MATLAB Curve Fitting

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Curve fitting in MATLAB is a powerful technique for modeling relationships between variables and analyzing data trends. It allows you to find the best mathematical function that describes your data points.

Basic Curve Fitting

MATLAB offers several methods for curve fitting, ranging from simple polynomial fits to more complex custom equations. The most common approach is using the polyfit function for polynomial fitting.

Polynomial Fitting

To fit a polynomial to your data, use the polyfit function:

x = [0 1 2 3 4 5];
y = [0 0.8 2.7 5.2 7.8 11.5];
p = polyfit(x, y, 2);  % Fit a 2nd-degree polynomial

The resulting p contains the coefficients of the polynomial. You can then use polyval to evaluate the fitted curve:

x_fit = linspace(0, 5, 100);
y_fit = polyval(p, x_fit);
plot(x, y, 'o', x_fit, y_fit, '-');

Custom Equation Fitting

For more complex relationships, you can define custom equations and use MATLAB's optimization tools to fit them to your data.

fun = @(b,x) b(1) * exp(b(2) * x);
b0 = [1, 0.1];  % Initial guess
b = lsqcurvefit(fun, b0, x, y);

Curve Fitting Toolbox

MATLAB's Curve Fitting Toolbox provides a comprehensive set of tools for curve and surface fitting. It offers a graphical interface and additional fitting options:

Interactive curve fitting app
Library of parametric and nonparametric models
Goodness-of-fit statistics
Confidence and prediction bounds

Using the Curve Fitting App

To launch the Curve Fitting App, type cftool in the MATLAB Command Window. This opens a graphical interface where you can import data, select fitting models, and visualize results.

Best Practices

Always plot your data before fitting to identify potential outliers or trends
Consider the physical meaning of your model when choosing a fitting function
Use statistical measures like R-squared to evaluate the goodness of fit
Be cautious of overfitting, especially with high-degree polynomials

Applications

Curve fitting in MATLAB is widely used in various fields:

Engineering: Modeling system responses and material properties
Physics: Analyzing experimental data and deriving empirical laws
Finance: Predicting trends and modeling economic behaviors
Biology: Studying growth patterns and population dynamics

By mastering curve fitting techniques in MATLAB, you'll be equipped to extract meaningful insights from your data and create accurate predictive models.