I have the following data:
x = [0 5 10 15 20 25 30 35].';
y = [72.3 73.6 75.1 77.0 77.6 77.9 79.2 80.4].';
When I enter this code:
pg7 = polyfit(x,y,7);
The following warning appears and I don't know why:
Warning: Polynomial is badly conditioned. Add points with distinct X values, reduce the degree of the polynomial, or try centering and scaling as described in HELP POLYFIT.
You are trying to do a polynomial regression of order 7 on 8 data points. This will not be a regression but an interpolation as 8 points uniquely determines a 7th order polynomial.
So do as the error message tells you, add more points or lower the degree.
Alternatively, if you truly are after the interpolation, then do a Lagrange interpolation instead of fitting.
The warning states that there are possible numeric issues related to the fitting process, because your x values are not centered around 0 and because you're using a determined model.
Using the curve fitting tool (cftool) you can see that the difference between centering and scaling and not doing so is between a fitting SSE of 1.831e-24 and 6.664e-27, respectively.
In other words - in this specific case, centering and scaling your data practically doesn't matter and the warning can be safely ignored.
On a different note, unless you have a good reason to do so, you probably shouldn't be fitting the maximum-possible-degree polynomial to your data (known as "overfitting"), as this is believed to captured noise and not the underlying phenomenon. Consider using a lesser-degree polynomial (e.g. 6), spline, pchip etc.
