How to formulate and use non linier curve-fitting

I have a dependent variabke Xd and three independent variabel X1, X2 and depth.

I want to formulate new equation using exponential function. I assume the equation is like this Xd = exp(b1 + b2* -dpth *(X1/X2)

Is there any one can help

Answer 1

[Star Strider]

Try this:

D = dlmread('Example.txt', '\t', 1, 0);
objfcn = @(b,x) exp(b(1) - b(2).*x(:,1).*x(:,2)./x(:,3));                           % Objective Function
[B,rnrm] = fminsearch(@(b) norm(D(:,4) - objfcn(b,D(:,1:3))), rand(2,1))            % Estimate PArameters

Xdfit = objfcn(B,D(:,1:3));                                                         % Results
Compare = [D(:,4), Xdfit, D(:,4)-Xdfit];                                            % Results

figure
plot(D(:,4), Xdfit, '-*')
grid

The independent variable matrix is created as:

[Depth X1 X2] = D(:,1:3)

with ‘Xd’ being ‘D(::,4)’.

The plot is of the actual ‘Xd’ and ‘Xdfit’, the modeled ‘Xd’.

[Skydriver]

The result wil be like this (Is it true?):

Xd = exp(-0.0221 + 0.0101* -dpth *(X1/X2)

I wish I can make a figure like in this .jpg

I got a massage like this:

Indexing cannot yield multiple results.

Error in NonlinierFitting (line 9)

[Depth X1 X2] = D(:,1:3)

What should I do?

[Star Strider]

This:

[Depth X1 X2] = D(:,1:3)

simply illustrates how the independent variable matrix is created. Do not use it in practice.

Use this instead:

D = dlmread('Example.txt', '\t', 1, 0);
objfcn = @(b,x) exp(b(1) - b(2).*x(:,1).*x(:,2)./x(:,3));                           % Objective Function
[B,rnrm] = fminsearch(@(b) norm(D(:,4) - objfcn(b,D(:,1:3))), rand(2,1))            % Estimate PArameters
Xdfit = objfcn(B,D(:,1:3));                                                         % Results
Compare = [D(:,4), Xdfit, D(:,4)-Xdfit];                                            % Results

figure
plot(D(:,4), Xdfit, '-*')
grid

The independent variable matrix is created and contained within the code.

[Skydriver]

Yes I am fault I should not enter the last command.

When I plot the figure in the Depth = 0 the vlues of XD is not 1. Can we adjust into 1 from this formulation: Xd = exp(-0.0221 + 0.0101* -dpth *(X1/X2) ?

Let me know what is the theorethical background behind this regression?

[Star Strider]

The ‘Xd’ values for ‘Depth=0’ are 0.978. The value of ‘Xdfit’ for ‘Depth=0’ is not 1 because this is a nonlinear regression based essentially on a least-squares fit of your data to your model. There are several different values of the other variables that correspond to ‘Depth=0’, and those differences will mean that the value that the regression estimates for ‘Depth=0’ may not be equal to 1. That can be seen in the ‘Compare’ matrix that shows and compares the ‘Xd’ data and the ‘Xdfit’ values the regression estimates for them.

[Skydriver]

How come if I add another b such as b3?

objfcn = @(b,x) exp(b(1) - b(2).*x(:,1)+b(3).*x(:,2)./x(:,3));

[B,rnrm] = fminsearch(@(b) norm(D(:,4) - objfcn(b,D(:,1:3))), rand(3,1))

But the result is different

[Star Strider]

The result will be different if you change the regression model. The new model is coded correctly, so you only need to interpret the results. Choose a model that most closely represents the process that created your data, or that most closely represents the physics of the system you are estimating. It is common to create and test several models (based on the appropriate assumptions about the data) to determine which model most closely reproduces the data.

[Skydriver]

Thank you, I will try to a test with several models as your suggestion

[Star Strider]

As always, my pleasure!