Question: An experiment was conducted to relate Yield in a chemical plant to temperature and pressure.

The following table gives the experimental data, which was originally published in the text “Introduction to Linear Models and the Design and Analysis of Experiments” by Mendenhall, W., Duxbury Press.

You need to enter the data manually to perform the analysis.

(a) Discuss the basic principles of experimentation in the context. You need to discuss how the experimenter would have applied the basic principles, for example, how the principle of randomisation must have been applied. [6 marks]

(b) Perform one-way ANOVA tests to see whether there is any temperature or pressure effect.

Discuss your answer stating the limitations of this test. [4 marks]

(c) Perform two-way ANOVA tests (with and without interactions) to see whether there is any temperature and/or pressure effects. Explore the residuals of the fitted models and suggest whether or not you obtain any clues for improving the model. [8 marks]

(d) Perform a multiple linear regression of Yield on temperature and pressure. Interpret the t

and F-tests done in the context. [4 marks]

(e) Compare the regression and ANOVA analyses and comment. Which approach is reliable,

and why? Explain your answer in the context. [4 marks]

(f) Build a more appropriate model relating Yield with temperature and pressure. Note that this question is open ended, and you need to provide necessary justifications in your answer. [4 marks]