This data was collected by Boeckmann, Sheiner and Beal(1994) based on a study performed by Dr. Robert Upton. The study examined the concentration of theophylline in twelve subjects over the course of twenty-five hours.

Note: Units are given in kg for weight, mg/kg for dose, and hrs for time. This data was provided in an R open source library.

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## Attaching package: 'plotly'

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• shows raw data of concentration of Theophylline over time in all the subjects

The linear fit for all twelve subjects is very similar, therefore we will only take a look at the linear fit for one subject.

Subject 1

## `geom_smooth()` using formula = 'y ~ x'

Note that line fit was adjusted to only include data after Time = 1.12. The reason why will be explained.

SubjectOne <- data.frame(filter(subject1, Time >= 1.12)) SubjectOnePlot <- ggplot(data = SubjectOne,aes(Time,conc)) SubjectOnePlot + geom_point() + geom_smooth(method=“lm”,se=F) + labs(subtitle = “Subject 1”,y = “concentration”,x = “time in hrs”, title = “Concentration vs Time”,caption = “Source: Theoph”)

If we are looking strictly at the slope when beginning Time = 0.00, the slope of the linear function can be defined as follows:

This is not an accurate representation because the data indicates it takes roughly an hour for the concentration of Theophylline in the blood to peak. Therefore if we start at Time = 1.12, the slope is:

The resulting slope found starting at Time = 1.12 makes more sense as the data from the graph clearly shows the overall decrease in concentration over time.

While the line fit for the data resembles a logarithmic relationship more closely (as shown below), however it is not very practical for everyday use and the linear fit is not skewed enough for it to have a significant difference.