Question

Keeping water supplies clean requires regular measurement of levels of pollutants. To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. 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 50 150 300 300 500 900 1300 1400 3400

Absorbance 5.3 7.5 13.2 26.8 40 95.9 130.6 182.2 230.6 232.1

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.

Answer 1

Solution:

a) Find the correlation r.

n = 10

X	Y	XY	X2	Y2
50	5.3	265	2500	28.09
50	7.5	375	2500	56.25
150	13.2	1980	22500	174.24
300	26.8	8040	90000	718.24
300	40	12000	90000	1600
500	95.9	47950	250000	9196.81
900	130.6	117540	810000	17056.36
1300	182.2	236860	1690000	33196.84
1400	230.6	322840	1960000	53176.36
3400	232.1	789140	11560000	53870.41
Sum = 8350.00	964.20	1536990	16477500.00	169073.60

r =  

= 0.8605

Answer : r = 0.8605