CFA Level II ExamQuantitative MethodsMedium
A quantitative analyst is building a multiple regression model to forecast quarterly GDP growth. The model includes several independent variables: consumer spending growth, business investment growth, and government expenditure growth. After running the regression, the analyst notices that the R-squared value is very high (0.95), but several of the independent variables' p-values are not statistically significant at the 5% level. Which of the following is the most likely issue with this model?
- AHeteroskedasticity
- BAutocorrelation
- COmitted variable bias
- DMulticollinearity
Show answer & explanationAnswer & explanation
Correct answer: D. Multicollinearity
High R-squared with insignificant individual coefficients is a classic symptom of multicollinearity. This occurs when independent variables are highly correlated with each other, making it difficult for the model to isolate the individual effect of each variable.
Why the other options are wrong
- A. Heteroskedasticity primarily affects the standard errors of the coefficients, making hypothesis tests unreliable, but doesn't necessarily lead to high R-squared with insignificant coefficients.
- B. Autocorrelation (serial correlation) is typically an issue in time-series data where error terms are correlated, affecting standard errors, but not directly causing this specific combination of symptoms.
- C. Omitted variable bias occurs when a relevant variable is left out, leading to biased coefficient estimates, but doesn't inherently explain high R-squared with insignificant coefficients for included variables.
Multicollinearity
Multicollinearity is a phenomenon in multiple regression where two or more independent variables are highly correlated with each other, making it difficult to estimate the individual impact of each variable on the dependent variable.
- Leads to inflated standard errors of coefficients.
- Results in insignificant t-statistics (high p-values) for individual coefficients.
- The overall model (R-squared, F-statistic) may still appear significant.
Memory trick: Regression problems are like a tangled web.