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Nick Cox
Nick Cox
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In the book, Linear Models with R by Julian Faraway, it says that if max(y)/min(y) is small, then Box Cox won't do anything because power transformations are well approximated by linear transformations over short intervals. Why does it say that power transformation is approximated by linear transformation over short intervals? And if so, why when max(y)/min(y) is small, Box Cox fails?

Thank you!

In the book, Linear Models with R by Julian Faraway, it says that if max(y)/min(y) is small, then Box Cox won't do anything because power transformations are well approximated by linear transformations over short intervals. Why does it say that power transformation is approximated by linear transformation over short intervals? And if so, why when max(y)/min(y) is small, Box Cox fails?

Thank you!

In the book, Linear Models with R by Julian Faraway, it says that if max(y)/min(y) is small, then Box Cox won't do anything because power transformations are well approximated by linear transformations over short intervals. Why does it say that power transformation is approximated by linear transformation over short intervals? And if so, why when max(y)/min(y) is small, Box Cox fails?

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WCMC
WCMC
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Why does Box-Cox transformation fail in following situation?

In the book, Linear Models with R by Julian Faraway, it says that if max(y)/min(y) is small, then Box Cox won't do anything because power transformations are well approximated by linear transformations over short intervals. Why does it say that power transformation is approximated by linear transformation over short intervals? And if so, why when max(y)/min(y) is small, Box Cox fails?

Thank you!