During the first 3 centuries AD, the Roman Empire produced coins in the Eastern provinces. Some historians argue that not all these coins were produced in local mints, and further that the mint of Rome struck some of them. Because the "style" of coins is difficult to analyze, the historians would like to use metallurgical analysis as one tool to identify the source mints of these coins. Investigators studied 11 coins known to have been produced by local mints in an attempt to identify a trace element profile for these coins, and have identified gold and lead as possible factors in identifying other coins as having been locally minted. The gold and lead content, measured as a % of weight of each coin, is given in the table at right, and a scatter plot of these data is presented below. Gold % by Weight Lead % by Weight 0.3 0.17 0.31 0.19 0.28 0.21 0.32 0.22 0.34 0.28 0.29 0.26 0.33 0.32 0.26 0.17 0.3 0.19 0.27 0.19 0.27 0.17 a) Suppose that the locally minted coins analyzed in the table

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Adam Frye

Mathematics

27 August, 21:58

During the first 3 centuries AD, the Roman Empire produced coins in the Eastern provinces. Some historians argue that not all these coins were produced in local mints, and further that the mint of Rome struck some of them. Because the "style" of coins is difficult to analyze, the historians would like to use metallurgical analysis as one tool to identify the source mints of these coins. Investigators studied 11 coins known to have been produced by local mints in an attempt to identify a trace element profile for these coins, and have identified gold and lead as possible factors in identifying other coins as having been locally minted. The gold and lead content, measured as a % of weight of each coin, is given in the table at right, and a scatter plot of these data is presented below. Gold % by Weight Lead % by Weight 0.3 0.17 0.31 0.19 0.28 0.21 0.32 0.22 0.34 0.28 0.29 0.26 0.33 0.32 0.26 0.17 0.3 0.19 0.27 0.19 0.27 0.17 a) Suppose that the locally minted coins analyzed in the table

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Demarcus Gilbert · Answer 1

1. a) What is the equation of the least squares best fit line? %Lead = 1.306 - 3.635 (%Gold)

1. b) (.24,.43)

1. c) r=.459 There is a moderately negative relationship between % of gold by weight and % or lead by weight.