Re: Polynomial Regression

From: *** Startz (richardstartz1_at_comcast.net)
Date: 10/31/04 

Date: Sun, 31 Oct 2004 01:50:38 GMT

On Sun, 31 Oct 2004 00:56:05 GMT, SomeOne <someone@somewhere.net>
wrote:

>*** Startz wrote:
>> On 30 Oct 2004 12:55:54 -0700, someone1560@hotmail.com (SomeOne)
>> wrote:
>>
>>
>>>I'm a complete noobie in stats so pardon me if i dont phrase my
>>>question correctly ;) but...
>>>is there a general equation for polynomial regression ? if not is
>>>there one for quadratic regression (ax^2+bx+c) ?
>>>
>>>I found that the coeffients of a linear regression are just some
>>>summation processes and i was hoping polynomial regression should be
>>>just as easy...
>>>
>>>Thanks.
>>
>>
>> Phrased perfectly sensible. This is just a multiple regression. Define
>> Z=x^2 and then just regress aZ+bx+c.
>>
>> -*** Startz
>> ----------------------
>> Richard Startz RichardStartz@comcast.net
>> Lundberg Startz Associates
>
>
>how would i calculate a,b,c (and other coefficient variables for higher
>degrees) ?

The practical answer is: use canned multiple regression software.
Microsoft Excel will do it for you, although purpose-built statistical
software is probably much better suited to the task. But if Excel is
easily available, check the help system for regression.

The theoretical answer is that the regression coefficients are given
by the matrix expression

beta = inv(X'X)X'y

where beta is a column vector of estimated regression coefficients, X
is matrix in which each column is one right-hand side vector, and y
is the variable you're trying to explain.

Your intuition that the coefficients are just summation formulas is
basically correct, but with more than one explanatory variable the
implementation gets really messy. Essentially, if you have k
explanatory variables, you have to solve k linear equations in k
unknowns.
-*** Startz
----------------------
Richard Startz RichardStartz@comcast.net
Lundberg Startz Associates