Polynomial Curve Fitting
This example shows how to fit a polynomial curve to a set of data points using the
polyfit function. You can use
polyfit to find the coefficients of a polynomial that fits a set of data in a least-squares sense using the syntax
p = polyfit(x,y,n),
yare vectors containing the
ycoordinates of the data points
nis the degree of the polynomial to fit
Create some x-y test data for five data points.
x = [1 2 3 4 5]; y = [5.5 43.1 128 290.7 498.4];
polyfit to find a third-degree polynomial that approximately fits the data.
p = polyfit(x,y,3)
p = 1×4 -0.1917 31.5821 -60.3262 35.3400
After you obtain the polynomial for the fit line using
polyfit, you can use
polyval to evaluate the polynomial at other points that might not have been included in the original data.
Compute the values of the
polyfit estimate over a finer domain and plot the estimate over the real data values for comparison. Include an annotation of the equation for the fit line.
x2 = 1:.1:5; y2 = polyval(p,x2); plot(x,y,'o',x2,y2) grid on s = sprintf('y = (%.1f) x^3 + (%.1f) x^2 + (%.1f) x + (%.1f)',p(1),p(2),p(3),p(4)); text(2,400,s)