Quadratic Least Squares Fit

Problem

Fit a quadratic y = a + b*x + c*x^2 to data by least squares.

Solve the 3x3 normal equations built from the power sums, using Gaussian elimination with partial pivoting. Return [a, b, c], or None if the normal matrix is singular (fewer than three distinct x values).

Hint

The normal equations for y = a + b*x + c*x^2 form a symmetric 3x3 system of power sums.

Test cases

case 1

in: [[0,1,2],[1,2,5]]

expected: [1.0000000000000009,-8.881784197001252e-15,1.0000000000000044]

case 2

in: [[0,1,2,3],[2,3,4,5]]

expected: [1.9999999999999978,1.0000000000000067,-2.1649348980190643e-15]

case 3

in: [[0,1,2],[0,0,3]]

expected: [3.3306690738754696e-16,-1.5000000000000049,1.5000000000000024]

case 4

in: [[1,1,1],[1,2,4]]

expected: null

case 5

in: [[0,0,1],[1,2,4]]

expected: null

Starter codePython

def quadratic_fit(xs, ys):
    # Your code here
    pass

5 test cases · run your code against them in the editor