3. Enzyme. The data in the le enzyme.csv gives the initial rate of reaction of an enzyme (y) and the substrate concentration (I). Consider the following nonlinear regression model: 3; +6: =62+I 1Iivhere E:- mild N (0.02), I91 3': U, and I92 r: I]. Assume noninformative priors for I91. 92, and 0'2 {in BUGS, we will specify a prior for the precision T = 715). For these constraints, the recommended priors in BUGS are Gammaml. 0.01). 1. Plot the marginal posterior densities of 31, 32, and 0'2. Use 31 = 200, 32 = [LlJ and 0'2 = 10D (equivalently, T = lll} for initializing the MCMC chain. 2. Compute 95% credible intervals for each of the three parameters. 3. Plot the posterior predictive distribution of y when :1: = 1.0 and provide its 95% credible intervals