Consider a linear regression model $Y = \alpha + \beta_1x_1+ \beta_2x_2 + \varepsilon$, and suppose we are interested in testing $H_0: \beta_1 = \beta_2$. These slopes are two population slopes.
This means that under $H_0$, we have $Y = \alpha + \beta(x_1 + x_2) + \varepsilon$ where $\beta$ is the common value of $\beta_1$ and $\beta_2$.
My question is, can we just use the incremental F-test, where you compare the incremental sum of squares?
Also, is this test meaningful? I feel like it doesn't make sense to perform this test if $x_1$ and $x_2$ have different units.
EDIT: I just found in the post
that I should use the Wald test. But how do you compute the test statistic? The one in Wikipedia is for comparing a parameter obtained by MLE with a constant.