Tech Challenge

2026-08-22

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Daily Tech Challenge

AI & ML

medium

Question 1 of 5

A linear model is fit on two features that are almost the same column. The fitted coefficients come out enormous and opposite in sign, yet R-squared is essentially identical to a fit on x1 alone. What is going on, and what does the Variance Inflation Factor measure?

Example

import numpy as np, statsmodels.api as sm

rng = np.random.default_rng(0)
x1  = rng.normal(size=500)
x2  = x1 + rng.normal(scale=0.01, size=500)   # almost a copy of x1
y   = 3.0 * x1 + rng.normal(scale=0.5, size=500)

X   = sm.add_constant(np.column_stack([x1, x2]))
fit = sm.OLS(y, X).fit()
print(fit.params)     # e.g. [0.01, 12.7, -9.7]  -- true signal is (0, 3, 0)
print(fit.bse)        # standard errors are huge
print(fit.rsquared)   # ~0.97, basically unchanged vs x1 alone

# VIF for feature j:  1 / (1 - R2 of regressing x_j on the OTHER features)

Saturday, August 22, 2026 · A new challenge drops every day