A single-regressor Breusch-Pagan test on a big sample

Question

You fit a simple regression (1 explanatory variable) on $n = 1{,}000$ observations. The auxiliary regression of squared residuals on that variable has $R^2 = 0.02$ .

Compute the Breusch-Pagan statistic and decide at the 5 percent level.

Accepted Answer

Compute the statistic. 	ext{LM} = n \cdot R^2{	ext{aux}} = 1{,}000 	imes 0.02 = 20.0. Degrees of freedom and cutoff. One regressor in the auxiliary regression means chi-square with 1 degree of freedom, whose 5 percent critical value is 3.841. Decision. 20.0 3.841, so we strongly reject homoskedasticity. Notice the lesson about sample size: an auxiliary R^2 of only 0.02 looks trivial, but multiplied by n = 1{,}000 it produces a decisive statistic. Large samples make even faint heteroskedasticity statistically detectable, which is a reason to judge practical importance (via a residual plot) …

A single-regressor Breusch-Pagan test on a big sample

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