Chapter 13.2, Problem 21E

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 agentis 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. Here is data on x 5 leaching time (h) and y 5 nitrate extraction percentage (seawater):

x	25.5	31.5	37.5	43.5	49.5	55.5
y	26.4	40.1	50.2	57.4	62.7	67.3
x	61.5	67.5	73.5	79.5	85.5	91.5
y	71.4	74.7	77.8	80.3	82.3	84.1
x	97.5	103.5	109.5	115.5	121.5	127.5
y	85.5	86.6	87.9	89.0	89.9	90.6
x	133.5	139.5	145.5	151.5	157.5
y	91.2	91.8	92.3	92.8	93.3

a. Construct a scatterplot. If the simple linear regression model were fit to this data, what would a plot of the (x, e*) pairs look like?

b. Construct a scatterplot of y versus x’ = 1/x and speculate on the value of r² after fitting the simple linear regression model to the transformed data. c. Obtain a 95% prediction interval for nitrogen extraction percentage when leaching time = 100 h.