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 yieldx = planting date (days after April 20)z = planting density (plants/ha)The following regression model with both quadratic terms where x₁ = x, X₂ = Z, X3 = x² and x4 = 2² provides a good description of the relationship between y andthe independent variables.y =a +B₁x₁ + B₂X₂ + B3X3+B₁x₁ + e(a) If a = 21.07, B₁ = 0.653, B₂ = 0.0022, B3 = -0.0207, and B4 = 0.00002, what is the population regression function?y = 509X(b) Use the regression function in Part (a) to determine the mean yield for a plot planted on May 7 with a density of 41,182 plants/ha. (Give the exactanswer.)(c) Would the mean yield be higher for a planting date of May 7 or May 23 (for the same density)?The mean yield would be higher for [May 7You may need to use the appropriate table in Appendix A to answer this question.

The variables are defined are defined as follows:The regression model:The quadratic termsWhere,,,,…

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 x₁ = x, X₂ = Z₁ X3 = x² and x4 = 2² provides a good description of the relationship between y and the independent variables. y = a +3₁x₁ + ₂x₂ + 3x3 + ₁x₁ + e (a) If a = 21.07, B₁ = 0.653, B₂= 0.0022, B3 = -0.0207, and 34= 0.00002, what is the population regression function? y = 509 X (b) Use the regression function in Part (a) to determine the mean yield for a plot planted on May 7 with a density of 41,182 plants/ha. (Give the exact answer.) (c) Would the mean yield be higher for a planting date of May 7 or May 23 (for the same density)? The mean yield would be higher for [May 7