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Unformatted text preview: bx i + ε i how does the estimated linear regression model change with such a distortion? 5. Another application of the conﬁdence band is to check whether a prespeciﬁed functional shape is acceptable. If the speciﬁed function is within the band, we accept the functional form. Otherwise, we reject the functional form. Based on this idea, check whether the relation between Y and X in data 1 and data 2 are linear regression 1 models? [Hint: ﬁt a linear regression to the data. check whether the ﬁtted regression is in the 95% pointwise conﬁdence bands] 6. Consider samples ( x i ,y i ) ,i = 1 , 2 , ··· ,n and linear regression model y i = a + bx i + ε i where ε i are IID N (0 ,σ 2 ). Suppose the least squares estimation is used. For any new point x , construct a 95% conﬁdence interval for the regression function m ( x ) = a + bx . 2...
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 Fall '09
 XIAYingcun
 Statistics, Linear Regression, Regression Analysis, Estimation theory, linear regression model, local linear kernel

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