The relationship between yield of maize, date of planting, and planting density was investigated in an article. let the variables be defined as follows. y = percent maize yield x = planting date (days after april 20) z = planting density (plants/ha)
the following regression model with both quadratic terms where x_1 = x, x_2 = z x_3 = x^2 and x_4 = z^2 provides a good description of the relationship between y and the independent variables. y = alpha + beta_1x_1 + beta_2x_2 + beta_3x_3 + beta_4x_4 + e if alpha = 21.08, beta_1 = 0.654, beta_2 = 0.0022, beta_3 = 0.0205, and beta_4 = 0.6, what is the population regression function?
y = 21.08 +.654x +.0022z -.0205x^2 +.6z^2 + e
use the regression function in part (a) to determine the mean yield for a plot planted on may 3 with a density of 41,181 plants/ha. (give the exact would the mean yield be higher for a planting date of may 3 or may 25 (for the same density)? the mean yield would be higher