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.)

Age: 9 10 11 12 13 14 33 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 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 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 . After estimating the regression coefficients, we can substitute into the estimated equation and then solve for a prediction of age . This “inverse” use of the regression line is called “calibration.” A PI for age with prediction level approximately is where Calculate this PI for and then address the question posed earlier.

y* 5 2.01 SE 5 s bˆ

1 e 1 1 1

n 1 (xˆ 2 x)2 Sxx f

1/2 xˆ 6 ta/2,n22 # 100(1 2 a)% SE xˆ

y* 5 2.01

%DAA 5 b0 1 b1x 1 P

%DAA 5 2.01.