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MathGroup Archive 2006

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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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