I wanted to provide an overview of how you analyze a classic nonlinear regression model. It is a difference of two exponential functions. This nonlinear function is used commonly in pharmocokinetic models and is a simply way to model the oral administration of a drug. I want to show how the model works in a mathematical sense and then how you fit it using R.

Here are some simple examples of nonlinear regression. We will use the built-in data set Theoph for all our examples.

`head(Theoph)`

```
## Subject Wt Dose Time conc
## 1 1 79.6 4.02 0.00 0.74
## 2 1 79.6 4.02 0.25 2.84
## 3 1 79.6 4.02 0.57 6.57
## 4 1 79.6 4.02 1.12 10.50
## 5 1 79.6 4.02 2.02 9.66
## 6 1 79.6 4.02 3.82 8.58
```

`tail(Theoph)`

```
## Subject Wt Dose Time conc
## 127 12 60.5 5.3 3.52 9.75
## 128 12 60.5 5.3 5.07 8.57
## 129 12 60.5 5.3 7.07 6.59
## 130 12 60.5 5.3 9.03 6.11
## 131 12 60.5 5.3 12.05 4.57
## 132 12 60.5 5.3 24.15 1.17
```

### look at just the first patient.

You can find an earlier version of this page on my blog.