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hw6.lyx
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#LyX 1.6.7 created this file. For more info see http://www.lyx.org/
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\begin_document
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\begin_body
\begin_layout Standard
John Hancock
\end_layout
\begin_layout Standard
CEN 6405
\end_layout
\begin_layout Standard
Homework 6
\end_layout
\begin_layout Standard
May 24th, 2014
\end_layout
\begin_layout Part*
Homework #6
\end_layout
\begin_layout Section*
18.1
\end_layout
\begin_layout Standard
Problem 18.1 requires us to analyze the design of a
\begin_inset Formula $2^{2}3$
\end_inset
experiment.
We borrow heavily from the example in chapter 18.
To get started we will construct the sign table for the experiment.
We will use the convention:
\end_layout
\begin_layout Standard
\begin_inset Formula \[
x_{A}\begin{cases}
-1 & \mbox{if processor A}\\
1 & \mbox{if processor B}\end{cases}\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula \[
x_{b}\begin{cases}
-1 & \mbox{if workload I}\\
1 & \mbox{if workload J}\end{cases}\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Tabular
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<row>
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Mean
\begin_inset Formula $\bar{y}$
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1
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-1
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-1
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1
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40.91
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1
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1
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-1
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-1
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62.22
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1
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-1
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1
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-1
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\begin_inset Formula $\left(51.50,52.50,50.50\right)$
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51.50
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1
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1
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1
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1
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48.05
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202.68
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17.86
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-3.58
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-24.75
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Total
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50.67
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4.46
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-0.89
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-6.19
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Total/4
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\begin_layout Standard
Sign Table
\end_layout
\begin_layout Standard
The bottom row of the table tells us the coefficients for our model
\begin_inset Formula \[
\hat{y}=q_{0}+q_{A}x_{A}+q_{B}x_{B}+q_{AB}x_{AB}+eij\]
\end_inset
\begin_inset Formula \[
\hat{y}=50.67+4.46x_{A}-0.89x_{B}-6.19x_{AB}+eij\]
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\end_layout
\begin_layout Standard
We now compute the error of the model in each observation
\end_layout
\begin_layout Standard
\begin_inset Tabular
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\end_layout
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\begin_layout Plain Layout
Measured Responses
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Errors
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