You estimate the multiple regression Y = a + b1X1 + b2X2 + u with a large sample

Question

You estimate the multiple regression Y = a + b1X1 + b2X2 + u with a large sample. Let t1 be the test statistic for testing the null hypothesis b1 = 0 and t2 be the test statistic for testing the null hypothesis b2 = 0. Suppose you test the joint null hypothesis that b1 = b2 = 0 using the principle ’reject the null if either t1 or t2 exceeds 1.96 in absolute value’, taking t1 and t2 to be independently distributed.
(a) The probability of error Type 1 is 5 percent in this case
(b) The probability of error Type 1 is less than 5 percent in this case
(c) The probability of error Type 1 is more than 5 percent in this case
(d) The probability of error Type 1 is either 5 percent or less than 5 percent in this case

Explanation / Answer

Solution :- (C)

The probability of error Type 1 is more than 5 percent in this case

Each of t1 and t2 has a 5% chance to be greater than 1.96 in absolute value even if b1 = b2 = 0.

Thus, the Type I error, which can occur as a result of either of these errors, has a chance of cropping up with a

probability of -

0.05 + 0.05 0.05 x 0.05 = 0.0975

or 0.0975 x 100 = 9.75 %

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