# [R] Obtaining a quadratic function igven three points on a curve

David Scott d.scott at auckland.ac.nz
Thu Jan 20 16:17:52 CET 2011

```I think you need poly(X, 2,  raw = TRUE) to interpret the coefficients
in the manner described below.

poly uses orthogonal polynomials by default:

poly                   package:stats                   R Documentation

Compute Orthogonal Polynomials

Description:

Returns or evaluates orthogonal polynomials of degree 1 to
'degree' over the specified set of points 'x'. These are all
orthogonal to the constant polynomial of degree 0.  Alternatively,
evaluate raw polynomials.

David Scott

On 21/01/2011 3:50 a.m., Joshua Wiley wrote:
> Hi Barth,
>
> Here is an option fitting a linear model toa  second order polynomial
> and extracting the coefficients.  The Intercept corresponds to "c" in
> your email, then poly(...)1 to "b" and poly(...)2 to "a".
>
> ################
> Y X
> 0.159529 0
> 0.5 0.773019
> 1 1"), header = TRUE)
> closeAllConnections()
>
> coef(lm(Y ~ poly(X, 2), data = dat))
> #################
>
> For details see:
>
> ?poly
> ?lm
> ?coef
>
> Hope this helps,
>
> Josh
>
> On Thu, Jan 20, 2011 at 6:42 AM, Barth B. Riley<bbriley at chestnut.org>  wrote:
>> Hello
>>
>> I would like to obtain the coefficients for a quadratic function (ax^2 + bx + c) given three sets of points on the quadratic curve. For instance:
>>
>> Y                       X
>> 0.159529                0
>> 0.5                     0.773019
>> 1                       1
>>
>> Is there a function in R to obtain the a, b and c ceofficients?
>>
>> Thanks
>>
>> Barth
>>
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>

--
_________________________________________________________________
David Scott	Department of Statistics
The University of Auckland, PB 92019
Auckland 1142,    NEW ZEALAND
Phone: +64 9 923 5055, or +64 9 373 7599 ext 85055
Email:	d.scott at auckland.ac.nz,  Fax: +64 9 373 7018

Director of Consulting, Department of Statistics

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