a theorem about pôwer transformation


New Member

while studying on Montgomery's Design and Analysis of experiments, i saw a theorem without proof of which I don't find the correct references. While discussing on how to use power transformations to data that exhibit heteroskedasticity due to a dependance of the variance to the mean, it stated that if the standard deviation of the data is proportional to (E[y])^a, then the standard deviation of y^b is proportional to (E[y])^(a+b-1), therefore to eliminate heteroskedasticity in this case one should set b=1-a.

How can I prove this, or where can I find the proof? I can't find it even in the supplemental text material....

Thanks in advance!