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Analysis of variance

Analysis of variance

Source Sum-of-squares DF Mean-square F-ratio P

Regression 2376.813 12 198.068 6,836 0.000 Residual 898.187 31 28.974

"Multiple R: .85 Squared multiple R: ,73

Adjusted squared multiple R: ,62 Standard error of estimate: 5.3

6A-E = Ingredients A to E, respectively; F = Cook process.

T Value = T test for significance of the coefficient. (T values in excess of

+1 or -1 denote significant coefficient«—vis, those significantly different from 0).

dP value = probability that the coefficient is really "0". (Low P value means that the coefficient is significantly different from 0).

1. Theory. We know from experimentation that liking does not continue to increase linearly with physical level ad infinitum., but eventually peaks, plateaus, and then drops. Curvature requires the quadratic term in the equation.

2. Parsimony. The quadratic equation is relatively parsimonious, allowing both curvature and interactions between variables. Other equations might fit the data better, but would demand more terms.

Whether the investigator fits a linear or quadratic model to the data, the utility of the model is the same—it predicts responses to combinations of independent variables, even when the combinations were not actually tested but lie within the range tested.

Tables 17 and 18 show the equations developed for the products (darkness, liking). The equations are simply mathematical statements. They lack substantive meaning for the product developer, until the developer substitutes meaningful values for the independent variables and estimates the attribute ratings.

Optimizing a Response by Finding the Highest Value

A major benefit of modeling is the ability to discover the particular combination of physical variables which coire-spond to a desired condition, such as the highest (optimal) rating on an attribute (eg, liking). Table 19 shows several optimizations, including overall optimization of liking (column A), three optimizations for liking subject to imposed cost constraints (columns B,C,D), and optimization of lik-

Table 18. Model Relating Formula and Process Variables to Perceived Darkness"

Variable6

Coefficient

STD error

T6

P6

Constant

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