Polynomial surface fitting failed

I am trying to use the polynomial fitting function to fit my surface X=[30 60 60 60 90] Y=[280 260 280 300 280] Z=[0.0060 0.0053 0.00438 0.0042 0.0034]

I am choosing degree of x to be 1, and degree of y to be 2, Matlab keeps telling me equation is badly conditioned. Remove repeated data points or trying center and scaling. It still gave me the same results when I checked the box of "center and scale".

I have several sets of other data similar to this by the fitting is working. I don't know what should I do now with this set of data.

Thanks!

[Star Strider]

Consider using Surface Fitting using gridfit by John D'Errico.

Answer 1

[John D'Errico]

You have 5 (count them, FIVE) data points. At least they are reasonably well scattered.

You are trying to estimate a model with how many terms? WHAT IS YOUR MODEL?

sf = fit([X',Y'],Z','poly12')
Warning: Equation is badly conditioned. Remove repeated data points or try centering and scaling. 
> In Warning>Warning.throw at 30
  In fit>iLinearFit at 690
  In fit>iFit at 396
  In fit at 108 
     Linear model Poly12:
     sf(x,y) = p00 + p10*x + p01*y + p11*x*y + p02*y^2
     Coefficients:
       p00 =   1.507e+14
       p10 =  -2.512e+12
       p01 =  -5.384e+11
       p11 =   8.973e+09
       p02 =   -4.48e-05

Your data simply does not justify fitting that model. At best, you have 5 coefficients and 5 data points. The fit would be exact if your data were more conducive to fitting that model, but the data is not sufficient to estimate ALL 5 coefficients uniquely.

Get better data. Or use a simpler model.

(While you COULD use gridfit, as Star Strider suggested) it depends on your goals here. Do you need a model, or do you just want a surface plot?