, 
, 
, 
and 
so that the design matrix is
If we fit a simple linear regression of the form
for which the design matrix is as above,
evaluate the non-centrality parameter of the t test of 
when in fact 
and 
. What would the power of a
two sided 1% level t test of this null hypothesis be? How many
times would we have to replicate this design to get a power of 0.9 for
a 1% level test?
as in the previous question evaluate the
non-centrality paramter of the F test of the hypothesis 
in the model
Assume that in fact 
and 
.
where the errors 
have variances 
and
the 
are known quantities.
Find an explicit algebraic formula for the weighted least squares
estimate of 
.