Graphical diagnostics for regression, model determinations with consideration of the bias/variance trade-off

Estimates of model parameters (regression coefficients forming the regression vector) for a multivariate linear model have been the subject of considerable discussion. Regression diagnostics utilized in chemometrics for a multivariate linear model are often based on a single number such as the coefficient of determination, root mean square error of cross-validation, selectivity, etc. Additionally, regression diagnostics commonly applied focus on model bias and do not include variance or model complexity. This paper demonstrates that substantial information is available through a graphical study of trends in model parameters as determined by plots of regression diagnostics using bias, variance, and/or model complexity measures. Also illustrated is that by using harmonious graphics which simultaneously use bias and variance information, determination of proper model parameters without cross-validation is possible, This paper concludes with comments on the next level of regression diagnostics, including use of color, sound, and virtual reality. (C) 2002 Elsevier Science B.V. All rights reserved.