Tennis Ball Experiment
An experiment is performed to see how differing amounts of three key components;
silica, silane and sulfur affect the bounciness of a tennis ball. A wide variety of values
for each component are used. Ultimately, the combination of components that produces a
bounce response of 450 is desired. The data appear below.
Silica
0.7
0.7
1.7
1.7
1.2
1.2
1.2
1.2
0.7
1.7
0.7
1.7
1.2
1.2
1.2
Sulfur
1.8
2.8
1.8
2.8
1.8
1.8
2.8
2.8
2.3
2.3
2.3
2.3
2.3
2.3
2.3
Silane
50
50
50
50
40
60
40
60
40
40
60
60
50
50
50
Bounce
570
285
260
433
422
351
278
392
451
372
474
394
398
394
396
A Response Surface Model includes each of the explanatory variables; silica, sulfur and
silane; all pair-wise interaction variables; silica*sulfur, silica*silane, sulfur*silane; and
all squared explanatory variables; silica2, sulfur2, silane2. Centering the variables in the
interaction and squared terms tends to reduce multicollinearilty.
Response: Bounce
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.999771
0.999543
1.700032
391.3333
15
Analysis of Variance
Source
Model
Error
C. Total
DF
7
7
14
Sum of Squares
88453.103
20.231
88473.333
Mean Square
12636.2
2.9
F Ratio
4372.207
Prob > F
<.0001*
1
Parameter Estimates
Term
Intercept
Silica
Sulfur
Silane
(Silica-1.2)*(Silica-1.2)
(Silica-1.2)*(Sulfur-2.3)
(Sulfur-2.3)*(Sulfur-2.3)
(Sulfur-2.3)*(Silane-50)
Estimate
561.07885
–80.25
–53.75
1.1
105.92308
458
–142.0769
9.25
Std Error
4.40724
1.202104
1.202104
0.060105
3.528414
3.400065
3.528414
0.170003
t Ratio
127.31
–66.76
–44.71
18.30
30.02
134.70
–40.27
54.41
Prob>|t|
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
Contour Profiler
2