(a) 3 pts Consider theunivariate prior formulation. Present (i) your R code for the list structure containing all of the data, and (ii) your JAGS code. Make sure to do the following: . Use centered predictor values. (You may choose whether to pre-compute the average age in R.) . Give the overall regression coefficients a prior mean of zero and a prigprecision of 1 x 10-6_ . Give all precision parameters gamma priors with = 0.001 and = 0001. . Define variables (deterministic nodes) appropriate for assessing the posterior distributions of the standard deviation of the response and the (population) standard deviations of the regression parameters (represented byry; and mi). (b) [3 pts] Run your model, and present a summary statistic table that includes at least the nodes for of 1, 0 = 1/ 73, 0.. = 1/ 72 , and3. = 1/ 72 (in the notation of Cowles, Sec. 10.4). Make sure to do the following: . Use at least three chains, with widely-separated starting points. . Remember to start with a burn-in period. . Use at least 100000 iterations from each chain (after burn-in). . DO NOT include any plots or convergence diagnostics in your submission. (c) [1 pt] Give an approximate 95% equal-tailed posterior credible interval for the population-mean rate at which the orthodontic measurement changes per year (in mm/year, during the ages represented in the data set)