% Simple curve fitting example using polyfit and polyval, and corrcoef
% Change the numbers in lines 6-10 to modify the data.  Change the 
% polynomial order in line 16 (quadratic=2, cubic=3, etc)

% Define the model parameters
x=[0:30]; % Defines the independent variable (x-axis)
intercept=1;
slope=1;
QuadraticTerm=0;
noise=2;

% Create the model data and add random noise
y=intercept+slope.*x+QuadraticTerm.*x.^2+noise.*randn(size(x));

% Fit a polynomial to the data
polyorder=1;
coef=polyfit(x,y,polyorder);

% Plot the data and the polynomial fit
xx=linspace(0,max(x));
yhat=polyval(coef,xx);
plot(x,y,'.r',xx,yhat,'-g')
axis([0 max(x) 0 max(y)]);
xlabel('x');ylabel('y')

% Compute the correlation coefficient and R-Squared
cc=corrcoef(polyval(coef,x),y);
RSquared=cc(2).^2;

% Label the graph with the fit information
text(1,.95.*max(y),[' Polynomial Order of fit = ' num2str(polyorder)] );
text(1,.9.*max(y),[' Fit coefficients = ' num2str(coef)] );
text(1,.85.*max(y),[' R-Squared = ' num2str(RSquared)] );