find the model parameters that minimizes the sum of the squared residuals in matlab

To find the model parameters that minimize the sum of squared residuals in Matlab, we can use the lsqcurvefit function from the Optimization Toolbox. The lsqcurvefit function performs nonlinear least-squares regression and returns the estimated parameters that minimize the sum of squared residuals.

Here's an example of how to use lsqcurvefit:

main.m
% Define the model function
model = @(x,xdata) x(1)*exp(x(2)*xdata);

% Define the values of xdata and ydata
xdata = [0:0.1:1];
ydata = [0.9 1.5 2.5 3.5 5.5 9.1 15.1 25.2 42.2 70.4 117.4];

% Define the initial guess for the model parameters
x0 = [1 1];

% Call lsqcurvefit to minimize the sum of squared residuals
x = lsqcurvefit(model, x0, xdata, ydata);

% Display the estimated parameters
disp(['Estimated Parameters: ',num2str(x)])
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In this example, we define a simple exponential model function, model = @(x,xdata) x(1)*exp(x(2)*xdata), with two parameters. We then define our input data (xdata) and output data (ydata).

Next, we define an initial guess for the model parameters (x0). We then call the lsqcurvefit function and pass it our model function, initial guess, xdata, and ydata. The function returns our estimated parameters x that minimize the sum of squared residuals.

Finally, we display the estimated parameters using disp(['Estimated Parameters: ',num2str(x)]).