Question: An article in Quality Engineering [Mean and Variance Modeling with Qualitative Responses: A Case Study (19981999, Vol. 11, pp. 141148)] studied how three active ingredients

An article in Quality Engineering [€œMean and Variance Modeling with Qualitative Responses: A Case Study€ (1998€“1999, Vol. 11, pp. 141€“148)] studied how three active ingredients of a particular food affect the overall taste of the product. The measure of the overall taste is the overall mean liking score (MLS). The three ingredients are identified by the variables x₁, x₂, and x₃. The data are shown in the following table.

Run MLS X3 1 1 -1 6.3261 1 1 6.2444 3 6.5909 6.3409 -1 5.907 1 1 1 -1 -1 6.488 -1 5.9773 6.8605 6.0455 -1 -1 1 10 1 6.34

(a) Fit a second-order response surface model to the data.

(b) Construct contour plots and response surface plots for MLS. What are your conclusions?

(d) This design has only a single center point. Is this a good design in your opinion?

Run MLS X3 1 1 -1 6.3261 1 1 6.2444 3 6.5909 6.3409 -1 5.907 1 1 1 -1 -1 6.488 -1 5.9773 6.8605 6.0455 -1 -1 1 10 1 6.3478 6.7609 11 1 12 -1 -1 -1 5.7727 13 6.1805 14 1 1 6.4894 15 -1 6.8182 45 6789=p:

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