1. 1 Response Surface A Response surface model is a special type of multiple regression model with: Explanatory variables Interaction variables Squared variables

2. 2 Response Surface A response surface model is often used to approximate a complicated relationship between a response variable and several explanatory variables.

3. 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.

4. 4 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.

5. 5 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.

6. 6 Tennis Ball Experiment Explanatory variables Amount of silica Amount of sulfur Amount of silane

7. 7 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

8. 8 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.

9. 9 SilicaSulfurSilaneBounce 0.71.850570 0.72.850285 1.71.850260 1.72.850433 1.21.840422 1.22.350396

10. 10 Response Surface Model

11. 11 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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14. 14 Summary The model is useful. F=2488.146, P-value < 0.0001 R 2 =0.999777, virtually all of the variation in Bounce is explained by the model.

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16. 16 Statistical Significance The interaction between Silica and Silane is not statistically significant. The squared term for Silane is not statistically significant.

17. 17 Reduced Model Remove the interaction term: Silica*Silane. Remove the squared term: Silane*Silane.

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19. 19 Summary The model is useful. F=4372.207, P-value < 0.0001 R 2 =0.999771, virtually all of the variation in Bounce is explained by the model. Only slightly lower than R 2 for the full model.

20. 20 Statistical Significance All variables in the model are statistically significant. This is the best response surface model.

21. 21 Prediction What combinations of silica, sulfur and silane will give you the target bounce of 450, on average?

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24. 24 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