# Is a partial F-Test on a model reduced by only one variable valid?

For a recent project, I used multiple linear regression to model data. I attempted to choose between my initial full model and a reduced model by performing a partial F-test. The models used were the following:

Full model: $\hat{Y}$ = $B_0$ + $B_1$$x_1 + B_2$$x_2$ + $B_3$$x_3 Reduced Model: \hat{Y} = B_0 + B_2$$x_2$ + $B_3$$x_3$

The reduced model has only one covariate removed - $x_1$. The partial F-Test returned a F-value of 2.162 and a P-value greater than 0.1, so I did not reject the null hypothesis and concluded that the addition of $x_1$ in the model may not make any significant linear contribution to the prediction of $Y$.

I was later told by my teacher that I should not run a partial F-Test on a reduced model of only one less variable. The teacher said that not only should I not do such a thing, but also that doing so would be wrong. I was told to instead just compare the two models using each model's $R^2$ values, F-values, and T-values.

I can see how the partial F-test in this case might not provide helpful information, since the null hypothesis it tests is that $B_1 = 0$, which is the same thing that the T-test on the parameter $x_1$ tests (in the full model). [Note: I'm not sure what the exact relationship between this T-value and the partial F-test's F-value is.] Nonetheless, why would it would be considered wrong to use and interpret the results from the partial F-test?