function [a_fit, sig_a, yy, chisqr] = linreg(x,y,sigma) % Function to perform linear regression (fit a line) % Inputs % x Independent variable % y Dependent variable % sigma Estimated error in y % Outputs % a_fit Fit parameters; a(1) is intercept, a(2) is slope % sig_a Estimated error in the parameters a() % yy Curve fit to the data % chisqr Chi squared statistic %* Evaluate various sigma sums sigmaTerm = sigma .^ (-2); s = sum(sigmaTerm); sx = sum(x .* sigmaTerm); sy = sum(y .* sigmaTerm); sxy = sum(x .* y .* sigmaTerm); sxx = sum((x .^ 2) .* sigmaTerm); denom = s*sxx - sx^2; %* Compute intercept a_fit(1) and slope a_fit(2) a_fit(1) = (sxx*sy - sx*sxy)/denom; a_fit(2) = (s*sxy - sx*sy)/denom; %* Compute error bars for intercept and slope sig_a(1) = sqrt(sxx/denom); sig_a(2) = sqrt(s/denom); %* Evaluate curve fit at each data point and compute Chi^2 yy = a_fit(1)+a_fit(2)*x; % Curve fit to the data chisqr = sum( ((y-yy)./sigma).^2 ); % Chi square return;