(d) Plot the estimate of each random effect against the corresponding time and consider whether there is any evidence of a trend over time that is not accounted for by the fixed-effect model.

N.B. As the level of available chlorine declines, the rate of decline becomes lower, and this exponential decay process is more naturally modelled by a non-linear function than by the polynomial function used for convenience here. The model fitted by Draper and Smith (1998, Section 24.3, pp. 518–519) is Y = ???? + (0.49 − ????)e−????(X−8) + ????

where Y=available chlorine, X=time and

???? and ???? are parameters to be estimated.