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% Given data
x = [0, 2, 4, 6, 9, 11, 12, 15, 17, 19];
y = [5, 6, 7, 6, 9, 8, 8, 10, 12, 12];
% Least-squares regression for a straight line
A = [x', ones(size(x'))];
b = y';
coefficients = A\b; % Compute the slope and intercept
slope = coefficients(1);
intercept = coefficients(2);
% Calculate the fitted values
y_fit = slope * x + intercept;
% Calculate the standard error of the estimate
error = y - y_fit;
standard_error = sqrt(sum(error.^2) / (length(x) - 2));
% Calculate the correlation coefficient
correlation_coefficient = corr(x', y');
% Plot the data and regression line
scatter(x, y, 'o', 'filled');
hold on;
plot(x, y_fit, 'r', 'LineWidth', 2);
hold off;
xlabel('x');
ylabel('y');
title('Least-Squares Regression: Straight Line');
legend('Data', 'Regression Line', "location", "northwest");
