Concept explainers
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 %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 = β0 + β1x + ϵ. After estimating the regression coefficients, we can substitute y* = 2.01 into the estimated equation and then solve for a prediction of age
Calculate this PI for y* = 2.01 and then address the question posed earlier.
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