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From Greg Sterijevski <gsterijev...@gmail.com>
Subject Re: [math] Re: Longley Data
Date Tue, 19 Jul 2011 01:31:34 GMT
```All,

I have pushed the implementation of the Miller Regression technique, along
with some tests. I am sure that there are a lot of sharp corners to file
down and improve. However, I thought it would be prudent to get it out and
then we can further refine the code.

On accuracy:

I seem to match all of the digits of longley and wampler data. Filippelli I
have a very hard time matching except to a tolerance of 1.0e-5. If you look
at LIMDEP's website:

http://www.limdep.com/features/capabilities/accuracy/linear_regression_3.php

I think that the code I am checking in does a bit better. I am happy about
that. However, there are some other issues with Filippelli. Namely, one can
affect the 'accuracy' of your results depending on how you present the data.
For example, if I generate the high order polynomial naively, x1 = x0 * x0,
x2  = x0 * x1, ..., x10 = x0 * x9, then I can hit the numbers within 1.0e-5.
If, however, I generate the Filipelli regressors by multiplying numbers
whose magnitudes are similar:
x1 = x0 * x0;
x2 = x0 * x1;
x3 = x0 * x2;
x4 = x2 * x2;
x5 = x2 *x3;
x6 = x3 * x3;
Then I have a very hard time making that 1.0e-5 tolerance.

Does anyone know if there is some article which explains the proper way to
set up Filippelli's test?

Speaking to Luc's point, maybe the correct thing to do is to move to
arbitrary precision. I wanted to avoid this until I was at a deadend.
Perhaps the time is now....

On tests:

I intend to push 3-4 tests soon. There are 17 tests in the first suite I
sent in.

-Greg

```
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