Robust Standard Error Ratio

Problem

Return the ratio of the HC1 robust standard error of a simple regression slope to the classical one: sqrt(n * sum(xc_i^2 e_i^2) / (Sxx * SSE)), where xc = x - mean(x). Return 0.0 when n < 3, the lengths differ, or Sxx or SSE is zero.

Hint

The ratio equals 1 under homoscedasticity and departs from 1 when error variance tracks x.

Test cases

case 1

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

expected: 1

case 2

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

expected: 1

case 3

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

expected: 1.0617310051386497

case 4

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

expected: 0

case 5

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

expected: 0

Starter codePython

def robust_se_ratio(x, residuals):
    # Your code here
    pass

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