I have the regression statistics for the same regression run on two different samples, and am asked to explain whether it is possible to test for equality of the coefficents, $\beta_1$and $\beta_2$ between the two samples.

$y_1 = X_1\beta_1 + \epsilon_1$

$y_1 = X_1\beta_2 + \epsilon_2$

My instinct is to treat it as if they came from the same regression, and do a t-test as follows:

$\frac{\beta_{1}-\beta_{2}}{sd(\beta_{11}-\beta_{21})}$

Would there be any issue doing it this way?

I have the regression statistics for the same regression run on two different samples, and am asked to explain whether it is possible to test for equality of the coefficents, $\beta_1$and $\beta_2$ between the two samples.

$y_1 = X_1\beta_1 + \epsilon_1$

My instinct is to treat it as if they came from the same regression, and do a t-test as follows:

$\frac{\beta_{1}-\beta_{2}}{sd(\beta_{11}-\beta_{21})}$

Would there be any issue doing it this way?