For Exercises 2.44 and 2.45, see page 82; for 2.46, see page 84; for 2.47, see page 86; for 2.48 and 2.49, see page 88; for 2.50, see page 90; for 2.51, see page 90; for 2.52, see page 91; and for 2.53, see page 94.

Question 2.69

2.69 Monitoring the water quality near a manufacturing plant

Manufacturing companies (and the Environmental Protection Agency) monitor the quality of the water near manufacturing plants. 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.10

nrates

Nitrates Absorbance Nitrates Absorbance
50 7.0 800 93.0
50 7.5 1200 138.0
100 12.8 1600 183.0
200 24.0 2000 230.0
400 47.0 2000 226.0
  1. 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?
  2. What is the equation of the least-squares line for predicting absorbance from concentration? 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?

2.69

(a) The correlation is 0.9999, so the calibration does not need to be repeated. (b) . For , . Because the relationship is so strong, , we would expect our predicted absorbance to be very accurate.