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Reading "An Introduction to Statistical Learning" (by James, Witten, Hastie and Tibshirani), on p.211 I came across the following formula for BIC in case of linear regression:

$ BIC = \frac{1}{n \hat{\sigma}^2} \left[ RSS + (\log{n}) d \hat{\sigma}^2 \right] $

up to a constant, and similarly for AIC. Here, $n$ is sample size and $d$ is the number of parameters. This seems contrary to the more popular formulation, where

$BIC = n \log(\hat{\sigma}^2) + d \log{n}$

The most obvious difference is that RSS in the first formula is not logged. Is the first formula wrong or am I missing something?

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