% Curve fitting is a useful tool for representing a data set in a linear
% or quadratic fashion.
% MATHPRO has two functions, polyfit and polyval, which can quickly
% and easily fit a polynimial to a set of data points.

% Enter independant variable of the data set
x = [0,1,2,4];

% Enter dependant variable of the data set
y = [5,4,7,25];

% coefficients = polyfit(x,y,n) finds the coefficients of a polynomial p(x)
% of degree n that fits the data, p(x(i)) to y(i), in a least squares sense.
% The result coefficients is a row vector of length n+1 containing the polynomial coefficients in descending powers.

coefficients = polyfit(x,y,2); % generates the coefficients of a second degree polynomial best characterizing the data set

% estimate y at xp
xp = 1.5;

% If coefficients is a vector whose elements are the coefficients of a polynomial,
% then polyval(coefficients,xp) is the value of the polynomial evaluated at xp.

yp = polyval(coefficients,xp); % generates a new value (estimate) of y based on the coefficients found with polyfit

% display the result
write("y value at xp = ",yp);
write("Coefficients of the polynomial are ",coefficients);