2. An experiment was conducted to determine the effect of recipe and baking temperature on chocolate cake quality. Fifteen batches of cake mix for each recipe were prepared. Each batch was sufficient for six cakes. Each of the six cakes was baked at a different temperature which was randomly assigned. Several measures of cake quality were recorded of which breaking angle was just one. The dataset is presented as 'choccake' in library(faraway). library (faraway) data (choccake) (a) Plot the data and comment. (b) This is an example of a split plot design. Explain. (c) Fit a linear model with an interaction between recipe and temperature as fixed effects and no random effects. Which terms are significant? Why is this analysis unreliable? NOTE: In this model you should treat temperature as a factor rather than a continuous variable. Why is that? (d) Fit a mixed effects model that takes account of the batch structure. Comment on how the variation is assigned to possible sources. (e) Test for the recipe effect. (f) Test for the temperature effect. Which temperatures differ? (g) Check the diagnostic plots of your favourite model and comment.