Box, Hunter, and Hunter (see References) studied the

Chapter 9, Problem 5E

(choose chapter or problem)

Box, Hunter, and Hunter (see References) studied the effects of catalyst charge ( 10 pounds \(=-1,20\) pounds \(=+1)\), temperature \(\left(220^{\circ} \mathrm{C}=-1,240^{\circ} \mathrm{C}=+1\right)\), pressure \((50 \mathrm{psi}=-1,80 \mathrm{psi}=+1)\), and concentration \((10 \%\) \(=-1,12 \%=+1\) ) on percent conversion \((X)\) of a certain chemical. The results of a \(2^{4}\) design, in standard order, are

\(x_{1}=71, x_{2}=61, x_{3}=90, x_{4}=82, x_{5}=68, x_{6}=61\), \(x_{7}=87, x_{8}=80, x_{9}=61, x_{10}=50, x_{11}=89\), \(x_{12}=83, x_{13}=59, x_{14}=51, x_{15}=85, x_{16}=78\).

(a) Estimate the main effects and the two-, three-, and four-factor interactions.

(b) Construct an appropriate \(q-q\) plot and assess the significance of the various effects.

Equation Transcription:

 

  )

 

 

,

  

Text Transcription:

=-1,20  

=+1)

(220^ circ C=-1,240^ circ C=+1)  

(50psi=-1,80psi=+1)  

(10% =-1,12%=+1 )

(X)  

2^4  

x_1=71,x_2=61,x_3=90,x_4=82,x_5=68,x_6=61

x_7=87,x_8=80,x_9=61,x_10=50,x_11=89, x_12=83,x_13=59, x_14=51, x_15=85, x_16=78     q-q