An agricultural scientist planted alfalfa on several plots of land, identical except for the soil pH. Following are the dry matter yields (in pounds per acre) for each plot.
pH Yield
4.6...............1056
4.8...............1833
5.2...............1629
5.4...............1852
5.6...............1783
5.8...............2647
6.0...............2131
a. Construct a scatterplot of yield (y) versus pH (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting yield from pH.
c. Compute the fitted value and the residual for each point.
d. If the pH is increased by 0.1, by how much would you predict the yield to increase or decrease?
e. Predict the yield for a pH of 5.5.
f. Can the least-squares line be used to predict the yield for a pH of 7? If so, predict the yield. If not, explain why not.
g. For what pH would you predict a yield of 1500 pounds per acre?