4.27 How many corn plants are too many? How much corn per acre should a farmer plant to obtain the highest yield?

Too few plants will give a low yield. On the other hand, if there are too many plants, they will compete with each other and yields will fall. To find the best planting rate, plant at different rates on several plots of ground and measure the harvest. (Be sure to treat all the plots the same except for the planting rate.)

Here are data from such an experiment:'^

Plants per acre

(thousands)

Yield

(bushels per acre)

12 150.1 113.0 118.4 142.6 16 166.9 120.7 135.2 149.8 20 165.3 130.1 139.6 149.9 24 134.7 138.4 156.1 28 119.0 150.5

(a) Make a scatterplot that shows how yield responds to plant ing rate. Use a scale of yields from 100 to 200 bushels per acre so that the pattern will be clear.

(b) Describe the overall pattern of the relationship. Is it lin ear? Is there a positive or negative association, or neither? Find the correlation r. Is r a helpful description of this relationship?

(c) Find the mean yield for each of the five planting rates.
Plot each mean yield against its planting rate oia your scatter plot and connect these five points with lines. This combination of numerical description and graphing makes the relationship clearer. What planting rate would you recommend to a farmer whose conditions were similar to those in the experiment?