Question

2.67/4 points Previous Answers Peck DevStat7 14.6.010. 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) 2-planting density (plants/ha) The following regression model with both quadratic terms where x - X,X2 2,3 and 4 provides a good description of the relationship between y and the independent variables. ya+ + + B + te (a) Ifa 21.09. - 0.651, P - 0.0021, B = -0.0208, and Be - 0.00006, what is the population regression function? y - 21:09 + 0.651x2 +0.002.x, + -0.0208x3 +0.00006x, (b) Use the regression function in Part(a) to determine the mean yield for a plot planted on May 6 with a density of 41,183 plants/ha. (Give the sact answer.) (c) Would the mean yield be higher for a planting date of May 6 or May 25 (for the same density)? The mean yield would be higher for May 6

Answer 1

the regression function is:-

$y=21.09+0.651x_{1}+0.0021x_{2}-0.0208x_{3}+0.00006x_{4}$

b). for May 6 with a density of 41183 plants /ha

x = 10+6 = 16 [ after 20 th April there are 10 days ]

z=41183

hence, $x_{1}=x=16$

$x_{2}=z=41183$

$x_{3}=x^2=16^2=256$

$x_{4}=z^2=41183^2=1696039489$

the mean yield for a plot planted on May 6 with a density of 41183 plants /ha be:-

= 21.09 + (0.651*16) + (0.0021*41183) - (0.0208*256) + (0.00006*1696039489)

= 101875.0348

c). the mean yield would be higher for May 6

[for May 25 with a density of 41183 plants /ha

x = 10+25 = 35 [ after 20 th April there are 10 days ]

z=41183

hence, $x_{1}=x=35$

$x_{2}=z=41183$

$x_{3}=x^2=35^2=1225$

$x_{4}=z^2=41183^2=1696039489$

the mean yield for a plot planted on May 25 with a density of 41183 plants /ha be:-

= 21.09 + (0.651*35) + (0.0021*41183) - (0.0208*1225) + (0.00006*1696039489)

= 101867.2486

for may 6 mean yield is = 101875.0348 ....this is > 101867.2486 ]

*** if you face any trouble to understand the answer to the problem please mention it in the comment box.if you are satisfied, please give me a LIKE if possible.