Good non linear Regression
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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.
4 个评论
Adam Danz
2020-4-30
Do you know the underlying function or do you have an expectation of what the function should be?
Alex Sha
2020-5-1
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
2020-5-1
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
2020-5-1
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.
采纳的回答
Ameer Hamza
2020-4-30
编辑：Ameer Hamza
2020-4-30
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
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