.. highlightlang:: us

.. index:: polyfit

.. _polyfit:

polyfit
=======

.. us.tag polyfit NOTREADYENGLISH Interpolation New5502

:ref:`polyfit` finds the coefficients of a polynomial of degree *N* using the 
least squares method. 

.. function:: p = polyfit(x, y, N)

.. us.return

**Return Value**

*p* is a vector with *N* + 1 polynomial coefficients in descending powers:

:math:`P(x) = p_1x^n + p_2x^{n-1}+ \dotsb + p_{n}x + p_{n+1}`

.. us.params

**Parameters**

.. uparam:: x

   *x* is a vector with x coordinates.

.. uparam:: y

   *y* is a vector with y coordinates. Same number of elements as *x*.

.. uparam:: N

   *N* is the degree of the polynomial. *N* >= 0 and *N* <= len(x)-1.

.. us.example

**Example**

::
   
   def test_polyfit()
   {
       x = 0:0.1:3;
       y = erf(x);
       print p = polyfit(x, y, 3);
       h1 = plot(x, y)
       y2 = polyval(p, x);
       h2 = plot(x, y2, h1[2])
       XYSetProps(h2[3], "curve-color='red'");
   }
   test_polyfit()

.. us.history

**History**

.. list-table::
   :header-rows: 1

   * - Version
     - Description
   * - R2013.2
     - Documented.

.. seealso::
   :ref:`overview-mathematic`,
   :ref:`polyval`

:sub:`id-204970`