### 8.2.8 Polynomial regression: polynomial_regression polynomial_regression_plot

If you want to find a more general polynomial y=a0xn + … + an which best fits a set of data points, you can use the polynomial_regression command. Given a set of points, either as a list of x-coordinates followed by a list of y-coordinates, or simply by a list of points, as well as a power n, the polynomial_regression command will return the list [an,…,a0] of coefficients of the polynomial. For example, if you enter

polynomial_regression([[1,1],[2,2],[3,10],[4,20]],3)

or

polynomial_regression([1,2,3,4],[1,2,10,20],3)

you will get

[-5/6,17/2,-56/3,12]

so the best fit polynomial will be y = (−5/6)x3 + (17/2)x2 − (56/3)x + 12.

To plot the curve, you can use the command polynomial_regression_plot; if you enter

polynomial_regression_plot([1,2,3,4],[1,2,10,20],3)

you will get