The relationship between yield of malze (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 x₂x₁² and x-x₂²provides a good description of the relationship between y and the independent variables. y=a + ₁x₂ + ₂x₂ + ₂xy + ₂x₂ + e (a) If a = 21.05, 8₁ = 0.654, 8₂=0.0023, 6₂ = -0.0207, and 8 = 0.3, 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 4 with a density of 41,179 plants/ha. (Round your answer to two decimal places.) (c) would the mean yield be higher for a planting date of May 4 or May 22 (for the same density)? yield would be higher for --Select-- The mean yi (d) Is it appropriate to interpret ₁ = 0.654 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? O No, since there are other terms involving x Yes, since there are other terms involving ₂. Yes, since there are no other terms involving x₁ No, since there are no other terms involving ₂
The relationship between yield of malze (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 x₂x₁² and x-x₂²provides a good description of the relationship between y and the independent variables. y=a + ₁x₂ + ₂x₂ + ₂xy + ₂x₂ + e (a) If a = 21.05, 8₁ = 0.654, 8₂=0.0023, 6₂ = -0.0207, and 8 = 0.3, 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 4 with a density of 41,179 plants/ha. (Round your answer to two decimal places.) (c) would the mean yield be higher for a planting date of May 4 or May 22 (for the same density)? yield would be higher for --Select-- The mean yi (d) Is it appropriate to interpret ₁ = 0.654 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? O No, since there are other terms involving x Yes, since there are other terms involving ₂. Yes, since there are no other terms involving x₁ No, since there are no other terms involving ₂
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Transcribed Image Text: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=a + B₁X₁ + B₂X2 + ₂xy + B₁X₁ + e
(a) If a = 21.05, ₁ = 0.654, B₂ = 0.0023, B3 = -0.0207, and ₁=0.3, what is the population regression function?
(b) Use the regression function in part (a) to determine the mean yield (In percent) for a plot planted on May 4 with a density of 41,179 plants/ha. (Round your answer to two decimal places.)
(c) Would the mean yield
The mean yield would
higher for a planting date of May 4 or May 22 (for the same density)?
higher for --Select--
(d) Is it appropriate to interpret , = 0.654 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?
O No, since there are other terms involving x₁.
Yes, since there are other terms involving x,
Yes, since there are no other terms involving x₁
O No, since there are no other terms involving x,
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