Suppose that many farmers in Iowa grow corn and they all use

Suppose that many farmers in Iowa grow corn, and they all use the same kind of fertilizer. A sample of three farmers, Jeb, Donald, and Carly, was chosen from the population of all corn farmers in Iowa, and for each of them two measures were recorded: the quantity of fertilizer he or she applied to her or his field during the previous growing season (measured in pounds per acre, and denoted F), and the quantity of corn harvested from his or her field the previous growing season (measured in bushels per acre, and denoted G). The data collected were as follows:

Farmer    Jeb Donald Carly

F (pounds per acre) 20 30 70

G (bushels per acre) 150 400 350

a) Make a scatter plot of this data, with F on the horizontal axis and G on the vertical axis. Partition the graph into four quadrants with a vertical line drawn at the mean of the F data and a horizontal line drawn at the mean of the G data.

b) Find FG s , the sample covariance between fertilizer use and corn production.

c) Find FG r , the sample correlation between fertilizer use and corn production.

d) It would make sense to say that the data for two of the farmers contributed something positive to the covariance and correlation, and the data for one of the farmers contributed something negative to the covariance and correlation. Which farmer was it whose data contributed something negative to the covariance and correlation, and what does that mean?

Solution