Analyze Mixture Design

Mixture Regression
Regression Table - P-Values

  

Use the p-values (P) to determine which of the effects in the model are statistically significant. To use the p-value, you need to:

·    identify the p-value for the effect you want to evaluate.

·    compare this p-value to your a-level. A commonly used a-level is 0.05.

-    if the p-value is less than or equal to a, conclude that the effect is significant.

-    if the p-value is greater than a, conclude that the effect is not significant.

Example Output

Estimated Regression Coefficients for Flavor (component proportions)

 

Term                     Coef  SE Coef      T      P     VIF

Emmentha                  500   141.50      *      *   24937

Gruyere                   -89    54.85      *      *     613

Wine                      395   143.73      *      *   43038

Emmentha*Gruyere         1200   375.92   3.19  0.019    2655

Emmentha*Wine           -1676   593.83  -2.82  0.030  102454

Gruyere*Wine             -869   409.98  -2.12  0.078    7888

Emmentha*Temperat        -572   141.50  -4.04  0.007   24937

Gruyere*Temperat          263    54.85   4.79  0.003     613

Wine*Temperat            -568   143.73  -3.95  0.008   43038

Emmentha*Gruyere*

Temperat                -1440   375.92  -3.83  0.009    2655

Emmentha*Wine*Temperat   2388   593.83   4.02  0.007  102454

Gruyere*Wine*Temperat    1433   409.98   3.50  0.013    7888

 

* NOTE * Coefficients are calculated for coded process variables.

Interpretation

For the fondue data, the regression table shows the following:

·    Interactions with Temperature: There are six terms in the model that consider the blend by temperature interaction.

-    Two-component blends with temperature: Each of the two-component blends have an interaction effect with Temperature. That is, the binary blending characteristics of all two-component blends differ depending in the serving temperature. These effects correspond to the following entries in the regression table:

·    Emmentha*Gruyere*Temperat: p-value = 0.009

·    Emmentha*Wine*Temperat: p-value = 0.007

·    Gruyere*Wine*Temperat: p-value = 0.013

-    One-component blends with temperature: Each of the one-component blends has an interaction effect with Temperature. That is, the blending characteristics of all one-component blends differs depending in the serving temperature. These effects correspond to the following entries in the regression table:

·    Emmentha*Temperat: p-value = 0.007

·    Gruyere*Temperat: p-value = 0.003

·    Wine*Temperat: p-value = 0.008

·    Binary blends: Two two-blend mixtures have a significant binary blending effect. That is, the flavor rating for the two-blend mixture differs from the simple mean of the two individual components. These effects correspond to the following entries in the regression table:

-    Emmentha*Gruyere: p-value = 0.019. In addition, the positive coefficient (1200) indicates that the two components act synergistically or are complementary. That is, the mean acceptance score for the blend is greater than you would obtain by calculating the simple mean of the two acceptance scores for each pure mixture.

-    Emmentha*Wine: p-value = 0.030. In addition, the negative coefficient (-1676) indicates the two components are antagonistic towards one another. That is, the mean acceptance score is lower than you would obtain by calculating the simple mean of the two acceptance scores.

-    Gruyere*Wine p-value = 0.078. The p-value is the least significant of the binary blends.

 


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