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Unformatted text preview: Practice Questions for Test 1 (1) Consider fitting the usual simple linear regression model to these data: x |-1 1 y | 1-1 1 (a) Find b β 1 , b σ , b se and a 95 percent confidence interval for β 1 . (b) Construct the ANOVA table. (c) Consider fitting the data to the model: Y i = β + i . Find b β and b σ . (2) Suppose we fit the usual model Y i = β + β 1 X i + i assuming E ( i ) = 0 and V ( i ) = σ 2 . Suppose, however, that E ( i ) = 5 and V ( i ) = x 2 i . How does this affect the mean and variance of b β 1 ? (3) Let X = 1- 1 1- 1 1- 1 1 1 1 1 1 1 . (a) Describe the column space L corresponding to X ? (b) Find H = X ( X T X )- 1 X T and verify that H is a projection matrix for L . (4) Suppose that Y = β + β 1 x + . Further, assume that β and β 1 are known. Given a value x * of x , find a 95 percent prediction interval for Y = β + β 1 x * + . Do you need to assume that is Normal for your interval to be valid?...
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- Spring '08
- Regression Analysis, regression model, Yi, 95 percent, usual regression model