问一道题：NO.PZ2020010801000030 [ FRM I ]

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 $1 - \alpha$, 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 $(1 - \alpha)^p$, where p is the number of variables considered.