Chemical Engineering Hand Written_Notes_Part_98

Chemical Engineering Hand Written_Notes_Part_98 - 198 5....

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198 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES from b y i . Thus, this correlation coe cient can be used to compare di f erent mod- els developed using same data. Further it can be shown that the quantity (6.63) f = N m m +1 μ R 2 1 R 2 has Fisher distribution with ( m +1) and ( N m ) degrees of freedom. When regression is signi f cant, we can test the hypothesis H 0 by rejecting H 0 with risk of α % . The test statistic is with risk of α % canbecomputedas (6.64) ε = F α ( m +1 ,N m ) where F denotes Fisher distribution. If f>ε , then we conclude that f is probably not a the Fisher distribution and the model is not suitable. If f<ε ,then smoothing is signi f cant and the model is satisfactory. In many situations, the model parameters have physical meaning. In such cases, it is important to determine con f dence interval for parameter θ i . De f ning variable (6.65) t i = b θ i θ i q b V ii where θ i isthetrueva lueofparameterand b
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Chemical Engineering Hand Written_Notes_Part_98 - 198 5....

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