# p-test for parameter

Statisticians, number magicians,

I was wondering what the best way is to check for the equality of two parameters including possibly a confidence interval and p-value.

$$H_0:\beta_1=\beta_2\vert\ \tilde{y}_1=\hat{\beta}_1\tilde{x}_1;\tilde{y}_2=\hat{\beta}_2\tilde{x}_2;n_1\not=n_2$$

Thanks, Rik

• There's not enough information here. What is known about the $x$ and $y$ variables? Is there really no error here (so that a single observed $x_1$ and $y_1$ will tell us $\beta_1$ exactly)? – Glen_b -Reinstate Monica Apr 14 '15 at 1:45
• Sorry they are not single observations, they are two different populations; so it is two regressions with no constant. I'm not sure what the right notation is. $x_1$ and $y_1$ are vectors... – Rik Apr 14 '15 at 1:51
• Are you testing equality of regression coefficients? – SmallChess Apr 14 '15 at 1:53
• Yes, but without a constant, only a slope... – Rik Apr 14 '15 at 1:54
• Isn't this just like the text-book method but with the constant be zero? – SmallChess Apr 14 '15 at 1:59