Leave-One-Out Cross-Validation R-Squared

Problem

Return the leave-one-out cross-validation R-squared for simple linear regression: 1 - SSE_loo/SST, where each point is predicted by a line fit on the other n-1 points and SST uses the overall mean. Return 0.0 when n < 3, the lengths differ, y is constant, or any leave-one-out x has zero variance.

Hint

Refit for every left-out point; the score can go negative.

Test cases

case 1

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

expected: 1

case 2

in: [[1,2,3,4],[2,4,6,9]]

expected: 0.9330324029923496

case 3

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

expected: 0.09426020408163249

case 4

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

expected: 0

case 5

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

expected: 0

Starter codePython

def leave_one_out_r2(x, y):
    # Your code here
    pass

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