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 table.

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

b. Fit the quadratic model E(y) = β_o + β₁x + β₂x² to the data.

c. Conduct a test to determine if a curvilinear relationship exists between dissolved phosphorus percentage (y) and soil loss (x). Test using α = .05.

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PHOSPHOR soil Loss x (kilometers per half-acre) Dissolved Phosphorus Percentage y Watershed 1 18 42.3 2 17 50.2 3 35 52.7 4 16 77.1 5 14 36.8 6. 54 17.5 7 153 66.4 8. 81 67.5 9 183 28.9 10 284 15.1 11 767 20.1 12 148 38.3 13 649 5.6 14 479 8.6 15 1,371 5.5 16 9,150 4.6 17 15,022 2.2 18 69 77.9 19 4,392 7.8 20 312 42.9