Re: Problem related to a linear regression
- From: matt271829-news@xxxxxxxxxxx
- Date: Thu, 01 Nov 2007 20:06:21 -0700
On Nov 1, 2:20 pm, MET <Marcel.E.Tschu...@xxxxxxxxx> wrote:
Hello
The problem I'm facing may arise from trying to do a regression of the
same one parameter set where x is the esimated value and y the actual
observed value. Let me explain step by step what I'm doing; may be you
can recognise from this if the way I proceed is (a) correct and (b)
the direct way, i.e. not performing a detour for obtaining the correct
result.
What I'm aiming at is to calculate the actual measured value (Y) from
the results of a fitting function (Xf) calculated with a set of other
parameters in the form:
Y=A+B*Xf
with A and B obtained by regression analysis.
In order to obtain the values for A and B a regression has been
calculated with the Xf and Y values by maximising the correlation
(R**2). Depending on the type of function and the parameters used (for
calculating Xf) the resulting points (Xf, Y) are 'somewhere' along the
x-axis around the regression line having a certain slope.
Assuming that this regression calculation would already be the final
result, the X-values were scaled with A and B of the regression line.
This shifted the data points (Xf and Y) around the regrression line
which after this transformation corresponded to Y=Xf. It was thought
that this regression line (Y=Xf) would correspond to the final result.
However, looking at the graph suggests that this line doesn't really
correspond to the 'best fit' and that it represents only to an
intermediate result;
I'm kind of confused. Initially you found the values of A and B that
give the best fit of the line y = A + B*x to the data points (Xf, Y)?
Then you applied the transformation Xf' = A + B*Xf, where Xf' is the
transformed X-value? (This is what I assume you mean by "the X-values
were scaled with A and B": you're transforming x so as to take the
line y = A + B*x to the line y = x.) And now you're wondering if this
choice of A and B actually gives the best fit of the transformed data
points (Xf', Y) to the line y = x?
Doesn't it amount to exactly the same thing? In the first case you're
choosing A and B so as to minimise the sum of (Y - (A + B*Xf))^2, and
in the second case you're choosing A and B so as to minimise the sum
of (Y - Xf')^2, where Xf' = A + B*Xf?
Maybe I misunderstood it...
therefore A+B*Xf is not yet Y but an intermediate
X (Xi):
Xi=A+B*Xf
requiering an additional regression (minimising the sum of dXf**2) for
obtaining Y:
Y=C+D*Xi
This regression line looks now more to correspond to the best fit
between Y (observed values) and Xf (results of fitting function).
Question: Is it really necessary to perform 2 regression for this
particular problem, or am I doing a detour for obtaining the correct
result?
Thank you for your help and suggestions.
Regards MET
.
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