The birds and the bees: interactive graphics and problem solving in the teaching of statistics

Software which allows interactive exploration of graphical displays is widely available. In addition there now exist sophisticated authoring tools which allow more general textual and graphical material to be presented in computer-based form. The role of an authoring tool in providing a graphical interface to a strategy for solving simple statistical problems in the context of teaching is discussed. This interface allows a variety of resources to be integrated. Specific examples, including the use of dynamic graphical displays in exploring data and in communicating the meaning of a model, are proposed. These ideas are illustrated by a problem involving the identification of the sex of a herring gull.     

Regression methods for high dimensional multicollinear data

To compare their performance on high dimensional data, several regression methods are applied to data sets in which the number of exploratory variables greatly exceeds the sample sizes. The methods are stepwise regression, principal components regression, two forms of latent root regression, partial least squares, and a new method developed here. The data are four sample sets for which near infrared reflectance spectra have been determined and the regression methods use the spectra to estimate the concentration of various chemical constituents, the latter having been determined by standard chemical analysis. Thirty-two regression equations are estimated using each method and their performances are evaluated using validation data sets. Although it is the most widely used, stepwise regression was decidedly poorer than the other methods considered. Differences between the latter were small with partial least squares performing slightly better than other methods under all criteria examined, albeit not by a statistically significant amount.