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

isabellesup@xxxxxxxxxxx schreef:
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.

The distribution of observations over X-values has effect on the precision of the regression, not on the lack of fit test.
.

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