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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