Drop one regressor and the other springs to life

Question

With two valuation signals in the model, neither coefficient is significant and one even carries a counterintuitive sign. You drop one signal; the remaining one immediately becomes strongly significant with a sensible, larger coefficient.

What does this sensitivity to dropping a regressor reveal?

Accepted Answer

The diagnosis: multicollinearity. Coefficients that swing wildly, in size or sign, when you add or remove a correlated regressor are a hallmark of multicollinearity. The two valuation signals overlap heavily, so the data cannot cleanly separate their individual effects. Small changes to the model (dropping one) reshuffle a lot of shared credit onto the other. Why the sign flips. When two regressors are strongly correlated, least squares can assign one a large positive coefficient and the other a large negative one that partly cancels, an arrangement the data barely pins down. Remove one, and …

Drop one regressor and the other springs to life

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