2D Linear Regression via Normal Equation

Problem

Fit y = w1*x1 + w2*x2 (no intercept) by solving the 2x2 normal equation (X^T X) w = X^T y, where X is a list of [x1, x2] rows.

Return [w1, w2] using Cramer's rule. If the determinant of X^T X is 0 (within 1e-12), return [0.0, 0.0]. Empty X also returns [0.0, 0.0].

Hint

Build s11, s12, s22 from X and t1, t2 from X^T y, then solve the 2x2 system with Cramer's rule.

case 1

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

expected: [1,2]

case 2

in: [[[1,2],[2,1],[3,3]],[5,4,9]]

expected: [1,2]

case 3

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

expected: [2,1]

case 4

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

expected: [0,0]

Starter codePython

def fit_2d_normal_equation(X, y):
    # Returns [w1, w2]
    # Your code here
    pass

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