Re: Question on Lack of Fit test in Simple Linear Regression.

On Sat, 22 Sep 2007 08:46:33 -0700, isabellesup@xxxxxxxxxxx wrote:

Dear Forum,

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.



If you want to test the fit of the model at just one point,
you can surely draw all your data at that *one* point.

If you want to test across the range, you sample across
the range - that is usually the case.

If you are sure that the data are generally linear, and that
the extreme won't hold the exceptions, then you will
get most power when you concentrate your sample at
the extremes.

__
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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