% MATLAB Built-In Function polyfit and polyval
%
% POLYFIT fit polynomial to data.
% P = POLYFIT(X, Y, N) finds the coefficients of a polynomial
% P(X) of degree N that fits the data Y best in a least-squares
% sense. P is a row vector of length N+1 containing the polynomial
% coefficents in descending powers, P(1)*X^N + P(2)*X^(N-1) + ... +
% P(N)*X + P(N+1).

%
% Example: Curve Fit: polyfit Function
% Using the polyfit function, find and plot the third degree 
% polynomial that best fits the data x and y arrays

% allocate array x from 0 to 1.2 with step 0.3
x = 0:0.3:1.2;

% specify y array
y = [3.6 4.8 5.9 7.6 10.9];

% call the polyfit function for a third-degree polynomial 
% that best fits the data in the x and y array
P = polyfit(x, y, 3);

% display the coefficients
disp(P);

% generate 100 points for plotting purposes
xi = linspace(0, 1.2);

% evaluate the polynomial at these points
yi = polyval(P, xi);

% draw the cubic polynomial fit
plot(xi, yi)

hold on

% draw the x and y array points
plot(x, y, 'o')