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.
1. a) What is the equation of the least squares line?
%Lead vs. %Gold b) Sketch the best fit line on the scatter plot.
c) What is the value of the correlation coefficient?
Interpret this value in context.
The scatterplot suggests a linear association between Gold % by Weight and
Lead % by Weight. The value of the correlation coefficient indicates that this association is moderately strong and positive.
d) What is the value of the coefficient of determination? Give an interpretation of this value in context.
48.7% of the variation in Lead % by Weight is accounted for by the LSRL with Gold % by Weight.
2. Suppose that the locally minted coins analyzed in problem 1 are representative of the metallurgical content of mints in the Eastern provinces of the Roman Empire during the first 300 years AD.
a) If a locally minted coin is selected at random, and it's gold content is 0.30% by weight, calculate the predicted lead content. Be sure to use correct notation and units.
b) One of the coins used to calculate the regression equations has a gold content