The purpose of this problem is to analyze a classical example of nonlinear regression which can be found in most textbooks discussing the subject.

The data, which are not of a financial nature, are contained in the data frame Puromycin included in the S-Plus distribution. They contain three variables pertaining to a specific set of biomedical experiments on cells which were either treated or untreated with the drug Puromycin (this information is given by the third variable state). The response variable y is the initial velocity vel of the reaction while the regressor variable x is the enzyme concentration given in the first column conc. It is expected that the regression function ?(x) will be given by the so-called Michaelis-Menten relationship:

where the constant V_a has the interpretation of an asymptotic velocity while K is a constant.

1. Attach the data frame Puromycin to your S-Plus session and extract the rows corresponding to the treated cases. Then perform a nonlinear regression of the velocity y against the enzyme concentration x, starting with initial values V_a = 200 and K = .1 for the parameters.

2. Give the values of the estimates obtained for the parameters V_a and K, and plot, on the same graph, the original data points of the  "treated" sub-sample together with a broken line going through the points fitted by the nonlinear regression.