formula for nonlinear regression model
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Dear MatLab Experts,
I have four column vectors with 14 elements representing respectively:
Area, Max.Diameter, Min.Diameter, Field Size Factor (FSF) of custom-made collimators.
I believe the FSF depends somehow on the other three quantities. The dependence is not linear.
I woud like to tryto model the FSF as a power law involving products of the other quantities.
For instance, FSF ~a*(Max.Diam*Min.Diam)^b + c*(Area/Max.Diam)^d + e*(Area/Min.Diam)^f + g*(Max.Diam/Min.Diam)^h + i
where a, b,c,d,e,f,g,h,i are the unknown model coefficients.
I am pretty sure most of the terms are useless. Perobably just one is necessary for the model. However, I do not know which one is the most important term. I expect the modeling function will figure that out.
My problem is that I do not know how to write the above formula in the proper format expected by the nonlinear regression functions.
I need some help to set up the above outlined particular model.
Thank you very much in advance.
Best regards,
Maura E. M.
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SYED IMTIAZ ALI SHAH
2019-8-14
Is this what you want?
x = MaxFDiam .* MinFDiam + Area ./ MaxFDiam + Area ./ MinFDiam + MaxFDiam ./ MinFDiam; % your formula
Linear model Poly7:
Your resultant equation with coefficients.
f(x) = p1*x^7 + p2*x^6 + p3*x^5 + p4*x^4 + p5*x^3 +
p6*x^2 + p7*x + p8
Coefficients (with 95% confidence bounds):
p1 = 2.961e-18 (-5.495e-18, 1.142e-17)
p2 = -6.914e-15 (-2.189e-14, 8.064e-15)
p3 = 6.708e-12 (-4.044e-12, 1.746e-11)
p4 = -3.496e-09 (-7.522e-09, 5.297e-10)
p5 = 1.054e-06 (2.132e-07, 1.895e-06)
p6 = -0.0001832 (-0.0002798, -8.656e-05)
p7 = 0.01691 (0.01138, 0.02244)
p8 = 0.3618 (0.2454, 0.4782)
Goodness of fit:
SSE: 5.048e-06
R-square: 0.9998
Adjusted R-square: 0.9995
RMSE: 0.0009173
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