An Empirical Model Building Criterion Based on Prediction with Applications in Parametric Cost Estimation.
CLEMSON UNIV SC DEPT OF MATHEMATICAL SCIENCES
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In the context of multiple linear regression, when a subset of k-out-of-p predictor variables is to be selected for the purpose of predicting the response at some known point in the predictor variables space, the width of the resulting prediction interval gives an indication of the precision with which the response is predicted and, thus, it may provide a suitable selection criterion. A review of commonly used selection criteria is given, with special emphasis on those which deal with the problem of prediction. The Mahalanobis distance is one of the quantities affecting the width of the prediction interval, and it is studied in some detail. The effects of adding a new variable to a model are investigated and a monotonicity theorem is derived. The influence of an observation on the width of the prediction interval, as measured by the effected change when that observation is set aside, is also investigated and an equivalence beteween observation deletions and variable augmentation is shown.
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