# How do I curve fit the data set

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Hello all,

I'm facing difficulty in fitting the data.

The red ones are from the data set, and I want to fit that as like blue one (Experimental Data). How can I do that. I have also attached the data set for your reference.

Thank You.

##### 2 Comments

Sam Chak
on 29 Jul 2023

Can you also suggest some candidate functions for fitting into the red data? Look up some Kernel functions.

Red data seems to have discontinuities at multiple intervals. Is it acceptable to have a piecewise function to fit the data?

### Accepted Answer

Sam Chak
on 29 Jul 2023

Not sure if this is what your want. But you can try finding the best math function to fit.

data = load('curve_fit.mat');

x = data.theta_degree';

y = data.x';

skewEqn = 'a/(sqrt(2*pi))*exp(- b*(x - c)^2)*((1/2)*(1 + erf(e*(x - c)/sqrt(2)))) + d';

fo = fitoptions('Method', 'NonlinearLeastSquares',...

'Lower', [ 0, 0, 5, 0, 0.1],... % {a, b, c, d, e}

'Upper', [100, 1, 20, 10, 1.0],...

'StartPoint', [50 0.5 10 5 0.5]);

ft = fittype(skewEqn, 'options', fo);

[yfit, gof] = fit(x, y, ft)

plot(yfit, x, y)

grid on, xlabel('\theta'), ylabel('x')

legend('Data', 'Fitted Skew Dist Fcn')

##### 2 Comments

### More Answers (1)

Alex Sha
on 29 Jul 2023

@Prajwal Magadi, one more function:

Sum Squared Error (SSE): 75571.6557870726

Root of Mean Square Error (RMSE): 2.74902993412354

Correlation Coef. (R): 0.962878352853849

R-Square: 0.927134722394541

Parameter Best Estimate

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

y0 3.57509887406416

a 10210313.7484567

xc 17.1109591760412

w1 18.7010167618592

w2 -1.38399464317597

w3 -1.49504622174935

##### 3 Comments

Alex Sha
on 29 Jul 2023

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