# Quants- Multicollinearity

I have a question on how to detect multicollinearity?

As per my understanding, F stat should be significant, R2 should be high and individual coeff. should not be significant.

In order for multicollinearity to be present, are all 3 requirements (high R2, significant F-stat, insignificant t-tests) need to be satisfied?

1. What is the threshold to consider R2 as a high value?

2. in below example one coefficient is insignificant, whereas one is significant. For multicollinearity to be present are all coefficients need to be insignificant?

for ex:

R2 is 0.414

F stat is significant

out of 2 coeff, 1 coefficient is significant

correlation between 2 independent variables is 0.015

CFA online practice question no 4 says that multicollinearity is not present. But why?

The best way to detect multicollinearity is when the model as a whole is “significant” (F-test) but individually independent variables are insignificant (T-test). The R2 most of the time would be high, but it’s not necessary to be 90% to have multicollinearity.

Yes, that’s what my understanding is. So in the example I mentioned, F stat is significant. Also, out of the 2 coefficients, 1 is significant and 1 is not. So, does that mean one of the significant coefficient (t stat) is contributing to high F stat and that’s why there is no multicollinearity?

I hope I’m not confusing you here!

You may be confusing necessary conditions and sufficient conditions. None of the conditions you list is necessary.

There’s no reason that R2 need be high: you can have a well-fitting model with multicollinearity or a poorly-fitting model with multicollinearity.

Similarly, the F statistic need not be significant, and the individual slope coefficients need not be insignificant.

Having a significant F statistic and (all) insignificant slope coefficients is sufficient to conclude multicollinearity, but not necessary.

High correlation between input variables is evidence of multicollinearity.

Why?

The extremely low correlation between the two input variables is prima facie evidence that there’s no multicollinearity.

Thanks S2000magician! That makes a lot of sense now.

My pleasure.

For OP, feel free to search threads where I’ve commented extensively on this.

The CFAI is incredibly terrible with presenting MC.

Multicollinearity is an aggregate picture. This is a frustrating topic for me because for years they’ve refused to change portions of their curriculum here where they’ve ignored many substantial, credible references I gave them on multicollinearity.

S2000 has helped here, but there’s a lot left out of the discussion (better indicators that multicollinearity is present in a problematic manner when coefficients have magnitudes or signs that are different from expected or that change dramatically when removing some of the potentially collinear predictors).

CFA Institute’s quant curriculum and standards are leaving a lot to be desired for a “World Class Education”, but S2000 has handled some of the specifics in the thread. Again, as he said, R2 isn’t “generally going to be high” when MC is a probleml; that’s just not true at all.

Thanks @tickersu

will keep this in mind-

(better indicators that multicollinearity is present in a problematic manner when coefficients have magnitudes or signs that are different from expected or that change dramatically when removing some of the potentially collinear predictors).