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I want to fully understand how F test is used to compare two nested models. Every information I found about it, is only standard use i.e. to compare model with model containing no variables.

How I perceive it

Let's say I have $\text{model}_1$:

$$y = \beta_0+\beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4$$

And $\text{model}_2$:

$$y = \beta_0 + \beta_1x_1 + \beta_2x_2$$

I want to compare those two models using F test. The null hypothesis in this case would be that:

$$H_0: \beta_3 = \beta_4 = 0$$

and alternative

$$H_1: \beta_3 \neq 0 \;\lor \beta_4 \neq 0$$

Now let's say that I fixed significance level at 0.05. It means that when for example $p-$value equals $0.2$ we have no evidence to say that null hypothesis is not true. In other words we have no evidence to reject $\text{model}_2$.

Am I correct with my perceiving of this model?

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    $\begingroup$ Does this answer your question? What are chunk tests? One common example of a chunk test that doesn’t compare to an intercept-only model is ANCOVA. $\endgroup$
    – Dave
    Commented Dec 10, 2021 at 14:12
  • $\begingroup$ I would be very thankful if you could comment my justification, whether it makes sense or not. $\endgroup$
    – John
    Commented Dec 10, 2021 at 14:24
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    $\begingroup$ What you propose is exactly a chunk test. $\endgroup$
    – Dave
    Commented Dec 10, 2021 at 14:46

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