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.