In 2013 Mock Answers, the answer says “The only cas in which correlation between independent variable may be a reasonable indicator of multicollinearity occurs in a regression with exactly two independent variables”

Does this mean, with three or more variables we cannot use pair-wise correlations to detect multi-collinearity? What would be the method for detection then?

Multicollinearity is a correlation of one independent variable with one or more independent variables.

When more than two IVs exist, you could use VIFs (variance inflation factors) or R-square from a regression of one independent variable on the remaining independent variables. Note that VIFs are calculated using this R-square value.

VIF= 1/(1- (R-square))

So divide 1 by 1 minus the R-square of xi on all other x variables. If this R-square is large, the denominator will be small, and the VIF will be large. This indicates a high degree of correlation between xi and the other x variables. A generally accepted cutoff for a VIF to indicate high multicollinearity is 10, but this is somewhat arbitrary and issues might be present with lower VIFs.

So yes, you cannot accurately assess multicollinearity using pairwise correlations with more than two IVs because there are multivariate relationships involved. A bivariate correlation doesn’t account for these relationships.

Yes, with three or more variables we cannot use pair-wise correlations to detect multi-collinearity.

Instead, we can see if multi-collinearity exists : classic symptom is significant F-test, high R square and insignificant individual t-stats on slope coefficients.

I take L1 in December for the first time, so I haven’t seen how CFAI covers this material and how it is presented in an exam. In practice, though, you would get VIFs from your statistical software and also look at the other indicators (as another poster mentioned).

I can reference you to several statistical or econometric textbooks (I’ve taken many statistics courses), but wikipedia is probably the fastest reference.

Also, the signs of the estimated coefficients may be different than your intuition or prior knowledge would suggest (positive coefficient instead of a negative, vice versa). If CFAI does not provide you with VIFs in the regression output, aghaali has listed additional ways to detect multicollinearity. Keep in mind, though, that even if the R-square is low/moderate in magnitude, you can still have the other symptoms (insignificant t-tests and significant F-test) that indicate multicollinearity to a potentially problematic degree.