

76 



only be applied historically to lakes that had not undergone changes 

 in trophic state or pH. 



Results of Stepwise Multiple Regression 

 Percent-Volume Infestation 



The maximum R2 method of the SAS STEPWISE procedure (SAS 

 Inst., Inc. 1985) was applied to percentage data for 17 diatom 

 taxonomic groups selected from plots of their abundance versus 

 percent-volume infestation (Appendix 3.1). The plot of Mallows' Cp 

 statistic versus the number of variables in each model is shown in 

 Figure 7. Models with larger Cp values have larger total error than 

 models with smaller Cp values (Daniel and Wood 1971). Models in 

 which Cp is larger than the number of independent variables plus 

 the intercept (p) are subject to bias error. Models with Cp values less 

 than p are subject to random errors. Figure 7 shows that the model 

 for predicting percent-volume infestation that consisted of one 

 diatom taxon (p = 2) showed substantial bias. All other multivariate 

 models predicting percent-volume infestation from percentage data 

 were subject to random error. 



Stepwise regression to predict percent-volume infestation was 

 attempted by using sedimentary concentration data for 17 diatom 

 taxonomic groups (Appendix 3.2). All models demonstrated random 

 error. Better results were obtained when log-transformed 

 sedimentary concentrations were used in the stepwise procedure. 

 Figure 8 is the plot of Cp versus p for models using log-transformed 

 diatom concentrations. The model using 2 diatom taxonomic groups 

 (p = 3) shows bias. The model using 3 taxonomic groups (p = 4) 



