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Unformatted text preview: [ n( p + 1 ) n1 ]1 , ( R 2p n1 )( n1 n( p + 1 ) ) ˆ σ 2 = [ 1adjR 2 ] Syy n1 , ˆ σ 2 = RSS ( n( p + 1 )) = MSE As adj R 2 increases ˆ σ 2 decrease. Comments Let p variables in model R 2 can viewed as a coefﬁcient of simple determination between the response Y i and the ﬁtted values ˆ Y i A large value of R 2 does not necessarily imply that the ﬁtted model is useful one. ⇒ Despite a high R 2 , the ﬁtted model may not be useful if most predictions require extrapolations outside the region of observations. Again even though R 2 is large, MSE may still be too large for inferences to be useful when high precision is required....
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 Fall '11
 Staff
 Statistics, Normal Distribution, Regression Analysis, Predictor, ﬁrst adjustment

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