Weak Instrument F-Statistic

Problem

Return the first-stage F statistic for a single instrument: R^2/((1 - R^2)/(n - 2)) from regressing treatment on instrument with an intercept. Return 0.0 when n < 3, the treatment has no variance, or the fit is perfect.

Hint

A rule of thumb is that F above 10 signals a strong instrument.

Test cases

case 1

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

expected: 4.500000000000002

case 2

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

expected: 0

case 3

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

expected: 0.4999999999999999

case 4

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

expected: 0

case 5

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

expected: 0

Starter codePython

def weak_instrument_f(instrument, treatment):
    # Your code here
    pass

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