# 16.4: Higher Order Polynomial Fitting

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Let’s try fitting a fifth degree polynomial to the data in example 38.

Example 9.2.1

>> x=0:5;y=[12,10,9,6,2,0];
>> coeffs5=polyfit(x,y,5)

returns

coeffs5 =
-0.0167 0.3333 -2.0833 4.6667 -4.9000 12.0000

which are the coefficients for the approximating 5th order polynomial, namely
y = −0.0167x5 + 0.3333x4 − 2.0833x3 + 4.6667x2 − 4.9x + 12.

We could type out the full polynomial, but there is a shortcut. We can use the function polyval along with linspace to give a smooth approximating curve.

>> x5=linspace(0,5);
>> y5=polyval(coeffs5,x5);

We plot the curves
>> plot(x,y,’o’,x,besty,x5,y5)

This page titled 16.4: Higher Order Polynomial Fitting is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Troy Siemers (APEX Calculus) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.