
Explanation:
This is a classic case of multicollinearity in multiple regression analysis. Let's analyze why option D is correct:
High correlations between independent variables:
Symptoms in regression output:
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.
This is an example of imperfect multicollinearity since the variables are not perfectly correlated but highly correlated, which still causes estimation problems.
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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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