An article in Quality Engineering [Mean and Variance Modeling with Qualitative Responses: A Case Study (19981999, Vol.

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.

(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?

(c) Analyze the residuals from this experiment. Does your analysis indicate any potential problems?

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

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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 6789으=p: