Is having an equal number of replications an advantage? (Question on Lack of Fit test in Simple Linear Regression)

Dear Forum,

Sorry for reposting this.

The lack of fit test (for simple linear regression) tests the
following hypotheses:
Ho:E{Y}=beta0+beta1*X
Ha:E{Y} not equal to beta0+beta1*X

Basically, the test works as follows:

1/Write a "full" model Y_ij=mu_j+eps_ij
compute SSE(Full)=Sum(i,Sum(j,{Y_ij-Ybarj}^2))

2/Write a "reduced" model Y_ij=beta0+beta1*Xj+eps_ij
compute SSE(Reduced)=Sum(i,Sum(j,{Y_ij-beta0+beta1*Xj}^2))

3/Set up a F test that compares SSE(Full) with SSE(Reduced)

This test requires repeat observations at one or more X levels.

I am trying to answer the following question:
Is there any advantage in having an equal number of replications
at each of the X levels? Is there any disadvantage?

At this point, I cannot find a reason why an equal number of
replications would be an advantage.

Many thanks for your input.

.

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