An experiment was conducted to investigate the effect of

Chapter 11, Problem 74E

(choose chapter or problem)

An experiment was conducted to investigate the effect of four factors—temperature \(T_{1}\), pressure P, catalyst C, and temperature \(T_{2}\)—on the yield Y of a chemical.

a The values (or levels) of the four factors used in the experiment are shown in the accompanying table. If each of the four factors is coded to produce the four variables \(x_{1}, x_{2}, x_{3}\), and \(x_{4}\), respectively, give the transformation relating each coded variable to its corresponding original.

b Fit the linear model

\(Y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\beta_{4} x_{4}+\varepsilon\)

to the following table of data.

c Do the data present sufficient evidence to indicate that \(T_{1}\) contributes information for the estimation of Y ? Does P? DoesC? Does \(T_{2}\)? (Test the hypotheses, respectively, that \(\beta_{1}=0, \beta_{2}=0, \beta_{3}=0\) and \beta_{4}=0) Give bounds for the p-value associated with each test. What would you conclude if you used α = .01 in each case?

Equation transcription:

Text transcription:

T{2}

T{1}

x{1}, x{2}, x{3}

X{4}

Y=beta{0}+beta{1} x{1}+beta{2} x{2}+beta{3} x{3}+beta{4} x{4}+varepsilon

beta{1}=0, beta{2}=0, beta{3}=0

beta{4}=0