Suppose that you are interested in testing a joint null hypothesis consisting of three restrictions, say B, = B2 = B3 = 0 in multiple regression. Assume that you have three individual t-statistics for...


Suppose that you are interested in testing a joint null hypothesis consisting of three<br>restrictions, say B, = B2 = B3 = 0 in multiple regression. Assume that you have three<br>individual t-statistics for B; = 0, where j = 1,2,3. Consider the following testing<br>procedure: reject the joint null hypothesis if at least one of t-statistics exceeds 1.96 in<br>absolute value. If t-statistics are independent of each other, what is the probability of<br>rejecting the joint null hypothesis when it is true?<br>

Extracted text: Suppose that you are interested in testing a joint null hypothesis consisting of three restrictions, say B, = B2 = B3 = 0 in multiple regression. Assume that you have three individual t-statistics for B; = 0, where j = 1,2,3. Consider the following testing procedure: reject the joint null hypothesis if at least one of t-statistics exceeds 1.96 in absolute value. If t-statistics are independent of each other, what is the probability of rejecting the joint null hypothesis when it is true?

Jun 11, 2022
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