Answer-first summary for fast verification
Answer: White's correction should be applied to Model 1
## Explanation The Breusch-Pagan test is used to detect heteroskedasticity in regression models: - **Null Hypothesis**: Homoskedasticity (constant variance of errors) - **Alternative Hypothesis**: Heteroskedasticity (non-constant variance of errors) At 5% significance level: **Model 1**: - BP statistic = 5.458, p-value = 0.0195 - Since p-value (0.0195) < 0.05, we **reject** the null hypothesis - Conclusion: Model 1 exhibits heteroskedasticity **Model 2**: - BP statistic = 0.046, p-value = 0.8302 - Since p-value (0.8302) > 0.05, we **fail to reject** the null hypothesis - Conclusion: Model 2 does not exhibit significant heteroskedasticity **Analysis of options**: - **A**: Incorrect - Model 1 shows heteroskedasticity, not homoskedasticity - **B**: Correct - When heteroskedasticity is detected (Model 1), White's correction for heteroskedasticity-consistent standard errors should be applied - **C**: Incorrect - Model 2 shows no significant heteroskedasticity, so t-statistics can be relied upon **Correct Answer: B** - White's correction should be applied to Model 1 to address the detected heteroskedasticity.
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A Breusch–Pagan (BP) test is run on the residuals from two regression models to detect heteroskedasticity, with the following results:
| BP Test Statistic | P-Value |
|---|---|
| Model 1 | 5.458 |
| Model 2 | 0.046 |
If the level of significance is 5%, which of the following is the most appropriate conclusion that can be drawn?
A
Model 1 has homoskedastic residuals
B
White's correction should be applied to Model 1
C
The t-statistics for Model 2 cannot be relied upon
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