I have lost an article that deals with appropriate adjustment of slope,
and I have lost the complete reference. The only remaining clue I have
is (Feldmann, 1981). The paper provides a formula for adjusting the OLS
slope to a more appropriate slope that takes into account measurement
error in the X variable. I have that formula, but nothing else.
My immediate problem is that I believe the article provides this formula
with the statement (paraphrased): If the measurement errors for X and Y
are equal, then the formula for the new slope will reduce to
(OLSslope)/corr(x,y).
On the other hand, that statement may have come from another source,
perhaps talking about the "Deming slope." (A similar adjustment)
Regardless, I believe the former and am concerned that my check for
correctness of the formula did not yield (OLSslope)/corr(x,y) when I set
the measurement errors to be equal (that part does not come from the
actual data, necessarily).
I wish that I could write out the formula here, but I am afraid it would
cause confusion. I can, however, email it as a Word document, if that
Feldmann article is not handy to you.
I contrived data so that I might check. My OLS slope = 1.99273, the
slope divided by the correlation = 2.04886, and Feldmann's formula (with
equal errors) yields 2.08448. Here's the data X, Y that I used:
X Y
2 3
5 4
9 15
14 22
25 21
35 52
37 89
42 58
49 94
64 100
71 150
81 155
81 174
92 162
I am wondering if there is a mistake in the paper's formula, or if I am
simply wrong in my assumption that the formula reduces so simply when
the errors are equal (in which case I apologize profusely). Any help is
greatly appreciated. Again, I will gladly send along the formula I have
if requested to do so.
Thank you, Todd
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