Weak Instrument F

Problem

Compute the first-stage F statistic for a weak instrument: with R^2 the squared Pearson correlation between z and x, F = R^2 * (n - 2) / (1 - R^2).

Return 0.0 when n < 3, a variance is 0, or |r| is 1.

Hint

Rule of thumb: first-stage F below 10 signals a weak instrument.

case 1

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

expected: 0

case 2

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

expected: 4.481481481481476

case 3

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

expected: 0

case 4

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

expected: 0

Starter codePython

def weak_instrument_f(z, x):
    # Your code here
    pass

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