# How to define a custom equation in fitlm function for linear regression?

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Spirit 2017 年 11 月 22 日

I'd like to define a custom equation for linear regression. For example y = a*log(x1) + b*x2^2 + c*x3 + k. This is a linear regression problem - but how to do this within FitLm function?
Thanks, Shriram

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### 回答 (2 件)

the cyclist 2017 年 11 月 22 日

% Set the random number seed for reproducibility
rng default
% Make up some pretend data
N = 100;
x1 = rand(N,1);
x2 = rand(N,1);
x3 = rand(N,1);
a = 2;
b = 3;
c = 5;
k = 7;
noise = 0.2*randn(N,1);
y = a*log(x1) + b*x2.^2 + c*x3 + k + noise;
% Put the variables into a table, naming them appropriately
tbl = table(log(x1),x2.^2,x3,y,'VariableNames',{'log_x1','x2_sqr','x3','y'});
% Specify and carry out the fit
mdl = fitlm(tbl,'y ~ 1 + log_x1 + x2_sqr + x3')
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the cyclist 2021 年 6 月 16 日
Where I define those variables, that is just part of me creating a pretend dataset. In a real-life problem, you wouldn't do that. You'd just have the observations of the x and y data to fit.

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laurent jalabert 2021 年 12 月 19 日

To proceed with a custom function it is possible to use the non linear regression model
The example below is intended to fit a basic Resistance versus Temperature at the second order such as R=R0*(1+alpha*(T-T0)+beta*(T-T0)^2), and the fit coefficient will be b(1)=R0, b(2) = alpha, and b(3)=beta.
The advantage here, is that the SE will be computed directly for R0, alpha and beta.
beta0 is an initial range of [R0 alpha beta]
b(n) is retrieved using mdl.Coefficients.Estimate(n), for n=1,2,3
standard deviation on the coefficients are retrieved by mdl.Coefficients.SE(n)
(Curve fitting toolbox and Statistical/Machine Learning toolbox are both requiered)
clear tbl mdl
% your vector data T_T0 and R of same dimension
tbl = table(T_T0,R);
modelfun = @(b,x)b(1).*(1+b(2).*x(:,1)+b(3).*x(:,1).^2);
beta0 = [100 1e-3 1e-6];
mdl = fitnlm(tbl,modelfun,beta0,'CoefficientNames',{'R0';'alpha';'beta'})

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