3. Hocking-Pendleton Data. This popular data set was constructed by Hocking and Pendelton (1982) to illustrate influential and outlier observations in regression. The data are organized as a matrix of size 26 4; the predictors x1, x2, and x3 are the first three columns, and the response y is the fourth column. The data are given in hockpend.dat.

(a) Fit the linear regression model with the three covariates, report the parameter estimates and Bayesian R2 .

(b) Is any of the 26 observations influential or outlier (in the sense of CPO and comulative)?

(c) Find the mean response and prediction response for a new observation with covariates x 1 = 10, x 2 = 5, and x 3 = 5. Report the corresponding 95% credible sets.

Datafile found here: https://textuploader.com/1e7cu