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jm is the number of predictors in M The Akaike's information criterion (AIC) essentially minimizes the Kullback-Leibler distance between model M (gm(y) ) and the

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jm is the number of predictors in M

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The Akaike's information criterion (AIC) essentially minimizes the Kullback-Leibler distance between model M (gm(y) ) and the true model ( f(y) approximated by the empirical distribution) which is given by 1 ( f , 8 M ) = f ( y ) 108 f ( ) dy = ( f ( y ) logf ( y ) dy - / f ( y ) loggm ( y ) ~ | f ( y ) log f ( y ) dy - - [ loggM ( yi ) . The AIC approximates the second component above and has the form: AIC = -210g L(BM, OM) + 2jm, where M, O'M are MLE under model M, L is the likelihood function, and jm is the number of predictors in M. For multiple LRM with normality assumption, AIC is of the form: AIC = nlog(am) + 2jm + C, where o'M = 1 ER-1 (yi - yim)2 and C = n(In(27) + 1). (i) The data is fitted to the following model log.Y = Bo+ >B; X; + E. The following provides some fitted results: Residual standard error: 0.2093 on 45 degrees of freedom Multiple R-squared: 0.8461, Adjusted R-squared: 0.8188 F-statistic: 30.93 on 8 and 45 DF, p-value: 7.8e-16 Using only the results above, compute the AIC and BIC of the model with jM replaced by ju + 2

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