The relationship between yield of maize (a type of corn), date of planting, and planting density was investigated in an article. Let the variables be defined as follows. y = maize yield (percent) x1 = planting date (days after April 20) x2 = planting density (10,000 plants/ha) The following regression model with both quadratic terms where x3 = x12 and x4 = x22 provides a good description of the relationship between y and the independent variables. y = ? + ?1 x1 + ?2 x2 + ?3 x3 + ?4 x4 + e (a) If ? = 21.05, ?1 = 0.652, ?2 = 0.0025, ?3 = −0.0204, and ?4 = 0.5, what is the population regression function? y = (b) Use the regression function in part (a) to determine the mean yield (in percent) for a plot planted on May 8 with a density of 41,182 plants/ha. (Round your answer to two decimal places.) % (c) Would the mean yield be higher for a planting date of May 8 or May 22 (for the same density)? The mean yield would be higher for . (d) Is it appropriate to interpret ?1 = 0.652 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? Yes, since there are no other terms involving x1.Yes, since there are other terms involving x1. No, since there are other terms involving x1.No, since there are no other terms involving x1.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

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Question

The relationship between yield of maize (a type of corn), date of planting, and planting density was investigated in an article. Let the variables be defined as follows.

y = maize yield (percent)
x₁ = planting date (days after April 20)
x₂ = planting density (10,000 plants/ha)

The following regression model with both quadratic terms where

x₃ = x₁²

and

x₄ = x₂²

provides a good description of the relationship between y and the independent variables.

y = ? + ?₁ x₁ + ?₂ x₂ + ?₃ x₃ + ?₄ x₄ + e

(a)

If ? = 21.05, ?₁ = 0.652, ?₂ = 0.0025,

?₃ = −0.0204,

and

?₄ = 0.5,

what is the population regression function?

y =

(b)

Use the regression function in part (a) to determine the mean yield (in percent) for a plot planted on May 8 with a density of 41,182 plants/ha. (Round your answer to two decimal places.)

(c)

Would the mean yield be higher for a planting date of May 8 or May 22 (for the same density)?

The mean yield would be higher for .

(d)

Is it appropriate to interpret

?₁ = 0.652

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?

Yes, since there are no other terms involving x₁.Yes, since there are other terms involving x₁. No, since there are other terms involving x₁.No, since there are no other terms involving x₁.

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