You must show all work for full credit (except for plots and things computed entirely in R, in which case just state "from R" and give the key commands for computations). Please staple your assignment if it is more than one page.

Required problems:

1) Problem 14.5 (modified): The data in the file tape are from a study of the effects of three factors on the percent elongation of electrical tape (which is how much it stretches before it breaks). The three factors and limits are:

Factor	Description	Low Value (-1)	Mid Value (0)	High Value (1)
X1	% Plasticizer in Formulation	10%	25%	40%
X2	Temperature of Compounding	200 F	275 F	350 F
X3	Extruder Speed	300 rpm	450 rpm	600 rpm

  a) Analyze the experimental results to find the best equation.
  b) Verify that any assumptions in your analysis are reasonable (via plots of residuals).
  c) Use that model to determine the optimum operating conditions (maximum elongation), either via graphical display of the equation, by using nlm in R, or by using calculus if you are so inclined.
  d) What is your expected response at the optimum conditions, and what are its error limits (give either a CI for the fitted value or a prediction interval).

2) Project Progress: Describe how you will collect your data. For most people, this means "give the experimental design". For the few people who won't be doing a planned experimental design, you should describe the data collection process and what steps are being taken to ensure that a good sample is collected.
Please be specific here - for example in specifying a design, state what your factors are, what levels you are using, and exactly what design you are using.