Use Eqs. (12.18) and (12.19) to show that each of the leverages is between 0 and 1,

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Use Eqs. (12.18) and (12.19) to show that each of the leverages is between 0 and 1, and therefore the variances of the predicted values and residuals are between 0 and σ².

Equation 12.18

Equation 12.19

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Modern Mathematical Statistics With Applications

ISBN: 9783030551551

3rd Edition

Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton

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Question Posted: Aug 28, 2023 06:51 AM

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Use Eqs. (12.18) and (12.19) to show that each of the leverages is between 0 and 1,

Question:

Cov(Y) = HCov (Y)H' = X(X'X)¯¹X'[o²1]X(X'X)-¹X' =o²X(X'X)-¹X' = 6²H

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Modern Mathematical Statistics With Applications

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