how to calculate the exponential regression of two vectors in matlab

To calculate the exponential regression of two vectors in MATLAB, you can use the fit function. The fit function uses nonlinear least squares regression to fit data to a mathematical model. In this case, we will use the exponential model y = a * exp(b * x) to fit our two vectors.

Here is an example code that demonstrates how to do it:

main.m
x = [1 2 3 4 5];
y = [1.5 3.7 8.5 18.2 33.6];

% Define the exponential model with unknown coefficients
fun = @(c,x) c(1) .* exp(c(2) .* x);

% Use nonlinear regression to fit the exponential model to the data
coefficients = nlinfit(x, y, fun, [1 1]);

% Extract the fitted values
y_fitted = coefficients(1) .* exp(coefficients(2) .* x);

% Plot the original data and the fitted curve
plot(x, y, 'o', x, y_fitted, '-');
legend('Data', 'Exponential Fit');
455 chars
16 lines

In this example, we first define two vectors x and y that we want to fit an exponential model to. We then define the exponential model using an anonymous function fun, where c(1) represents the amplitude of the exponential curve and c(2) represents the decay factor. We then call the nlinfit function to fit the exponential model to the data, by providing the vectors x and y, the fun function, and an initial guess for the coefficients [1 1]. Finally, we extract the fitted values y_fitted and plot the original data and the fitted curve using the plot function.

This should give you a good idea of how to use MATLAB to calculate the exponential regression of two vectors.