问题如下:
If you use a general-to-specific model selection with a test size of a, what is the probability that one or more irrelevant regressors are included when the regressors are uncorrelated?
解释:
If the regressors are uncorrelated, then their joint distribution has no correlation, and so the probability that one-or-more irrelevant regressors is included is 1 minus the probability that none are. The probability of including a single irrelevant regressor is , where a is the test size. This is the definition of the size of a test. The probability that no irrelevant regressors are included is , where p is the number of variables considered.