Box G.E.P., Wetz J. Criteria for judging adequacy of estimation by an approximating response function

Technical report №9. — University of Wisconsin, 1973. — 95 p.One possible viewpoint of a useful or worthwhile model fit is that the range of values predicted by the fitted equation over the X-space should be considerably greater than the size of the errors with which these predictions are made. In this report this viewpoint was investigated by the authors. They concluded that in order that an equation should be regarded as a satisfactory predictor (in the sense that the range of response values predicted by the equation is substantial compared with the standard error of the response), the observed F-ratio of (regression mean square)/(residual mean square) should exceed not merely the selected percentage point of the F-distribution, but several times the selected percentage point.