Chapter 14.1, Problem 10E

The relationship between yield of maize (a type of com), 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 = Maize yield (percent)

x₁ = Planting date (days after April 20)

x₂ = Planting density (10.000 plants/ha)

The regression model with both quadratic terms (y = α + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₄ + e where x₃ = $x_1^2$ and x₄ = $x_2^2$) provides a good description of the relationship between y and the independent variables.

1. a. If α = 21.09, β₁ = 0.653, β₂ = 0.0022, β₃ = 2.0206, and β₄ = 0.4, what is the population regression function?
2. 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.
3. c. Would the mean yield be higher for a planting date of May 6 or May 22 (for the same density)?
4. d. Is it appropriate to interpret β₁ = 0.653 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?