The U.S. Department of Agriculture has developed and adopted the Universal Soil Loss Equation (USLE) for predicting water erosion of soils. In geographical areas where runoff from melting snow is common, 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-five-year snowmelt runoff amount, x (measured in millimeters).

a. The data points are plotted in the scattergram shown below. 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:

Use this information to construct a 90% confidence interval for ß₁.

d. Interpret the interval, part c.