9.2.8  Polynomial regression: polynomial_regression polynomial_regression_plot

The polynomial_regression command finds a more general polynomial y=a₀xⁿ + … + a_n which best fits a set of data points.

• polynomial_regression takes three arguments:
  • xcoords, a list of x-coordinates.
  • ycoords, a list of y-coordinates.
  • n, the degree of the polynomial.
  You can combine the first two arguments into a matrix with two columns (each list becomes a column of the matrix).
• polynomial_regression(xcoords,ycoords,n) returns the list [a_n,…,a₀] of coefficients of the best fit polynomial.

Example.
Input:

or:

Output:

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

The polynomial_regression_plot command draws the best fit polynomial.

• polynomial_regression_plot takes three arguments:
  • xcoords, a list of x-coordinates.
  • ycoords, a list of y-coordinates.
  • n, the degree of the polynomial.
  You can combine the first two arguments into a matrix with two columns (each list becomes a column of the matrix).
• polynomial_regression_plot(xcoords,ycoords,n) draws the best fit polynomial of degree n, and puts the equation and R² value above the graph.

Example.
Input:

Output: