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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