The relationship between yield of maize, date of planting, and planting density

Question

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 = 0.00006, what is the population regression function? y = 21.08 +.654x +.0022z -.0205x^2 +.00006z^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 answer.)________ 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 for______.

Explanation / Answer

Answer

Part b

The regression equation is given as below:

Y = 21.08+.654x+.0022z-.0205x^2+.00006z^2

Y = 21.08+.654*3+.0022*41181-.0205*9+.00006*41181^2

Y = 101865.9

Part c

It would be higher for the date of May 25.

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