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I am currently doing a test of model complexities for two linear regression models:

First Model:

$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$

vs.

Second Model:

$Y = \beta_0 + \beta_1X_1 + \epsilon$

and am using the lrtest function in R to do it. I would like to draw a power curve where the x-axis varies the values of $\beta_2$. The y-axis would report the power of the test at each value of $\beta_2$. Power is defined as the probability of rejecting the null when the null is false with the null being that the two models are the same.

I am wondering how I might be able to do such a test and if it can be done using the lrtest function.

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Maybe you can follow my idea presented here Power Analysis for a mixed two-way ANOVA with unqual sample sizes.

You need to generate the data according to the first model.

Need to specify the following: 1) sample size, 2)$\beta_0$ and $\beta_1$, 3)$Var(\epsilon)$, 4)structure of $X_1$ and $X_2$, especially their correlation, and 5)$\alpha$ level.

Of course, you need the several different values of $β_2$ for x-axis.

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