As final part of my paper helicopter experiment analysis (part I, part II) I do a reanalysis for one more data set. In 2002 Erik Erhardt and Hantao Mai did an extensive experiment, see The Search for the Optimal Paper Helicopter. They did a number of steps, including variable screening, steepest ascend and confirmatory experiment. For my part, I have combined all those data in one data set, and checked what kind of model would be used.

Data

The data extracted contains 45 observations. These observations have a number of replications, for instance a central composite design has a replicated center and the optimum found has been repeatedly tested.
After creation of a factor combining all variables it is pretty easy to examine the replications. The replications are thus. Here the first eight variables are the experimental settings, allvl is the factor combining all levels, Time is response and Freq the frequency of occurrence for allvl:
   RotorLength RotorWidth BodyLength FootLength FoldLength FoldWidth
1         8.50       4.00        3.5       1.25          8       2.0
2         8.50       4.00        3.5       1.25          8       2.0
3         8.50       4.00        3.5       1.25          8       2.0
4         8.50       4.00        3.5       1.25          8       2.0
5         8.50       4.00        3.5       1.25          8       2.0
6         8.50       4.00        3.5       1.25          8       2.0
7        11.18       2.94        2.0       2.00          6       1.5
8        11.18       2.94        2.0       2.00          6       1.5
9        11.18       2.94        2.0       2.00          6       1.5
10       11.18       2.94        2.0       2.00          6       1.5
11       11.18       2.94        2.0       2.00          6       1.5
12       11.18       2.94        2.0       2.00          6       1.5
13       11.50       2.83        2.0       1.50          6       1.5
14       11.50       2.83        2.0       1.50          6       1.5
15       11.50       2.83        2.0       1.50          6       1.5
   PaperWeight DirectionOfFold                                 allvl  Time Freq
1        heavy         against  8.5.4.0.3.5.1.2. 8.2.0.heavy.against 13.88    3
2        heavy         against  8.5.4.0.3.5.1.2. 8.2.0.heavy.against 15.91    3
3        heavy         against  8.5.4.0.3.5.1.2. 8.2.0.heavy.against 16.08    3
4        light         against  8.5.4.0.3.5.1.2. 8.2.0.light.against 10.52    3
5        light         against  8.5.4.0.3.5.1.2. 8.2.0.light.against 10.81    3
6        light         against  8.5.4.0.3.5.1.2. 8.2.0.light.against 10.89    3
7        light         against 11.2.2.9.2.0.2.0. 6.1.5.light.against 17.29    6
8        light         against 11.2.2.9.2.0.2.0. 6.1.5.light.against 19.41    6
9        light         against 11.2.2.9.2.0.2.0. 6.1.5.light.against 18.55    6
10       light         against 11.2.2.9.2.0.2.0. 6.1.5.light.against 15.54    6
11       light         against 11.2.2.9.2.0.2.0. 6.1.5.light.against 16.40    6
12       light         against 11.2.2.9.2.0.2.0. 6.1.5.light.against 19.67    6
13       light         against 11.5.2.8.2.0.1.5. 6.1.5.light.against 16.35    3
14       light         against 11.5.2.8.2.0.1.5. 6.1.5.light.against 16.41    3
15       light         against 11.5.2.8.2.0.1.5. 6.1.5.light.against 17.38    3

Transformation

Model selection

Adding interactions and quadratic effects via stepwise regression did not improve much.
This model does is quite extensive. For prediction purpose I would probably drop a few terms. For instance FootLength:PaperWeight could be removed, lessen the fit yet improve predictions, since its p-value is close to 0.15. As it is currently the model does have some issues. For instance, quite some points have high leverage.