Badly conditioned equations - how can I centre and scale properly

After writing my own best fit line. I can see that the results are pretty great, however the equation is apparantly badly scaled.

% 
alumina_610 = [
25  90  
1200  120
1300  150
1350  310
1400  450
1500  790 ];
%%
% % Nextel 610
figure1 = figure;
% 
hold on
% 
x = (alumina_610(:,1));
y = (alumina_610(:,2));
[xData, yData] = prepareCurveData( x, y );
% Set up fittype and options.
ft = fittype( {'x^12', '100'}, 'independent', 'x', 'dependent', 'y', 'coefficients', {'a', 'b'} );
% 
[fitresult, gof] = fit( xData, yData, ft );

Warning: Equation is badly conditioned. Remove repeated data points or try centering and scaling.

% plot fit:
x_fit = linspace(1,1600,100);
y_fit = fitresult(x_fit);
plot(x_fit,y_fit,':r')
% Label axes
xlabel( 'x', 'Interpreter','latex' );
ylabel( 'y', 'Interpreter','latex' );
plot(alumina_610(:,1),alumina_610(:,2),'ro', ...
    'MarkerFaceColor','r')
ylim([0 900])
ylabel('Grainsize [nm]','Color',[ 0 0 0 ])
xlim([0 1600])
% 
xlabel('Temperature$^{o}$C', 'Interpreter','latex')

% % % 
% 

How do I correctly scale a best fit line?

Thanks in advance

Answer 1

[Torsten]

Your problem is linear, but fitting data with an independent coordinate up to 1500 by a polynomial of degree 12 is nonsense.

alumina_610 = [
25  90  
1200  120
1300  150
1350  310
1400  450
1500  790 ];
M = [alumina_610(:,1).^12 1e38*ones(size(alumina_610,1),1)];
rank(M)

ans = 2

b = alumina_610(:,2);
p = M\b

p = 2×1

1.0e-35 * 0.5620 0.0792

hold on
plot(alumina_610(:,1),alumina_610(:,2),'o')
x = linspace(alumina_610(1,1),alumina_610(end,1),100);
plot(x,p(1)*x.^12+p(2)*1e38)
hold off

[A Poyser]

Thanks, that works a treat.