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 = percent maize yield x₁ = planting date 1days after April 202 x₂ = planting density 110,000 plants/ha2 The regression model with both quadratic terms (y = a ± ß₁x₁ + ß₂x₂ + ß₃x₃ ± ß₄x₄ + e where X₃ = X₁² and x₄ = x₂²) provides a good description of the relationship between y and the independent variables.

a. If a = 21.09, b1 = .653, b₂ = .0022, b3 = 2.0206, and b4 = 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 legitimate to interpret b₁ = .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?

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and x4 x2) provides a good description of the rela tionship between y and the independent variables