14.10 The relationship between yield of maize, date of planting, and planting density was investigated in the article “Development of a Model for Use in Maize Replant Decisions” (Agronomy Journal [1980]: 459–464).

Let y 5 percent maize yield x1 5 planting date sdays after April 20d x2 5 planting density s10,000 plantsyhad The regression model with both quadratic terms

( y 5 a 1 b1x1 1 b2x2 1 b3x3 1 b4x4 1 e where x3 5 x21 and x4 5 x22 d provides a good description of the relationship between y and the independent variables.

a. If a 5 21.09, b1 5 .653, b2 5 .0022, b3 5 2.0206, and b4 5 0.4, what is the population regression function?

b. Use the regression function in Part

(a) to determine the mean yield for a plot planted on May 6 with a density of 41,180 plants/ha.

c. Would the mean yield be higher for a planting date of May 6 or May 22 (for the same density)?

d. Is it appropriate to interpret b1 5 .653 as the average change in yield when planting date increases by one day and the values of the other three predictors are held fixed? Why or why not?