Required problems:

1) Problem 12.5: You are trying to help an ice cream vendor to be able to predict how many ice cream cones he will sell in a given afternoon (so that he knows how much ice cream to buy). He decides, with your help, to run a half fraction of a 2^5 design to study the influence of several factors on scales. The data are in the file cones. The factors studied are:

Factor	Low Value (-)	High Value (+)
X1=Temperature (F)	75	85
X2=Weather	Cloudy	Sunny
X3=# of Flavors	5	10
X4=Cone Type	Regular	Waffle
X5=Personality	Surly	Happy

From this dataset, is a prediction equation justified? (i.e., are any of the factors significant?) If so, what is it? (Note that the prediction equation should be given in terms of numeric values for X1 and/or X3 if those factors are in it, so you would need to convert these from numeric to factor in your equation. Since it is a prediction equation, you are finding coefficients, not factor effects, so DON'T multiply your regression coefficients by 2. When fitting your regression model, remember to include the appropriate number of terms, which will include some interaction terms.) Justify your answers (i.e., include the relevant output from R and explain it).

2) Problem 12.7: Consider the 2^(5-2) fractional factorial design with generators 4=12 and 5=123.
  a) Specify the factor level combinations for this design.
  b) Determine the complete confounding pattern.
  c) What is the resolution of this design?

3) Project Progress:
  a) What methodology from this class will you be using in your project? (For example, using factorial or fractional factorial designs to screen for potentially important factors; or using regression or response surface methods to build a model for an output)
  b) do one run of the simulator, and state here what the input values were, the response, and the approximate length of time it took to complete this run (if less than one second, you can just state that).