Fitting Question

Hi guys, I am new to matlab. I was wondering if you can help me with fitting some data. These are my values: x= [0.0 0.5 1.0 2.0 5.0 8.0 10.0 12.0 15.0 18.0 20.0] y= [4.92 7.06 18.88 14.12 76.14 32.92 76.49 47.97 35.75 16.11 17.19]

I would like to obtain the best fit. Can you help me with the syntax?

regards,

Answer 1

[Oleg Komarov]

If you have the Curve Fitting TB use cftool to fit the data interactively.

Otherwise an example:

x = [0.0 0.5 1.0 2.0 5.0 8.0 10.0 12.0 15.0 18.0 20.0].';
y = [4.92 7.06 18.88 14.12 76.14 32.92 76.49 47.97 35.75 16.11 17.19].';
[b,S] = polyfit(x,y,3);

plot(x,y,'.',0:0.1:20,polyval(b,0:0.1:20),'-r')

ylim([-100,100])

Answer 2

[Nima Azar]

Oleg, Thank you for your response. This fit gives me an "ok" fit, is there any way to get a better fit for such dataset? I dont have cftool.

Answer 3

[Walter Roberson]

You can get a perfect fit (to within roundoff error) by using polyfit(x,y,length(x))

Unfortunately when you interpolate the function any further, you will very likely decide that the extended values are nonsense. Every polynomial fitting goes to either +infinity or -infinity at the extremes.

If you do not have a model of what the function "should" look like, then there is no way to rank any fitted function as being better or worse than another.

Oleg's suggestion of polyfit() with degree 3 provides (to within roundoff error) the best least-squared degree 3 polynomial over that data. You could keep increasing the polynomial degree until the fitting residue was less than some particular value, but if you do not already have reason to expect a polynomial fit within that degree range, then the solution will be more or less bunk.

Answer 4

[Alex Sha]

How about the function below:

y=y0+A*exp(-0.5*((x-xc)/w)^2)+A1*exp(-exp(-(x-xc1)/w1)-(x-xc1)/w1+1);

Root of Mean Square Error (RMSE): 4.08162493636905

Sum of Squared Residual: 183.256283333086

Correlation Coef. (R): 0.985835143591926

R-Square: 0.971870930340914

Adjusted R-Square: 0.964838662926143

Determination Coef. (DC): 0.971870930340914

Chi-Square: 5.73409196786601

F-Statistic: 23.0336076224438

Parameter Best Estimate

---------- -------------

y0 9.50129005851808

a -61.9721900986626

xc 8.00164037070495

w 0.182284401674019

a1 87.8175531846905

xc1 7.19692083049562

w1 3.25672482403779