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 93.0 138.0 183.0 229.0 226.0 (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.) r = (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 = + x (d) What is the estimated nitrate level in a water specimen with absorbence 41? (Use 1 decimal place.) mg/l (e) Do you expect estimates of nitrate level from absorbence to be quite accurate? Since the calibration is so important, it is inaccurate to use this regression to predict. This prediction should be very accurate because the relationship is so strong as indicated by r. This prediction should be very inaccurate because the relationship is too perfectly linear. This prediction is of a value that is not in the range of the data and therefore cannot be accurate.

Answer 1

Answer:

  Let me first upload excel ouput as follow.

a) From the regression output multiple R = r = 0.999897 = 0.9999 ( After rounding four decimal places)

Consider the given statement "The 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."
and we find r = 0.9999 which is > 0.997

So that we do not need to repeat the calibration procedure

b) Your answer of part b is correct because r from the given data = 0.9999 > 0.997

c) The calibration process sets nitrate level and measures absorbence. After calculating the linear relationship between Absorption and Nitrate level, the linear equation is Y^ = -15.13 + 8.811 X

(d) What is the estimated nitrate level in a water specimen with absorbence 41?

Y^ = -15.13 + 8.811 X

==> Y^ = -15.13 + 8.11 * 41

==> Y^ = 317.4 mg/l

(e) Do you expect estimates of nitrate level from absorbence to be quite accurate?

Y^ = 317.4 mg/l for X = 41 this prediction would be very accurate because the relationship is so strong as r = 0.999897.