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st: Calculating inflection points using centered data


From   Claude Francoeur <[email protected]>
To   "[email protected]" <[email protected]>
Subject   st: Calculating inflection points using centered data
Date   Sun, 18 Jan 2009 15:17:54 -0500

Hello,

Doing a quadratic regression, I get the following coefficients on X1 and X1_squared :
-0.0035474, , 0.0006169
The inflection point is 2.87518236

With centered data, I get the following coefficients on X1 and X1_squared :
-0.0001749 and 0.0006169

The inflection point  is 0.14175717

The difference between the inflection points (2.87 - 0.14) is 2.73 which is the mean of X1. This is understandable since the data were centered using this mean.

Now, if do a cubic regression with the same data, I get the following coefficients on X1, X1_squared and X1_cubed :
0.0291735,  -0.0134094 and 0.0014875

The first inflection point  is 1.08780035
The second inflection point  is 3.00490756

With centered data, I get the following coefficients on X1, X1_squared and X1_cubed :
-0.0107918, -0.0012108 and 0.0014875

The first inflection point  is -4.45647506
The second inflection point  is 0.27132773

The difference between the second inflection points (3.00 – 0.27) is -2.73 which represents the mean of X1.

The difference between the first inflection points (1.087 + 4.456) is 5.54 which does not represent the mean of X1. Could anyone explain why this is so?

If I subtract the mean from the first inflection point, I get a negative value which is out of the original data range. How do I convert centered inflection points to uncentered ones correctly?

Your help is very much appreciated.

Thank you.

Claude




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