Hi, I'd like to adjust a set of points to an expression like this "E=c1*H+c2​*H*T^(-2)+​c3*T", please help!!...Thanks

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Fred
Fred 2014-7-10
回答： Star Strider 2014-7-10
"E=c1*H+c2*H*T^(-2)+c3*T"
where
E,H,T are variables c1, c2, c3 are the regression coefficients
I have all the data necessary of the three variables from a 1 month period, I'd like to know how to obtain the regression coefficients I think that it's a multiple non linear regression but, I don't know what functions of matlab I could use, I'll be thankful for your help.
Thank you very much!!

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回答（2 个）

Brian B
Brian B 2014-7-10
This is a linear regression problem, since it is linear in the coefficients. Assuming E, H, and T are column vectors, you might simply try:
R = [H H.*T.^(-2) T];
c = R\E;
This finds the least-squares solution for the linear equation E = R*c.
Star Strider
Star Strider 2014-7-10
See if this example does what you want:
H = randi(10, 5, 1); % Define H
T = randi(10, 5, 1)+10; % Define T
c = [3 5 7]'; % Define c
X = [H H./(T.^2) T]; % Design matrix
Y = X*c + 0.1*rand(5,1); % Create dependent variable + noise
c = X\Y % Solve for coefficients
If you have the Statistics Toolbox, see the documentation for the LinearModel class.

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