[R] Confidence intervals and polynomial fits

[peter dalgaard]

On May 7, 2011, at 16:15 , Ben Haller wrote:

> On May 6, 2011, at 4:27 PM, David Winsemius wrote:
> 
>> On May 6, 2011, at 4:16 PM, Ben Haller wrote:
>>> 
>> 
>>> As for correlated coefficients: x, x^2, x^3 etc. would obviously be highly correlated, for values close to zero.
>> 
>> Not just for x close to zero:
>> 
>>> cor( (10:20)^2, (10:20)^3 )
>> [1] 0.9961938
>>> cor( (100:200)^2, (100:200)^3 )
>> [1] 0.9966219
> 
>  Wow, that's very interesting.  Quite unexpected, for me.  Food for thought.  Thanks!
> 

Notice that because of the high correlations between the x^k, their parameter estimates will be correlated too. In practice, this means that the c.i. for the quartic term contains values for which you can compensate with the other coefficients and still have an acceptable fit to data. (Nothing strange about that; already in simple linear regression, you allow the intercept to change while varying the slope.)


-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
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Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com