----- Original Message -----
From: ELN/fisackson <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Monday, January 17, 2000 6:12 PM
Subject: Linear Correlation with errors in both variables
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Your statement does not sound right.
Given two variables, (X and Y) and a set of measurements of X and Y, there
is not sufficient information in the data set to simultaneously regress and
also obtain estimates of the error in Y and the error in X. You have to
input additional information. One is that the relationship is linear. Two
that the ratio of the X error variance to the Y error variance is known.
When these two are known, then there is a solution.
If however the X is a matrix of 2 or more X values then I can use Total
Least Squares techniques (Van Huffel and others) to obtain estimates of the
errors-in-variables. There are a variaty of approaches, some of which
consider the error in the linear relationship as being significant, others
look at the instrumental error in X, and others look at methods to reduce
the rank of the X matrix and as a result obtain estimates of errors in X.
The process is quite complicated in terms of matrix operations, the
assumptions, the interpretaions of what is the natrure of the distribution
of eigenvalues, the model being investigated and which guru you are
following.
DAHeiser
> Gentlefolk,
>
> There exists a technique known as Orthogonal Distance Regression (aka
> Deming regression) to establish if a linear relationhsip exists between
> two variables when both are subject to error. A few statistics packages
> even calculate it. I wonder if there exists a similar technique to
> calculate a correlation coefficient bewteen two such variables, of if the
> old Pearson correlation coefficient does not assume inerrancy in one
> variable and is thus a sound measure. ID the Pearson moment is
> unsatisfactory and someone knows of an algorithm or equations from which
> one might calculate a suitable measure, I'd be grateful to hear from you.
>
> I apologize if the question is trivial but all my reference materials are
> stil in an unpacked state somewhere between Atlantis and Atlanta (;-)
>
> Thanks for your indulgence,
>
> Frank Isackson
>
