Trying to remember term for a type of statistical regression/transformation

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?

It seems like you are trying to do something related to a Normalized Principal Component Analysis. The normalization procedure would replace x by (x-mean(x))/SD(x) and y by (y-mean(y))/SD(y), which is equivalent to the transformation you describe, and the PCA is closely related to the Deming regression. Does this help?

Although related, it’s not just normalization of x and y, in perpetration for further analysis (by PSA or something else), it is a transformation or regression that gives me an approxmation of y as a function of x.

This is not the only way to get the mean and standard deviation of F(x) to equal those of y. Note that if x and y are negatively related, F(x) and x will still be positively related. So it doesn’t seem like a very good one. A regression is

F(x)= (x-mean(x))*Corr(y,x)*SD(y)/SD(x) + mean (y)

So I’d think doing that but adding some nose would be better.