The U.S. Department of Agriculture has developed and adopted the Universal Soil Loss Equation (USLE) for predicting water erosion of soils. In geographic areas where runoff from melting snow is common, calculating the USLE requires an accurate estimate of snowmelt runoff erosion. An article in the Journal of Soil and Water Conservation (Mar.–Apr. 1995) used simple linear regression to develop a snowmelt erosion index. Data for 54 climatological stations in Canada were used to model the McCool winter-adjusted rainfall erosivity index, y, as a straight-line function of the once-in-5-year snowmelt runoff amount, x (measured in millimeters).

a. The data points are plotted in the scattergram. Is there visual evidence of a linear trend?

b. The data for seven stations were removed from the analysis due to lack of snowfall during the study period. Why is this strategy advisable?

c. The simple linear regression on the remaining n = 47 data points yielded the following results: ŷ = -6.72 + 1.39x, s_β̂1 = .06. Use this information to construct a 90% confidence interval for β₁. 

d. Interpret the interval, part c.

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700 600 500 400 300 200 100 100 200 300 400 500 Once/5-year Winter Runoff (mm) McCool Winter R-Adjustme nt