For the simple linear regression model, show that the elements of the hat matrix are h i j frac 1 n frac left(x i bar x ight) left(x j bar x ight) S x x text and h i i frac 1 n frac left(x i bar x ight) 2 S x x Discuss the behavior of these quantities as $x i $ moves farther from $ bar x $, ...

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For the simple linear regression model, show that the elements of the hat matrix are [h_{i j}=frac{1}{n}+frac{left(x_{i}-bar{x}

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For the simple linear regression model, show that the elements of the hat matrix are

\[h_{i j}=\frac{1}{n}+\frac{\left(x_{i}-\bar{x}\right)\left(x_{j}-\bar{x}\right)}{S_{x x}} \text { and } h_{i i}=\frac{1}{n}+\frac{\left(x_{i}-\bar{x}\right)^{2}}{S_{x x}}\]

Discuss the behavior of these quantities as $x_{i}$ moves farther from $\bar{x}$,

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Introduction To Linear Regression Analysis

ISBN: 9781119578727

6th Edition

Authors: Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining

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Question Posted: Apr 20, 2024 02:00 PM

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For the simple linear regression model, show that the elements of the hat matrix are [h_{i j}=frac{1}{n}+frac{left(x_{i}-bar{x}

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Introduction To Linear Regression Analysis

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