You are given a "blackbox":
$RSS = (Y - X\beta)'(Y-X\beta)$
for any linear model $Y=X\beta+\epsilon$
You have $n=60$ observations, and two predictor variables. You want to test
$H_0: \beta_1 = \beta_2$ in the model:
$Y = \beta_0+\beta_1X_1+\beta_2X_2+\epsilon$
Describe how you would accomplish this using the "black box"?
My professor has outlined changing
$H_0: \beta_1 = \beta_2$ to be $\theta = \beta_1 - \beta_2 = 0$, so $H_0: \theta = 0$.
Then rewrite the linear regression (scalar) form as:
$Y = \beta_0 + (\beta_2+\theta) X_1 + \beta_2 X_2 + \epsilon$
I don't understand where we take the algebra from here...