[R] multivariate multi regression

David Winsemius dwinsemius at comcast.net
Tue Dec 14 03:57:07 CET 2010

On Dec 13, 2010, at 9:21 PM, Bastiaan Bergman wrote:

> That doesn't work, one would get two different answers depending on  
> the
> order of execution.
> The physics is: Overlay error on a Silicon wafer. One wafer has many  
> flash
> fields, each flash field has multiple locations where the overlay  
> error is
> measured (as: dX,dY offset). If one contemplates that the error is  
> caused by
> a rotation of the flash field then we can say (dX,dY)=(-Y,X)*RotAngle.

Some sort of linearized approximation of a rotation matrix?

> If in
> addition we have a scaling error: (dX,dY)=(X*XScale,Y*YScale) than  
> the total
> model is:
> dX~X*XScale-Y*RotAngle
> dY~Y*YScale+X*RotAngle
> Now I want to find the values for XScale, YScale and RotAngle

... that does _what_? Minimize the sum of squares of dY and dX?

> Length(dX)==length(dY)==length(X)==length(Y)==number of measured  
> sites on a
> wafer

So dY and dX are measured and X and Y are measured how many times?   
And are we doing this for several different wafers so that we need to  
have nested models that incorporate an error term for each wafer? (And  
if that is the case this may need to be transferred to the mixed- 
models mailing list or at the very least answered by someone with a  
better ax swing for such complexities that I can wield.)


> Hope this clarifies...
> -----Original Message-----
> From: David Winsemius [mailto:dwinsemius at comcast.net]
> Sent: Monday, December 13, 2010 6:06 PM
> To: Bastiaan Bergman
> Cc: r-help at r-project.org
> Subject: Re: [R] multivariate multi regression
> On Dec 13, 2010, at 8:46 PM, Bastiaan Bergman wrote:
>> Hello,
>> I want to model my data with the following model:
>> Y1=X1*coef1+X2*coef2
>> Y2=X1*coef2+X2*coef3
>> Note: coef2 appears in both lines
>> Xi, Yi is input versus output data respectively
>> How can I do this in R?
>> I got this far:
>> lm(Y1~X1+X2,mydata)
>> now how do I add the second line of the model including the cross
>> dependency?
> The usual way would be to extract coef2 from the object returned from
> the first invocation of lm(...)  and use it to calculate an offset
> term in a second model. It would not have any variance calculated
> since you are forcing it to be what was returned in the first model.
> Now, what is it that you are really trying to do with this procedure?
> -- 

David Winsemius, MD
West Hartford, CT

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