Say I have a full model $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3x_3 + \beta_4 x_4$. I have regression output giving an overall F-test, standard errors, coefficients, t-test for each coefficient. I would like to preform an F-test on $H_0: \beta_1 = \beta_2 = 0$ against $H_a: \beta_1 \neq 0$ or $\beta_2 \neq 0$. However, my restricted model is $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$, instead of $y = \beta_0 + \beta_3x_3 + \beta_4 x_4$, which would usually be used to test $H_0: \beta_3 = \beta_4 = 0$. I have the same regression output for the restricted model. Am I still able to test my hypothesis even though my restricted model is the opposite of what is usually used?


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