The LM (Lagrange Multiplier)test generates a test statistic N * R² ~$\chi$²_(S-1).To what does the S in this distribution refer? A)the number of explanatory variables in the auxiliary regression B)the number of explanatory variables in the initial model C)N-K-the degrees of freedom in econometric model of interest D)the statistical significance level chosen for the LM test

Question

Quizplus · Accepted Answer

The "S" in the distribution notation for the LM (Lagrange Multiplier) test statistic refers to the number of explanatory variables in the auxiliary regression. This is because the LM test involves running an auxiliary regression and then using the sum of squared residuals from this regression, where "S" denotes the number of restrictions being tested, which corresponds to the number of explanatory variables in the auxiliary regression.

The LM (Lagrange Multiplier)test Generates a Test Statistic N χ\chiχ 2(S-1)

The LM (Lagrange Multiplier)test Generates a Test Statistic N $\chi$ ²_(S-1)