P-value, median coefficients, system of equations

Hi!

I am running a system of 28 equations, using OLS. I wish to determine the significance of the median coefficients by calculating the associated p-values.

What standard deviation should I use?

To give more details:

My sample is partitioned into 28 industries, I thus estimate:

Y1 = a1 + b1X1 + c1W1 + e1

...

y28=a28 +b28X28 + c28W28 + e28

I want to assess how significantly different from zero is median(X), and similarly for W and a.

So my p-value should be p-value=2*(1-prob((med(x)-0))/std).

Problem is, what is the correct standard deviation? The standard deviation of the 28 estimated coefficients? The standard deviation of the X variable in the sample at large?

Thank you!