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 Va 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 Va = 200 and K = .1 for the parameters.
2. Give the values of the estimates obtained for the parameters Va 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.