Residual standard error: 0.8195605 Degrees of freedom: 108 total; 102 residual
The AIC and BIC are model selection tools, and there is little to say about them at this point as we have passed the model selection stage. The information on the different standard deviations (multiplication factors of a) is interesting, as it shows the different variances (or better: the ratio with the standard error) per treatment-nutrient combination. The estimated value for a is 0.819. Note that the combination enrichment with algae and NH4 has the largest variance, namely (8.43 x 0.819)2.
The estimated regression parameters, standard errors, i-values, p-values, and other relevant information are given as well. Note that all terms are significantly different from 0 at the 5% level. To understand what the model is trying to tell us, it can be helpful to consider a couple of scenarios and obtain the equations for the fitted values or just graph the fit of the model. The easiest way of doing this is
> boxplot(predict(MFinal) ~ fTreatment * fNutrient,
This only works because all the explanatory variables are nominal. The resulting graph is shown in Fig. 4.10 and clearly shows that the observations exposed to algae treatment and NH4 enrichment have the highest values. This explains why the interaction term is significant. Unfortunately, at the time of writing, the predict.gls function (which is the one used to obtain the predicted values) does not give standard errors for predicted values. To obtain the 95% confidence bands around the fitted values, you need to use equations similar to those used for linear regression
Algae.NH4 NoAlgae.NH4 Algae.NO3 NoAlgae.NO3 Algae.PO3 NoAlgae.PO3
Fig. 4.10 Fitted values for the optimal model. Note the high values for the algae-NH4 combination data = Biodiv)
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