2. During the first three 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 below. Use the table to answer the following questions: (a)
What is the equation of the regression line for this data set? (b) Determine if the
regression line is a good predictor of the percentage of gold by weight and the
percentage of lead by weight in different coins from the Roman Empire. Explain
why or why not. (c) Use the regression equation to predict the percentage of lead
by weight given that the percentage of gold by weight is 0.25.
*