Explanation:
Multicollinearity arises when independent variables are highly correlated.
A common symptom of multicollinearity is that the model's coefficients are jointly statistically significant (as indicated by a high and a significant F-statistic), but individually they may appear insignificant (low t-statistics) due to inflated standard errors. Thus, B is correct.
Option A is incorrect because multicollinearity typically does not violate the core OLS assumptions (estimators remain BLUE: Best Linear Unbiased Estimators), so it doesn't pose technical problems in parameter estimation (unless it's perfect multicollinearity), but rather makes inference difficult. Option C is incorrect because a variable with a high Variance Inflation Factor (VIF) indicates high multicollinearity and is considered for exclusion, not inclusion. Option D is incorrect because while the estimates remain unbiased, multicollinearity leads to inflated standard errors, making the estimates imprecise, not precise.
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Q.32 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?
A
Multicollinearity does pose technical problems in parameter estimation, and data modeling.
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 in the model.
D
Multicollinearity ensures that the model is unbiased and provides precise estimates of the coefficients.
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