%% Use Centering and Scaling to Improve Numerical Properties
% Create a table of population data for the years 1750 - 2000 and plot the data points.

year = (1750:25:2000)';
pop = 1e6*[791 856 978 1050 1262 1544 1650 2532 6122 8170 11560]';
T = table(year, pop)
plot(year,pop,'o')

%
% Use polyfit with three outputs to fit a 5th-degree polynomial using centering and scaling, which improves the numerical properties of the problem. polyfit centers the data in year at 0 and scales it to have a standard deviation of 1, which avoids an ill-conditioned Vandermonde matrix in the fit calculation.

[p,~,mu] = polyfit(T.year, T.pop, 5);

%
% Use polyval with four inputs to evaluate p with the scaled years, (year-mu(1))/mu(2). Plot the results against the original years.

f = polyval(p,year,[],mu);
hold on
plot(year,f)
hold off

% Copyright 2015 The MathWorks, Inc.