Mineral mining is one of the most important economic activities in Chile. Mineral products are frequently found in saline systems composed largely of natural nitrates. Freshwater is often used as a leaching agent for the extraction of nitrate, but the Chilean mining regions have scarce freshwater resources. An alternative leaching agent is seawater. The authors of “Recovery of Nitrates from Leaching Solutions Using Seawater” (Hydrometallurgy, 2013: 100–105) evaluated the recovery of nitrate ions from discarded salts using freshwater and seawater leaching agents. Tests were performed in salt columns irrigated at the same rate for a period of more than 150 hours.

Here is data on x leaching time (h), y_{fw} nitrate extraction percentage (freshwater), and y_{sw} nitrate extraction percentage (seawater):

a. Construct scatterplots of y_{fw} versus x and y_{sw} versus x. Note the nonlinearity of the plots. Would it be reasonable to describe the patterns in both plots as curved and monotonic?

b. In Section 3.4, we described how a power transformation can be applied to create a linear pattern in the transformed data. Using the transformation 1/x, construct scatterplots of y_{fw} versus x , and y_{sw} versus . For each set of pairs, calculate point estimates of the slope and intercept of the respective population regression line.

c. Does the simple linear regression model appear to specify a useful relationship between either dependent variable and in part (b)? State and test the relevant hypotheses.

d. The researchers concluded that the freshwater and seawater leaching agents yield similar nitrate extraction efficiencies. Using the regression models from part (b), calculate a point estimate of true nitrate extraction percentage when leaching time is 150 hours. Are the two estimates similar?