What will you conclude about a regression model if the Breusch-Pagan test results in a small p-value?
A The model contains heteroskedasticty.
B The model omits some important explanatory factors.
C) The model contains dummy variables.
D The model contains homoskedasticty.
The correct answer and explanation is:
The correct answer is A: The model contains heteroskedasticity.
The Breusch-Pagan test is used to check for heteroskedasticity in a regression model. Heteroskedasticity refers to a situation where the variance of the residuals (errors) from the regression model is not constant across all levels of the independent variable(s). This violates one of the assumptions of ordinary least squares (OLS) regression, which assumes homoskedasticity (constant variance of the residuals).
When performing the Breusch-Pagan test, a small p-value (typically below 0.05) suggests strong evidence against the null hypothesis, which states that the residuals have constant variance (homoskedasticity). A small p-value indicates that heteroskedasticity is likely present in the model, meaning the variance of the errors is not constant.
This result implies that the model’s predictions may be biased, leading to inefficient estimates of regression coefficients. Specifically, heteroskedasticity can make standard errors unreliable, which may result in misleading inferences about the significance of predictor variables. In the presence of heteroskedasticity, you might need to adjust your model, often by using robust standard errors, or apply other techniques like weighted least squares to correct for this issue.
Options B, C, and D are incorrect because:
- B: While omitted variables can cause model issues, the Breusch-Pagan test specifically tests for heteroskedasticity, not for omitted variables.
- C: The presence of dummy variables does not directly relate to heteroskedasticity.
- D: If the p-value is small, it indicates heteroskedasticity, not homoskedasticity.
Thus, the Breusch-Pagan test with a small p-value suggests that the model contains heteroskedasticity, and adjustments may be necessary for more reliable estimates.