Linear Regression in Matlab Programming
Linear regression models the relationship between a dependent target variable (y) and an independent predictor variable (x) using a straight-line equation (y = mx + c). In MATLAB, you can perform linear regression using polynomial fitting, matrix algebra, or high-level statistical modeling objects.
Define predictor variable vector x and response variable vector y:
x = [1 2 3 4 5 6];
y = [2.2 2.8 3.6 4.5 5.1 5.9];% Fit 1st-degree (linear) polynomial coeff = polyfit(x, y, 1);
slope = coeff(1);
intercept = coeff(2);
fprintf('Slope (m): %.4f, Intercept (c): %.4f ', slope, intercept);% Construct design matrix with intercept column X = [x(:) ones(length(x), 1)];
Y = y(:);
% Solve normal equations: theta = (X^T * X)^(-1) * X^T * Y theta = (X' * X) (X' * Y);
slope = theta(1);
intercept = theta(2);
fprintf('Slope (m): %.4f, Intercept (c): %.4f ', slope, intercept);% Fit LinearModel object mdl = fitlm(x, y);
disp(mdl);Compute fitted values y_fit and plot the linear regression fit against raw data:
y_fit = slope * x + intercept;
figure;
scatter(x, y, 'filled', 'MarkerFaceColor', 'b');
hold on;
plot(x, y_fit, 'r-', 'LineWidth', 2);
title('Linear Regression Model Fit');
xlabel('Independent Variable (x)');
ylabel('Dependent Variable (y)');
legend('Observed Data', 'Fitted Line', 'Location', 'northwest');
grid on;
hold off;Calculate the Coefficient of Determination ((R^2)) to measure goodness-of-fit:
SS_res = sum((y - y_fit).^2);
SS_tot = sum((y - mean(y)).^2);
R_squared = 1 - (SS_res / SS_tot);
fprintf('R-squared (R^2): %.4f ', R_squared);Real feedback from students across top engineering universities worldwide.
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