Question: 75 Keeping water clean. Manufacturing companies (and the Environmental Protection Agency) monitor the quality of the water near facilities. Measurements of pollutants in water are indirect-a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its “absorbance’. To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbance to pollutant concentration. This is usually done every day. Here is one series of data on the absorbance for different levels of nitrates. Nitrates are measured in milligrams per liter of water.

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Nitrates 50 50 100 200 400 800 1200 1600 2000 2000

Absorbance 7.0 7.5 12.8 24.0 47.0 93.0 138.0 183.0 230.0 226.0

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(a) Chemical theory says that these data should lie on a straight line. If the Correlation is not at least 0.997, something went wrong and the calibration procedure is repeated. Plot the data and find the correlation. Must the calibration be done again?

(b) What is the equation of the least-squares line for predicting absorbance fromconcentration? If the lab analyzed a specimen with 500 milligrams of nitrates per liter, what do you expect the absorbance to be? Based on your plot and the correlation, do you expect your predicted absorbance to be very accurate?