Question

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 50 50 125 250 300 500 900 1200 1500 2500 Absorbance 5.5 7.2 11.7 22.7 48.6 96.7 148.6 192.3 227 221.4 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 =

(b) Must the calibration be done again? (Answer YES or NO). ANSWER:

Answer 1

a. Here we will find r

X Values
∑ = 7375
Mean = 737.5
∑(X - M_x)² = SS_x = 5734062.5

Y Values
∑ = 981.7
Mean = 98.17
∑(Y - M_y)² = SS_y = 75681.841

X and Y Combined
N = 10
∑(X - M_x)(Y - M_y) = 605198.75

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 605198.75 / √((5734062.5)(75681.841)) = 0.919

b. As we see that r<0.997, so calibration is to be done again