I want to find the coefficients for the regression equation using nonlinear regression analysis.

We want to find the coefficients for the regression equation using nonlinear regression analysis.

For example

M=3, 3, 3, 3, 4, 4, 4, 4
R=0, 10, 20, 30, 0, 10, 20, 30

The corresponding (M,R)=SA and the SA value is not calculated, but I enter it.

SA=5, 10, 20, 16, 15, 10, 30, 13

In other words

(3,0)=5
(3,10)=10
(3,20)=20
(3,30)=16
(4,0)=15
(4,10)=10
(4,20)=30
(4,30)=13

Using this data, I want to find the coefficients a, b, c, and d that satisfy the regression equation SA=a*M+b*log(R+c)+d. How to try...

Answer 1

[Matt J]

fminspleas from the file exchange

https://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

would be particularly appropriate,

M=[3, 3, 3, 3, 4, 4, 4, 4].';
R=[0, 10, 20, 30, 0, 10, 20, 30].';
SA=[5, 10, 20, 16, 15, 10, 30, 13].';

MR=[M,R];

funlist={ @(c,mr) mr(:,1)  ,  @(c,mr)log(mr(:,2)+c),  1 };

[c,abd]=fminspleas(funlist,0,MR,SA,0);

[a,b,c,d]=deal(abd(1),abd(2), c, abd(3))

a =

    4.2500


b =

    5.6953


c =

    7.4083


d =

  -16.7902