Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements 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 " absorbence." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. This is usually done every day. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water. Nitrates 100 50 125 250 300 300 800 1400 1700 3800 Absorbance 5.8 7.3 13.9 20.9 49.6 92.6 142.8 185.5 203.6 236.1 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. (a) Find the correlation r. r = (b) Must the calibration be done again? (Answer YES or NO). ANSWER:
Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements 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 " absorbence." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. This is usually done every day. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water.
| Nitrates | 100 | 50 | 125 | 250 | 300 | 300 | 800 | 1400 | 1700 | 3800 |
| Absorbance | 5.8 | 7.3 | 13.9 | 20.9 | 49.6 | 92.6 | 142.8 | 185.5 | 203.6 | 236.1 |
Chemical theory says that these data should lie on a straight line. If the
(a) Find the correlation r.
r =
(b) Must the calibration be done again? (Answer YES or NO).
ANSWER:
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