function [p, s, mu] = polyfit (x, y, n)

  if (nargin < 3 || nargin > 4)
    print_usage ();
  endif

  if (nargout > 2)
    ## Normalized the x values.
    mu = [mean(x), std(x)];
    x = (x - mu(1)) / mu(2);
  endif

  if (! size_equal (x, y))
    error ("polyfit: x and y must be vectors of the same size");
  endif

  if (! (isscalar (n) && n >= 0 && ! isinf (n) && n == round (n)))
    error ("polyfit: n must be a nonnegative integer");
  endif

  y_is_row_vector = (rows (y) == 1);

  ## Reshape x & y into column vectors.
  l = numel (x);
  x = x(:);
  y = y(:);

  ## Construct the Vandermonde matrix.
  v = vander (x, n+1);

  ## Solve by QR decomposition.
  [q, r, k] = qr (v, 0);
  p = r \ (q' * y);
  p(k) = p;

  if (nargout > 1)
    yf = v*p;

    if (y_is_row_vector)
      s.yf = yf.';
    else
      s.yf = yf;
    endif

    s.R = r;
    s.X = v;
    s.df = l - n - 1;
    s.normr = norm (yf - y);
  endif

  ## Return a row vector.
  p = p.';

endfunction