Financial Risk Manager Part 1
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Multicollinearity occurs when several variables can significantly explain one or more independent variables. Which one of the following is most likely to be true about multicollinearity?
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NNikitesh
A
Multicollinearity does pose technical problems in parameter estimation, and data modelling.
B
When there is multicollinearity in a model, the coefficients tend to be jointly statistically significant.
C
Multicollinearity can be detected using the Variance Inflation Factor, where a variable with high VIF is considered for inclusion from the model.
D
All of the above.
Explanation:
Correct Answer: B
Explanation:
When multicollinearity exists in a regression model, the individual coefficients may have high standard errors and be statistically insignificant individually, but the overall regression model (as measured by the F-statistic) tends to be jointly statistically significant. This is because multicollinearity makes it difficult to isolate the individual effects of correlated variables, but the variables together still explain the dependent variable well.
Why other options are incorrect:
A: Multicollinearity does not pose technical problems in parameter estimation in the sense that the OLS estimator still exists and is BLUE (Best Linear Unbiased Estimator). The issue is with the interpretation and stability of coefficients, not with the mathematical estimation itself.
C: Variables with high Variance Inflation Factor (VIF) values (typically VIF > 10) indicate high multicollinearity and should be considered for exclusion from the model, not inclusion. High VIF means the variable is highly correlated with other independent variables.
D: Since options A and C are incorrect, option D ("All of the above") cannot be correct.
Key Points about Multicollinearity:
- It occurs when independent variables are highly correlated with each other
- It increases standard errors of coefficients, making them less statistically significant individually
- The overall model F-statistic often remains significant
- VIF is a common diagnostic tool (VIF > 10 indicates problematic multicollinearity)
- Solutions include removing correlated variables, combining variables, or using regularization techniques
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