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Unformatted text preview: . 5 units of the true slope. 3. Let ( x 1 , Y 1 ) , . . ., ( x n , Y n ) and ( x * 1 , Y * 1 ) , . . . , ( x * n , Y * n ) denote two sets of observations (all independent), coming from a simple linear regression model Y i = a + bx i + i and Y * i = a * + b * x i + * i , respectively. Here i , * i N (0 , 2 ) all independent with 2 > 0 unknown. (a) Construct a 95%-condence interval for the dierence between the slopes b b * . (As always, begin with nding a pivot statistic. In this context it might be useful to recall that the sum of two independent 2-variables is also a 2-variables. More precisely, if X i 2 i , i = 1 , 2 then X 1 + X 2 2 1 + 2 . ) (b) Construct a test for the null-hypothesis b = b * versus the alternative hypothesis b n = b * . (HINT: Use what you did in part (a).)...
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- Spring '07