Theil-Sen Slope

Problem

Compute the Theil-Sen slope: the median of all pairwise slopes (y_j - y_i) / (x_j - x_i) for i < j with distinct x values (average the two middle slopes for an even count).

Return 0.0 when no valid pair exists.

Hint

The median of pairwise slopes is robust to outliers, unlike ordinary least squares.

Test cases

case 1

in: [[1,2,3],[2,4,6]]

expected: 2

case 2

in: [[1,2,3,4],[1,2,10,4]]

expected: 1

case 3

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

expected: 1.5

case 4

in: [[5],[3]]

expected: 0

Starter codePython

def theil_sen_slope(X, y):
    # Your code here
    pass

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