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In the book Elements of statistical Learning is given as below:

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But I am not able to derive how equation 7.36 comes from equation 7.35.

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Your question is answered directly in the text you quote -- it literally tells you how to get it.

$-2\log\mathcal{L} = \sum_i (y_i-\hat{f}(x_i))^2/\sigma^2_\epsilon = N\cdot \overline{\text{err}}/\sigma^2_\epsilon$ (up to an additive constant)

Substitute that directly into the formula for BIC.

The only thing that's left to do that they didn't explicitly say to do was pull out the factor $N/\sigma^2_\epsilon$ from both terms.

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