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3 Response Surface In order to get reliable data for a response surface model, a designed experiment is often used to collect the data on the explanatory variables and the response.
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Response Surface A Response surface model
is a special type of multiple regression model with: Explanatory variables Interaction variables Squared variables
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Response Surface A response surface model is
often used to approximate a complicated relationship between a response variable and several explanatory variables.
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Response Surface In order to get reliable data
for a response surface model, a designed experiment is often used to collect the data on the explanatory variables and the response.
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Designed Experiment In a designed experiment,
the experimenter chooses values of the explanatory variables to investigate and measures the response for the chosen combinations of explanatory variables.
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Tennis Ball Experiment In the manufacture of tennis
balls certain additives are thought to affect the bounciness of the tennis ball.
Response: A measure of bounce.
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Tennis Ball Experiment Explanatory variables
Amount of silica Amount of sulfur Amount of silane
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Tennis Ball Experiment Each explanatory variable
has three levels Silica: 0.7, 1.2, 1.7 Sulfur: 1.8, 2.3, 2.8 Silane: 40, 50, 60
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Tennis Ball Experiment A total of 15 combinations of
silica, sulfur and silane are examined and the bounce response is measured for each combination.
The target bounce response is 450.
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Silica Sulfur Silane Bounce
0.7 1.8 50 5700.7 2.8 50 2851.7 1.8 50 2601.7 2.8 50 4331.2 1.8 40 422
1.2 2.3 50 396
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Response Surface Model
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JMP – Fit Model Put Bounce in for the Y
response. Highlight silica, sulfur and
silane in Select Columns. Macros – Response Surface
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Summary The model is useful.
F=2488.146, P-value < 0.0001
R2=0.999777, virtually all of the variation in Bounce is explained by the model.
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Statistical Significance The interaction between
Silica and Silane is not statistically significant.
The squared term for Silane is not statistically significant.
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Reduced Model Remove the interaction
term: Silica*Silane. Remove the squared term:
Silane*Silane.
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Summary The model is useful.
F=4372.207, P-value < 0.0001 R2=0.999771, virtually all of
the variation in Bounce is explained by the model. Only slightly lower than R2 for the full model.
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Statistical Significance All variables in the model
are statistically significant. This is the best response
surface model.
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Prediction What combinations of silica,
sulfur and silane will give you the target bounce of 450, on average?
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Prediction There are several
combinations that will give a predicted bounce of 450. Silica = 1.0, Sulfur = 1.948, Silane = 50
Silica = 0.8, Sulfur = 2.251, Silane = 40