Minimum least square fitting with multiple variable

Hello

I am trying to fit my data with a linear trend using MLS fitting. However, I don't understand how the initial guess affects the final results. I realized that by changing the initial guess from x0 = [1 1], the result of my variable change and I'm confused about deciding which one gives me the best fitting.

My working code and data are found below

data = readtable('data.xlsx');
xdata = table2array(data(:,1));
ydata = table2array(data(:,3));
x = linspace(min(xdata), max(xdata));
fun = @(a)a(1).*xdata + a(2) - ydata;
x0 = [1 1];
x1 = lsqnonlin(fun, x0);
figure
plot(xdata,ydata,'o')
hold on
plot(x, x1(1).*x + x1(2))
hold off

Answer 1

[Stephan]

Hi,

you could use the resnorm to compare the quality of different approaches:

[x, resnorm] = lsqnonlin(...)

But the question is, why do you use a nonlinear approach for a linear problem? The kind of problem you have is usually solved optimal by mldivide (optimal in sense of least squares):

data = sortrows(readtable('data.xlsx'));
xdata = table2array(data(:,1));
ydata = table2array(data(:,3));
xdata(:,2)=1;
x = xdata\ydata;
scatter(xdata(:,1),ydata,'or')
hold on
plot(xdata(:,1), x(1).*xdata(:,1)+x(2))
hold off
fprintf('Results:\nx(1)=%.15f\nx(2)=%.9f',x(1),x(2))

Best regards

Stephan