pairwise correlations- this is really tripping me up
This is really tripping me up. A question on the Paul Charlent Case Scenario in practice questions. Ill summarize whats happening here. we are basically using some variables to explain the variation in set index returns.
1. 1st regression is
ln(1 + SET) = α + β × ln(1 + Libor) + ε
2. 2nd regression is
ln(1 + SET) = α + β × ln(1 + Libor) + β2 × ln(1 + Fed Funds) + β3 × £ + ε
3. as you can see they have added 2 extra variables for fed funds and exchange rate.
1st regression is f-stat is 2.355
intercept is significant and libor is not.
4. 2nd regression f stat is = 12.572
2 variables are significant. fed funds and exchange rate.
pairwise correlation between fed funds and libor is 0.9814 and fed funds and exchange rate is 0.6798.
Geoffrey Small, a colleague of Charlent, comments on the results of the two regressions. Small states that the highly significant F-statistic of the second regression along with the increased R2 of the second regression means that the addition of the Fed funds rate and the $/£ exchange rate to the analysis provides more reliable estimates of linear associations than the first regression.
the q asks
Regarding Geoffrey Small’s statement about the second regression, which of the following is most accurate?
- It is true that the second regression has substantially greater explanatory power than the first regression.
- The second regression displays multicollinearity.
- The F-statistic of the second regression is likely underestimated.
answer is 2.
this is really confusing me for the following reasons.
1. symptom of multicollinearity is very high f stat and very high r2 with none of the independent variables being significant. but here 2 independent variables are significant and r2 is not that higih.
2. the pairwise correlations are really high agreed but the cfa book specifically says “high pairwise correlations among the independent variables are not a necessary condition for multicollinearity, and low pairwise correlations do not mean that multicollinearity is not a problem. The only case in which correlation between independent variables may be a reasonable indicator of multicollinearity occurs in a regression with exactly two independent variables”
so why is it that multicollinearity is a problem here. the justification was that pairwise correlation is hgih but given the above statement this is really contradicting what has been said.
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