# Linear fitting with 2 variables

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Lotmeri on 14 Oct 2021
Edited: Lotmeri on 15 Oct 2021
Hi everybody,
I'm trying to solve a linear fitting using Matlab. In particular my function is: y=a*x+ b+ c*f, where I have y that it is a matrix 3x15, x is a vector 1x15 and f is a vector 1x3001.
Is there any particular function that is able to fit the coefficients a,b,c directly? Also taking into account that the vectors are not all of the same lenght.
Thank you so much.
PS. I do not have the GADS_Toolbox (for the function createOptimProblem).
##### 2 CommentsShowHide 1 older comment
Lotmeri on 14 Oct 2021
Of course.
y=[92.41, 91.69, 90.93, 90.48, 89.48, 88.33, 88.76, 88.18, 86.56, 85.54, 84.35, 82.73, 84.35, 81.08, 76.25;
97.18, 96.01, 96.08, 93.94 , 94.23, 93.94, 93.05, 92.81, 91.41, 90.77, 89.61, 88.18, 86.17, 84.31,81.00;
97.80, 96.97, 96.51, 95.85, 95.32, 94.72, 94.19, 93.63, 92.59, 91.45, 90.29, 88.53, 86.80, 84.69, 81.33];
x=[8.20, 7.92, 7.63, 7.32, 6.99, 6.63, 6.23, 5.80, 5.31, 4.77, 4.15, 3.42, 2.55, 1.46, -7.71e-15];
f=10*log10(linspace(270,300,3001));
I think that for adjust the dimensions I should use a "repmat"...

Matt J on 14 Oct 2021
Edited: Matt J on 14 Oct 2021
Assuming f is 3x1,
x=rand(1,15); %Example data
f=rand(3,1);
y=3*x+2+7*f;
[F,X]=ndgrid(f,x);
p=num2cell( [X(:), X(:).^0, F(:)]\y(:) );
[a,b,c]=p{:}
a = 3.0000
b = 2.0000
c = 7

Alan Weiss on 14 Oct 2021
I think that the Problem-Based Optimization Workflow would help. Write your optimization variables a, b, and c as you have done, then set the objective as the minimization of the sum of squares of differences between your data and your result using the optimization variables (I cannot be more specific here because I do not understand what you are etrying to minimize).
Alan Weiss
MATLAB mathematical toolbox documentation
Lotmeri on 14 Oct 2021
Ok thank you so much. It works!