Question: Snowmelt runoff erosion. 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 once­in-5-year snowmelt runoff amount, x (measured in mil­limeters).

a) The data points are plotted in the scattergram shown on p. 489. 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

\(\hat{y}=-6.72+1.39x\)

with \({{s}_{{{{\hat{\beta }}}_{1}}}}=0.06\). Use this information to construct a 90% confidence interval for \({{\beta }_{1}}\).

(d) Interpret the interval, part c.