53. The decline of water supplies in certain areas of the United States has created the need for increased understanding of relationships between economic factors such as crop yield and hydrologic and soil factors. The article Variability of Soil Water Properties and Crop Yield in a Sloped Watershed (Water Resources Bull., 1988: 281—288) gives data on grain sorghum yield (y, in g/m-row) and distance upslope (x, in m) on a sloping watershed. Selected observations are given in the accompanying table.
x 0 10 20 30 45 50 70 y 500 590 410 470 450 480 510 x 80 100 120 140 160 170 190 y 450 360 400 300 410 280 350

a. Construct a scatter plot. Does the simple linear regression model appear to be plausible?

b. Carry out a test of model utility.

c. Estimate true average yield when distance upslope is 75 by giving an interval of plausible values.