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Answer: Multicollinearity
## Explanation **Correct Answer: B** **Understanding the Pattern:** - **High R²**: Indicates the model explains a large portion of the variance in the dependent variable - **Few significant t-ratios**: Means individual independent variables are not statistically significant **Why Multicollinearity is the Answer:** 1. **Multicollinearity Definition**: Occurs when independent variables are highly correlated with each other 2. **Effects of Multicollinearity**: - Increases standard errors of coefficient estimates - Makes t-statistics smaller (less significant) - Coefficient estimates become unstable and sensitive to small changes in data - R² remains high because the variables collectively explain the dependent variable well 3. **Why Other Options are Incorrect:** - **A. Homoscedasticity**: Violation would affect standard errors but typically doesn't cause the specific pattern of high R² with insignificant t-ratios - **C. Error term normality**: Violation affects hypothesis testing but doesn't specifically cause high R² with insignificant coefficients - **D. No autocorrelation**: Affects efficiency of estimates but not the fundamental relationship between R² and t-statistics **Real-world Example**: In the previous question, we saw: - R² = 0.9 (very high) - All p-values > 0.05 (insignificant coefficients) - High correlations between independent variables (multicollinearity) This is the classic symptom of multicollinearity - the model appears to fit well overall, but individual predictors lack statistical significance due to their intercorrelations.
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Our linear regression produces a high coefficient of determination (R²) but few significant t ratios. Which assumption is most likely violated?
A
Homoscedasticity
B
Multicollinearity
C
Error term is normal with mean = 0 and constant variance = sigma²
D
No autocorrelation between error terms
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