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 + ǫ i and Y * i = a * + b * x i + ǫ * i , respectively. Here ǫ i , ǫ * i ∼ N (0 , σ 2 ) all independent with σ 2 > 0 unknown. (a) Construct a 95%con±dence interval for the di²erence 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 χ 2variables is also a χ 2variables. More precisely, if X i ∼ χ 2 ν i , i = 1 , 2 then X 1 + X 2 ∼ χ 2 ν 1 + ν 2 . ) (b) Construct a test for the nullhypothesis b = b * versus the alternative hypothesis b n = b * . (HINT: Use what you did in part (a).)...
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 Spring '07
 Polonik
 Statistics, Regression Analysis, Yi, linear regression model, regression model Yi

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