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 coefficients in
descending powers, P(1)*X^N + P(2)*X^(N-1) +...+ P(N)*X + P(N+1).
[P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a
structure S for use with POLYVAL to obtain error estimates for
predictions. S contains these fields:
R - Triangular R factor (possibly permuted) from a QR
decomposition of the Vandermonde matrix of X
df - Degrees of freedom
normr - Norm of the residuals
If the data Y are random, an estimate of the covariance matrix of P is
(Rinv*Rinv')*normr^2/df, where Rinv is the inverse of R.
[P,S,MU] = POLYFIT(X,Y,N) finds the coefficients of a polynomial in
XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
centering and scaling transformation improves the numerical properties
of both the polynomial and the fitting algorithm.
Warning messages result if N is >= length(X), if X has repeated, or
nearly repeated, points, or if X might need centering and scaling.
Example: simple linear regression with polyfit
% Fit a polynomial p of degree 1 to the (x,y) data:
x = 1:50;
y = -0.3*x + 2*randn(1,50);
p = polyfit(x,y,1);
% Evaluate the fitted polynomial p and plot:
f = polyval(p,x);
plot(x,y,'o',x,f,'-')
legend('data','linear fit')
Class support for inputs X,Y:
float: double, single
See also POLY, POLYVAL, ROOTS, LSCOV.
Documentation for polyfit
doc polyfit
Other uses of polyfit
codistributed/polyfit gpuArray/polyfit tall/polyfit
