Curve Fitting Basics
Fit polynomials and exponential models to experimental data and assess goodness-of-fit.
Step 1 — Linear fit with polyfit
polyfit(x, y, 1) fits a straight line (degree-1 polynomial) to the data. The returned coefficients [m, b] define y = m*x + b.
x = [1 2 3 4 5];
y = [2.1 3.9 6.2 7.8 10.1];
p = polyfit(x, y, 1);
printf('Slope: %.2f, Intercept: %.2f\n', p(1), p(2))▶ Run in SimLabExpected output: Slope near 2.0, Intercept near 0.1
Step 2 — Evaluate and plot the fit
polyval(p, x) evaluates the fitted polynomial at any x values. Plot both the original data points ('o') and the fitted line to judge the quality visually.
x = [1 2 3 4 5];
y = [2.1 3.9 6.2 7.8 10.1];
p = polyfit(x, y, 1);
x_fine = linspace(1, 5, 100);
y_fit = polyval(p, x_fine);
plot(x, y, 'o', x_fine, y_fit);
legend('Data', 'Linear fit');
title('Curve Fitting')▶ Run in SimLabExpected output: Scatter of data points with a fitted line through them
Step 3 — Higher-degree polynomial
Increase the degree to capture curvature. Degree 2 fits a parabola; watch out for overfitting with very high degrees.
x = linspace(0, 2*pi, 20);
y = sin(x) + 0.2*randn(1, 20);
p3 = polyfit(x, y, 3);
x_fine = linspace(0, 2*pi, 200);
plot(x, y, 'o', x_fine, polyval(p3, x_fine));
legend('Noisy data', 'Degree-3 fit');
title('Polynomial Curve Fitting')▶ Run in SimLabExpected output: Smooth cubic curve fitting the noisy sine data
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