Least squares regression of a quadratic without bx term.

Hi,

I'm trying to find the least squars regression formula and R squared value.

However, the data has to fit y=ax^2+c without the bx term, so polyfit will not work.

The two sets of data y and x are a 1x119 double vector.

Thanks in advanced.

Answer 1

[Star Strider]

Try this:

DM = [x(:).^2 ones(size(x(:)))];                        % Design Matrix
B = DM \ y(:);                                          % Parameters
yfit = DM * B;                                          % Calculated Fit

SStot = sum((y-mean(y)).^2);                            % Total Sum-Of-Squares
SSres = sum((y(:)-yfit(:)).^2);                         % Residual Sum-Of-Squares
Rsq = 1-SSres/SStot;                                    % R^2

To plot it:

figure
plot(x, y, 'p')
hold on
plot(x, yfit, '-r')
hold off
grid