I obtained some data from an experiment. I fitted the data using the Mat lab fitting tool , but I unable to get the curve back ?

Please refer the image :-

Blue line : Experimental data Red line : 6th order fit using fitting tool of Matlab ( equation displayed on the window )

( Equation : y = - 6.1e-11*x^{6} + 5.9e-09*x^{5} - 2.1e-07*x^{4} + 3.5e-06*x^{3} - 2.3e-05*x^{2} + 2.8e-05*x + 0.00045 )

So I went back to Matlab to check if this correct ...so I typed :

>> x = [ 0 : 0.01 : 32];
>> y =(( - 6.1e-11.*x.^(6)) + (5.9e-09.*x.^(5)) - (2.1e-07.*x.^(4)) + (3.5e-06.*x.^(3))-(2.3e-05.*x.^(2)) + (2.8e-05.*x) +( 0.00045));
>> plot(x,y)

I am getting the black curve ... Is it the problem with small coefficients of the polynomials ? Please help!

Answer 1

[Star Strider]

I suspect you’re correct. The curve fitting tool is significantly truncating the precision of the coefficients it presents to you to two significant figures, while it keeps — and calculates — using full double precision maths it has available to it. I am not surprised that a truncated version of the coefficients and constants produces a different curve from the full precision calculations, although I would not expect it to be so extreme a deviation as it is.

[Suhas]

Thanks for your input...The curve fitting tool does have the option to select number of significant digits. I did not try for 6th order but my 4th order with 5 significant digits sits on the curve perfectly.I was very surprised with the deviation myself!

[Star Strider]

My pleasure!

I don’t have the Curve Fitting Toolbox (Statistics and Optimization Toolboxes make it redundant for me), so I thought you were simply cutting and pasting the display from the output. I always suggest using the full precision for all calculations, although truncating them to the appropriate number of significant digits for publication purposes is appropriate.