SUMMARY
Statistical models usually involve some degree of approximation and therefore are nearly always wrong. Because of this inexactness, an assessment of the influence of minor perturbations of the model is important. We discuss a method for carrying out such an assessment. The method is not restricted to linear regression models, and it seems to provide a relatively simple, unified approach for handling a variety of problems.
A methodolgy for assessment of the predictive ability of regression models is presented. Attention is given to models obtained via subset selection procedures, which are extremely difficult to evaluate by standard techniques. Cross-validatory assessments of predictive ability are obtained and their use illustrated in examples.
Characteristics of observations which cause them to be important in a least squares analysis of data arising from a non-designed experiment are investigated and related to residual variances, residual correlations and the convex hull of the observed values of the independent variables. It is shown how deleting an observation can substantially alter an analysis by changing the partial F-test, studentized residuals, residual variances, convex hull of the independent variables and the estimated parameter vector. Outliers are discussed briefly and an example is presented.
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