... regression models with several explanatory variables for two reasons. First, they quantify the effects of collinearity, summarizing the impact of redundancies among the explanatory variables. Second, they save a lot of time. Consider the Fama-French variable High-Low. Is High-Low not statistically significant in this multiple regression because it is redundant (as is the case for Dow % Change), or is it simply unrelated to the response? To decide, look at the VIF. Because the VIF of High-Low is near 1, collinearity has little effect on this explanatory variable. High-Low is not related to returns on Sony stock once we’ve taken account of the other explanatory variables.

There’s no definitive rule for what constitutes a large VIF. We could have VIF > 10 ...

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