Question

Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirecta 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 50 50 100 200 400 800 1200 1600 2000 2000

Absorbence 7.0 7.6 12.9 24.0 47.0 94.0 138.0 183.0 229.0 226.0

(a) Chemical theory says that these data should lie on a straight line and if the correlation is not at least 0.997 then the calibration procedure is repeated. Find the correlation. (Use 4 decimal places.)

(b) Must the calibration be done again? Yes/ No

(c) The calibration process sets nitrate level and measures absorbence. Once established, the linear relationship will be used to estimate the nitrate level in water from a measurement of absorbance. What is the equation of the line used for estimation? (Use 2 decimal places for intercept and 3 decimal places for slope.) y hat =

(d) What is the estimated nitrate level in a water specimen with absorbence 38? (Use 1 decimal place.)

Answer 1