I keep getting a warning that says polynomial is badly conditioned when I use polyfit() to find the polynomial.

x  y
  0  0 
  0  13.46857 
  1  14.40183 
  2  15.30334 
  3  16.17611 
  4  17.02267 
  5  17.84523 
  6  18.6457 
  7  19.42574 
  8  20.18682 

(... ....more, till x = 2000).

These are teh data I import

This is the error I got. I don't get it why. When I tested with 0 is not 12.5, instead, it's always larger. Other students can get 12.5. I don't know where the problem is.

Answer 1

[Walter Roberson]

If your x values range from 0 to 2000, then you cannot numerically justify a degree 10 polynomial fit. Consider that for x = 1, the leading term C10*x^10 would be C10*1^10 -> C10 and that for x = 2000, the leading term C10*x^10 would be C10*2000^10 -> C10 * 1.024E33 . The difference between those is so large that the x = 1 version is effectively meaningless.

You can try using centering and rescaling; see the polyfit() documentation. But the main thing you should do is not use a degree 10 polynomial to fit; the results are typically numerically meaningless.

[Yingyi Huang]

I asked my professor why it can't be 2 degree today, and he says we should have a 10 degree polynomial to increase the agreement between the polynomial equation and the data. If we get an equation for the polynomial, and plug in the same x values as provided, we will receive slightly different y values than the ones provided. We can compare the actual data to the estimated curve with an R^2 correlation value. This values goes between 0 - 1, with 0 being a poor fit and 1 being an identical fit. If we are doing a 2 degree polynomial we will have an R^2 value of ~0.900, while a 10 degree polynomial will have an R^2 of ~0.999, which is more accurate. (We are scaling cone to better print the cone perfectly)