If I have a set of paired data (x,y) and I want to find a linear transformation such that F(x) is approximately equal to y.
Now I could fit a simple regression, but that will assume that all of the error is coming from y and so will result in a flat (regressed to the mean) curve.
Instead I choose a linear transformation that will have the result that over my data set the mean and standard deviation (SD) of F(x) equals the mean and standard deviation of y.
this is computed as
F(x)= (x-mean(x))*SD(y)/SD(x) + mean (y)
This transformation has a name (I think beginning with an M) and associated wikipedia entry but I can’t for the life of me remember what it is. and my google abilities are failing me. All I can figure out is that its a special case of Deming regression.
Any statistically savvy Dopers know what I’m talking about, or have better google skills?