2. In a training course for engineers, the trainees were given an assignment to go into a manufacturing company to design and analyse an experiment. One engineer designed an experiment to compare the strain of glass cathode supports across all of the five production machines in the plant. Each machine has components called heads that produce the glass. The engineer randomly selected four heads from each machine, and took four samples of glass from each. The data is in the file nestglass.csv.
(a) Identify the factors and the number of levels of each factor, indicating any nesting present.
(b) Write down the model equation, constraints, and assumptions that would apply in this case.
(c) Use the lme function to carry out an ANOVA test for mean differences between machines. Write down your conclusion.
(d) Use output from the lme function to estimate the variance components $\sigma_B^2$ and $\sigma^2$.
(e) Use the aov function to carry out an ANOVA test for mean differences between machines. Write down your conclusion.
(f) Use output from the aov function to estimate the variance components $\sigma_B^2$ and $\sigma^2$.