Forensic scientists are often interested in making a measurement of some sort on a body (alive or dead) and then using that as a basis for inferring something about the age of the body. Consider the accompanying data on age (yr) and % D-aspertic acid (hereafter %DAA) from a particular tooth ("An Improved Method for Age at Death Determination from the Measurements of D-Aspertic Acid in Dental Collagen," Archaeometry, 1990: 61-70.)

Suppose a tooth from another individual has 2.01%DAA. Might it be the case that the individual is younger than 22? This question was relevant to whether or not the individual could receive a life sentence for murder. A seemingly sensible strategy is to regress age on %DAA and then compute a PI for age when %DAA = 2.01. However, it is more natural here to regard age as the independent variable x and %DAA as the dependent variable y, so the regression model is %DAA = 0 + 1 + ε. After estimating the regression coefficients, we can substitute y* = 2.01 into the estimated equation and then solve for a prediction of age x^. This "inverse" use of the regression line is called "calibration." A PI for age with prediction level approximately 100(1 - α)% is ( t α/2,n-2 · SE where

Calculate this PI for y* = 2.01 and then address the question posed earlier?

A 9 10 11 12 13 14 3 39 52 65 69 %DAA 1.13 1.10 1.11 1.10 1.24 1.31 2.25 2.54 2.93 3.40 4.55