Linear Regression Plot in MATLAB: polyfit, lsline & fitlm Guide

Notes on Plotting Linear Regression in MATLAB

Linear regression finds the best-fitting straight line through data points using the least-squares method. MATLAB provides simple built-in functions to compute and plot it.

Key Methods

1. polyfit() + polyval() – Most common for simple linear (degree 1).
2. lsline() – Quick overlay on scatter plot.
3. fitlm() – For detailed statistics (from Statistics Toolbox).

Basic Steps (polyfit Method)

% Sample data x = [1 2 3 4 5 6 7 8 9 10]; y = [2.3 4.1 5.8 7.2 9.0 10.5 12.1 13.8 15.2 16.9]; % Roughly linear with noise % Compute linear fit (slope m, intercept c) p = polyfit(x, y, 1); % Returns [m c] % Generate fitted line x_fit = linspace(min(x), max(x), 100); y_fit = polyval(p, x_fit); % Plot figure; scatter(x, y, 'filled', 'b'); hold on; plot(x_fit, y_fit, 'r-', 'LineWidth', 2); grid on; xlabel('X'); ylabel('Y'); title(['Linear Regression: y = ' num2str(p(1),3) 'x + ' num2str(p(2),3)]); legend('Data Points', 'Best Fit Line'); hold off;

Quick Method with lsline

scatter(x, y, 'filled'); lsline; % Adds least-squares line automatically title('Scatter with Linear Regression Line');

Advanced: fitlm for Statistics

mdl = fitlm(x, y); % Creates linear model plot(mdl); % Plots data, fit, and confidence bounds disp(mdl); % Shows R-squared, p-values, coefficients

Tips

• Use polyfit(x,y,1) for slope and intercept.
• Confidence intervals: Use polyfit with output [p,S] and polyconf.
• Multiple regression: polyfit for higher degrees or fitlm for multi-variable.

Ideal for data analysis, trend lines, and curve fitting.