Data are available on the number of counts (atomic disintegration events that take place within a radiation source) recorded with a Geiger counter at a nuclear plant. The counts were registered at each second over a 30 second period for a short-lived, man-made radioactive compound. The first few rows of the dataset are displayed below.

Describe the model being fitted with the following $\mathrm{R}$ command.

$>$ fit $1<-\operatorname{lm}($ Counts $~$Time, data=geiger)

Below is a plot against time of the residuals from the model fitted above.

Referring to the plot, suggest how the model could be improved, and write out the $R$ code for fitting this new model. Briefly describe how one could test in $R$ whether the new model is to be preferred over the old model.