- #1
squenshl
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Homework Statement
Suppose (Y1, Y2, Y3, Y4) = (5.2, 6.8, 11.9, 17.0) are the average yields (in tonne/ha) of potato grown in soil with 4 different levels of superphosphate fertiliser, x1 = 1.20, x2 = 1.75, x3 = 2.30, x4 = 2.85. We want to fit the model E[Yi] = [tex]\beta[/tex]1 + [tex]\beta[/tex]2xi + [tex]\beta[/tex]3zi where zi = 3xi2 - 4.4875 for i = 1,...,4.
Suppose that the observations (Y1, Y2, Y3, Y4) are independent with common variance [tex]\sigma[/tex]2
How do I find the design matrix X and hence write the model in the form E(Y) = X[tex]\beta[/tex]
Homework Equations
The Attempt at a Solution
I found z1, z2, z3, z4 using x1, x2, x3, x4 to get z1 = -0.1675, z2 = 4.70, z3 = 11.3825, z4 = 19.88 so from E(Yi) do I get
X =
(1 1.20 -0.1675
1 1.75 4.70
1 2.30 11.3825
1 2.85 19.88)
hence E(Y) = X[tex]\beta[/tex] where [tex]\beta[/tex] = ([tex]\beta[/tex]i)T
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