- #1

- 479

- 4

## Homework Statement

Suppose (Y

_{1}, Y

_{2}, Y

_{3}, Y

_{4}) = (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, x

_{1}= 1.20, x

_{2}= 1.75, x

_{3}= 2.30, x

_{4}= 2.85. We want to fit the model E[Y

_{i}] = [tex]\beta[/tex]

_{1}+ [tex]\beta[/tex]

_{2}x

_{i}+ [tex]\beta[/tex]

_{3}z

_{i}where z

_{i}= 3x

_{i}

^{2}- 4.4875 for i = 1,...,4.

Suppose that the observations (Y

_{1}, Y

_{2}, Y

_{3}, Y

_{4}) 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 z

_{1}, z

_{2}, z

_{3}, z

_{4}using x

_{1}, x

_{2}, x

_{3}, x

_{4}to get z

_{1}= -0.1675, z

_{2}= 4.70, z

_{3}= 11.3825, z

_{4}= 19.88 so from E(Y

_{i}) 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}

Last edited: