Leave-One-Out MSE

Problem

Compute the leave-one-out mean squared error of a simple linear regression without refitting. Fit the OLS line, form residuals e_i, and use the PRESS shortcut sum((e_i / (1 - h_i))^2) / n with leverage h_i = 1/n + (x_i - mean_x)^2 / Sxx. Fewer than two points returns 0.0.

Hint

The PRESS formula deletes each point analytically, so no OLS refits are needed.

Test cases

case 1

in: [[1,2,3,4],[2,4,6,8]]

expected: 0

case 2

in: [[1,2,3,4],[1,3,5,8]]

expected: 0.44784580498866317

case 3

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

expected: 3.4999999999999987

case 4

in: [[2,4,6,8],[1,5,4,8]]

expected: 3.684807256235827

case 5

in: [[1],[2]]

expected: 0

Starter codePython

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

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