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GARP Book 2 EOC Question 9.4

Hi David, the solution to this problem says that for a test with size alpha, the probability of including a single irrelevant regressor is 1-alpa. Shouldn't this probability be alpha instead, which is basically the probability of making a Type 1 error (reject a true null is equivalent to including an irrelevant regressor)? Or am I mixing up things?

Here is the question and answer:

Q. If you use a general-to-specific model selection with a test size of alpha, what is the probability that one or more irrelevant regressors are included when the regressors are uncorrelated?

A. The probability of including a single irrelevant regressor is 1-alpha. The probability that no irrelevant regressors are included is (1-alpha)^p where p is the number of variables considered.
 
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