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60L(Y −B |M, B) = L IND (Y −B |M) − N 02 log(1 − R2 ) (4.62)Equation 4.62 shows that the loglikelihood with the RSA model can be computedby adjusting the independence loglikelihood with an additive term based onR 2 .I now proceed to show that σY 2 can also be expressed as a function of the modelcoefficients (the β values) and σɛ 2 . This is not needed for the BIC; it is presentedonly for completeness. The rest of this section can be skipped without loss ofcontinuity.Begin with the RSA model of equation 4.53. Take expectations and let µdenote the expected value of Y i .E[Y i ] = µ =C(1 − β W +1 − β W − β W −1 − β 1 )(4.63)C = µ(1 − β W +1 − β W − β W −1 − β 1 ) (4.64)Subtract µ from both sides of equation 4.53 and substitute in for C.(Y i −µ) = β W +1 (Y i−(W +1) −µ)+β W (Y i−W −µ)+β W −1 (Y i−(W −1) −µ)+β 1 (Y i−1 −µ)+ɛ iMultiply both sides by (Y (i−j) − µ) and take expectations.(4.65)