# Box and Liu (1999) describe an experiment flying paper helicopters where the objective is to maximize flight

## Question:

Box and Liu (1999) describe an experiment flying paper helicopters where the objective is to maximize flight time. They used the central composite design shown in Table 14E.9. Each run involved a single helicopter made to the following specifications: x1 = wing area (in2), ˆ’1 = 11.80 and +1 = 13.00; x2 = wing-length-to-width ratio,
ˆ’1 = 2.25 and +1 = 2.78; x3 = base width (in), ˆ’1 = 1.00 and +1 = 1.50; and x4 = base length (in), ˆ’1 = 1.50 and
+1 = 2.50. Each helicopter was flown four times, and the average flight time and the standard deviation of flight time were recorded.

The design and data are in the Minitab worksheet Ex14-16.MTW.
(a) Fit a second-order model to the average flight time response.
(b) Fit a second-order model to the standard deviation of flight-time response.
(c) Analyze the residuals for both models from parts (a) and (b). Are transformations on the response(s) necessary? If so, fit the appropriate models.
(d) What design would you recommend to maximize the flight time?
(e) What design would you recommend to maximize the flight time while simultaneously minimizing the standard deviation of flight time?

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