qattachments_1fd0afc8b3af584821e31a609b2113c64bc93f1f Carbonate Calcite 21.7 27 26.7 27 27.2 29 27.6 28 28 28 29.4 30 29.

The data in Display 11.21 are the isotopic composition of struc- tural bone carbonate .X/ and the isotopic composition of the coexisting calcite cements .Y / in 18 bone samples from a specimen of the dinosaur Tyrannosaurus rex. Evidence that the mean of Y is positively associated with X was used in an argument that the metabolic rate of this dinosaur resembled warm-blooded more than cold-blooded animals.

(a) Examine the effects on the p-value for significance of regression and on R-squared of deleting (i) the case with the smallest value of X , and (ii) the two cases with the small- est values of X . (b) Why does R-squared change so much? (c) Compute the case influence statistics, and discuss interesting cases. (d) Recompute the case statistics when the case with the smallest X is deleted. (e) Comment on the differences in the two sets of case statistics. Why may pairs of influen- tial observations not be found with the usual case influence statistics? (f) What might one conclude about the influence of the two unusual observations in this data set?