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, X2 z, X3 X2 and X4 z provides a good description of the relationship between y and the independent variables. (a) If a 21.08 B1 0.651 B2 0.0025 B3 0.0207, and B 0.00006, what is the population regression function? 00006-2 x 21.08 .651x 00252 0207x (b) Use the regression function in Part (a) to determine the mean yield

Explanation / Answer

Part a

y = 21.08+ 0.651x + .0025z-0.0207x^2 + 0.00006z^2

Part b

X = may 2 - April 20 = 12 days, z = 41179

y = 21.08+0.651*12+0.0025*41179-0.0207*12^2 +41179^2*0.00006 = 101871

Part C

X = may 20, 30 days would be y = 21.08+0.651*30+0.0025*41179-0.0207*30^2 +41179^2*0.00006 = 101867

Thus yield would be higher for may 2

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