What distribution does the LM test statistic follow in the context of regression diagnostic tests?

Understand the Problem

The question is asking about the statistical distribution that the LM (Lagrange Multiplier) test statistic follows specifically in the realm of regression diagnostics. It requires knowledge of statistical theory and regression analysis to answer correctly.

More Information

In the context of regression diagnostic tests, the Lagrange Multiplier (LM) test is used to check if simpler models are adequate. The test statistic follows an asymptotic chi-squared distribution under the null hypothesis, which assumes that the simpler model is adequate.

Tips

A common mistake is to assume the LM test statistic always follows the same distribution as other test statistics like the F-distribution. However, for large samples, it typically follows a chi-squared distribution.

Sources

• Lagrange Multiplier Test - an overview | ScienceDirect Topics - sciencedirect.com