[R] surf.ls

[Roger Bivand]

On Thu, 9 Dec 2004, m p wrote:

> Hello,
> I am looking into description of surf.ls(spatial)
> and see under value $beta - the coefficients.
> When I use polynomial of degree 2 to fit surface
> I expect to get 4 coefficients:
> 
> z = a_1 x^2 + a_2 xy + a_3 y^2 + a_4
> 
> What do beta really stand for and why do I get
> $beta vector of length 6?

No, z = a_1 x^2 + a_2 xy + a_3 y^2 + a_4 + a_5 x + a_6 y,

if you like, order 2 is linear + quadratic, see p. 420 in MASS (4th 
edition), eq. 15.1:

f((x,y)) = \sum_{r+s \leq p} a_{rs} x^r y^s, 

with P = (p+1)(p+2)/2 coefficients for order p; for p=2, P=6.

> 
> Thakns,
> Mark
> 
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Breiviksveien 40, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
e-mail: Roger.Bivand at nhh.no