%% A simple quadratic polynomial model in 1-d, compared to polyfitx = -10:10;y = 3*x.^2 + 2*x + 1;P1 = polyfit(x,y,2);Pn = polyfitn(x,y,2);% The differences should be near epsP1 - Pn.Coefficients%% Evaluate the above regression model at some set of pointspolyvaln(Pn,0:.1:1)%% Fit a 1-d model to cos(x). We only need the even order terms.x = -2:.1:2;y = cos(x);p = polyfitn(x,y,'constant x^2 x^4 x^6')if exist('sympoly') == 2  % Conversion to a sympoly. If nothing else, its a nice way to display the model.  polyn2sympoly(p)endif exist('sym') == 2  % Conversion to a symbolic toolbox form. Its also nice.  polyn2sym(p)end%% A surface model in 2-d, with all terms up to third (cubic) order% Use lots of data.n = 1000;x = rand(n,2);y = exp(sum(x,2)) + randn(n,1)/100;% Note the parameter statisticsp = polyfitn(x,y,3)if exist('sympoly') == 2  polyn2sympoly(p)endif exist('sym') == 2  polyn2sym(p)end% Evaluate on a grid and plot:[xg,yg]=meshgrid(0:.05:1);zg = polyvaln(p,[xg(:),yg(:)]);surf(xg,yg,reshape(zg,size(xg)))hold onplot3(x(:,1),x(:,2),y,'o')hold off%% A linear model, but with no constant term in 4-dimensions%   w(u,v,x,y) = a1*u + a2*v + a3*x + a4*y% All the coefficients should be approximately 1.0 in% this truncated Taylor series model.uv = (rand(100,4)-.5)/10;w = sin(sum(uv,2));p = polyfitn(uv,w,'u, v, x, y');if exist('sympoly') == 2  polyn2sympoly(p)endif exist('sym') == 2  polyn2sym(p)end%% A model in 5-d, with all terms up to fourth (quartic) order% Use LOTS of data.n = 10000;x = rand(n,5);y = sin(sum(x,2)) + randn(n,1)/100;p = polyfitn(x,y,4)if exist('sympoly') == 2  polyn2sympoly(p)endif exist('sym') == 2  polyn2sym(p)end%% A model with various exponents, not all positive integers.% Note: with only 1 variable, x & y may be row or column vectors.x = 1:10;y = 3 + 2./x + sqrt(x) + randn(size(x))/100;p = polyfitn(x,y,'constant x^-1 x^0.5');if exist('sympoly') == 2  polyn2sympoly(p)endif exist('sym') == 2  polyn2sym(p)endxi = 1:.1:10;yi = polyvaln(p,xi);plot(x,y,'ro',xi,yi,'b-')