177 Soil loss during rainfall. Phosphorus used in soil fertilizers can contaminate freshwater sources during rainfall runoff. Consequently, it is important for water quality engineers to estimate the amount of dissolved phosphorus in the water. Geoderma (June 1995) presented an investigation of the relationship between soil loss and percentage of dissolved phosphorus in water samples collected at 20 fertilized watersheds in Oklahoma. The data are given in the accompanying table and saved in the PHOSPHOR file.

a. Plot the data in a scatterplot. Do you detect a linear or curvilinear trend?

b. Fit the quadratic model E(y) = b0 + b1 x + b2 x2 to the data.

c. Conduct a test to determine whether a curvilinear relationship exists between dissolved phosphorus percentage

( y ) and soil loss ( x ). Use a = .05

Transcribed Image Text:

Watershed Soil Loss x (kilometers per half-acre) Dissolved Phosphorus Percentage y 11 1234567ROUNDBARTRAG 18 42.3 17 50.2 35 52.7 16 77.1 14 36.8 54 17.5 153 66.4 8 81 67.5 9 183 28.9 10 284 15.1 767 20.1 148 38.3 649 5.6 479 8.6 1,371 5.5 9,150 4.6 15,022 2.2 18 69 77.9 19 4,392 7.8 20 312 42.9 Based on Sharpley, A. N., Robinson, J. S., and Smith, S. J. "Bioavailable phosphorus dynamics in agricultural soils and effects on water quality." Geoderma, Vol. 67, No. 1-2, June 1995, p. 11 (Table 4).