Two predictors correlate at 0.95. Does it matter?

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Answer

$It depends entirely on what you want from the model.$
$For prediction, collinearity is largely harmless: the fitted values and out-of-sample error are barely affected, because the pair jointly carries the information regardless of how the coefficient is split between them.$
$For interpretation it matters a great deal, since the coefficients become unstable, their standard errors inflate, and the split between the two is nearly arbitrary, so a sign can flip when you add a few observations.$
$Diagnose it with the variance inflation factor rather than pairwise correlation, which misses multi-way collinearity.$
$Remedies are to drop one, combine them into a single index, or use ridge regularization, which trades a little bias for a large reduction in coefficient variance and is the standard answer when you must keep both.$

Check yourself — multiple choice

It always invalidates the model
It barely affects prediction but destabilizes coefficients and inflates standard errors, so it matters for interpretation — diagnose with VIF and use ridge, combination, or dropping one
It only affects R-squared
It never matters

Collinearity harms coefficient interpretation, not predictive accuracy; ridge is the usual remedy.

#regression#assumptions

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