Calculating the year of birth of cadavers is a tricky enterprise. One method proposed is based on the radioactivity of the enamel of the body’s teeth. The proportion of the radioisotope 14C in the atmosphere increased dramatically during the era of aboveground nuclear bomb testing between 1955 and 1963. Given that the enamel of a tooth is non-regenerating, measuring the 14C content of a tooth tells when the tooth developed, and therefore the year of birth of its owner. Predictions based on this method seem quite accurate (Spalding et al. 2005), as shown in the accompanying graph. The xaxis is Δ¹⁴C, which measures the amount of ¹⁴C relative to a standard (as a percentage).

There are three sets of lines on this graph. The solid line represents the least squares regression line, predicting the actual year of birth from the estimate based on amount of ¹⁴ C. One pair of dashed lines shows the 95% confidence bands, and the other shows the 95% prediction interval.

a. What is the approximate slope of the regression line?

b. Which pair of lines shows the confidence bands? What do these confidence bands tell us?

c. Which pair of lines shows the prediction interval? What does this prediction interval tell us?

Transcribed Image Text:

of birth Date 1995 1990- 1985- 1980- 1975 1970 1965- 1960 0 --- 100 200 300 400 500 600 700 A¹4C