Re: vertical or perpendicular offets?
- To: mathgroup at smc.vnet.net
- Subject: [mg67304] Re: vertical or perpendicular offets?
- From: Bill Rowe <readnewsciv at earthlink.net>
- Date: Sat, 17 Jun 2006 04:36:25 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On 6/16/06 at 12:27 AM, dantimatter at gmail.com (dantimatter) wrote:
>Does anyone know what the Regress and NonlinearRegress functions in
>Mathematica are minimizing? Is it the sum of the squares of the
>perpendicular offsets or the vertical offsets? I would think that
>it would be the vertical offsets, but then points that lie along a
>steep part of a curve are weighted more heavily than points that lie
>along a shallow part of the curve.
The assumed model in both of these packages is
y = f(x) + error
where the error term is assumed to come from a normal distribution. Standard regression packages (which include Regress and NonlinearRegress) minimize Sum[error^2, {1,n}] for the set of n data points.
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