Good non linear Regression

I have the following data:

x = [15, 25, 35, 45, 55, 65, 75]

y = [22.3, 27.5, 28.8, 29.9, 29.6, 27.4, 23.3]

How could I create a good regression that would fit the data above best. I'm trying to plot them both on the same graph so you can see the different between both lines.

[Adam Danz]

Do you know the underlying function or do you have an expectation of what the function should be?

[Alex Sha]

The fitting model below is good enough:

y = p1+p2*x+p3*ln(x)+p4/x+p5/x^2

Root of Mean Square Error (RMSE): 0.00486074972111081
Sum of Squared Residual: 0.000165388214958952
Correlation Coef. (R): 0.999998485296235
R-Square: 0.999996970594765

Parameter	Best Estimate
----------	-------------
p1	-1030.61369989144
p2	-2.88996744088543
p3	271.393077102476
p4	7919.34753749812
p5	-37493.8788669532

[Ameer Hamza]

Is this result also from 1stOpt? Did you specify the equation or the toolbox is also able to find a suitable equation to fit the data points automatically? I have never tried it, so I am not aware of all the features.

[Alex Sha]

If matlab, refer: https://www.mathworks.com/matlabcentral/fileexchange/32225-interface-with-eureqa-featuring-symbolic-regression

There is also a function in 1stOpt in which the best fit model function could be serached automatically according to the data user provided.

Answer 1

[Ameer Hamza]

One option is to use smoothingspline option from the curve fitting toolbox

x = [15, 25, 35, 45, 55, 65, 75];
y = [22.3, 27.5, 28.8, 29.9, 29.6, 27.4, 23.3];

model = fit(x(:), y(:), 'smoothingspline');

plot(x, y, 'r+');
hold on
xv = linspace(min(x), max(x));
plot(xv, model(xv), 'b-');

You can also try this FEX package: https://www.mathworks.com/matlabcentral/fileexchange/19564-local-linear-kernel-regression

[Jessica Larry]

I was able to resolve it, thank you so much for the help!!

[Ameer Hamza]

Glad to be of help.