Answer-first summary for fast verification
Answer: The high correlations between each pair of index returns indicate that multicollinearity exists between the variables in this regression.
## Explanation This is a classic case of **multicollinearity** in multiple regression analysis. Let's analyze why option D is correct: ### Evidence of Multicollinearity: 1. **High correlations between independent variables**: - Russell 1000 vs Russell 3000: 0.998 (almost perfect correlation) - Russell 1000 vs Russell 2000: 0.813 - Russell 2000 vs Russell 3000: 0.845 2. **Symptoms in regression output**: - **High R² (0.905)** but **insignificant individual coefficients** (all p-values > 0.05) - **Large standard errors** for the coefficients - **Low t-statistics** (all < 1) ### Why other options are incorrect: **Option A**: The coefficient magnitude (0.3533) doesn't indicate statistical significance. All coefficients have high p-values (> 0.05), meaning none are statistically significant. **Option B**: High R² only indicates the model explains variance well overall, but doesn't guarantee individual coefficients are significant. In fact, multicollinearity can cause high R² with insignificant coefficients. **Option C**: High p-values (like 0.9452) indicate **low** statistical significance, not high significance. ### Multicollinearity Impact: - Makes coefficient estimates unstable and unreliable - Increases standard errors - Can cause incorrect signs on coefficients - Makes it difficult to determine the individual effect of each variable This is an example of **imperfect multicollinearity** since the variables are not perfectly correlated but highly correlated, which still causes estimation problems.
Author: LeetQuiz Editorial Team
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Regression Statistics | Multiple R | 0.951 | | R-Squared | 0.905 | | Adjusted R-Squared | 0.903 | | Standard Error | 0.009 | | Observations | 192 |
Regression Output
| Regression Output | Coefficients | Standard Error | t-Stat | P-Value |
|---|---|---|---|---|
| Intercept | 0.0023 | 0.0006 | 3.5305 | 0.0005 |
| Russell 1000 | 0.1093 | 1.5895 | 0.0688 | 0.9452 |
| Russell 2000 | 0.1055 | 0.1384 | 0.7621 | 0.4470 |
| Russell 3000 | 0.3533 | 1.7274 | 0.2045 | 0.8382 |
Correlation Matrix
| Portfolio Returns | Russell 1000 | Russell 2000 | Russell 3000 | |
|---|---|---|---|---|
| Portfolio Returns | 1.000 | |||
| Russell 1000 | 0.937 | 1.000 | ||
| Russell 2000 | 0.856 | 0.813 | 1.000 | |
| Russell 3000 | 0.945 | 0.998 | 0.845 | 1.000 |
Based on the regression results, which statement is correct?
A
The estimated coefficient of 0.3533 indicates that the returns of the Russell 3000 Index are more statistically significant in determining the portfolio returns than the other two indexes.
B
The high adjusted R² indicates that the estimated coefficients on the Russell 1000, Russell 2000, and Russell 3000 Indexes are statistically significant.
C
The high p-value of 0.9452 indicates that the regression coefficient of the returns of the Russell 1000 Index is more statistically significant than the other two indexes.
D
The high correlations between each pair of index returns indicate that multicollinearity exists between the variables in this regression.
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