Analyze Mixture Design

Mixture Regression
Analysis of Variance Table

  

Use the p-values (P) in the analysis of variance table 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

Analysis of Variance for Flavor (component proportions)

 

Source                             DF   Seq SS    Adj SS   Adj MS       F      P

Regression                         11  3693.03  3693.029  335.730  152.04  0.000

  Component Only

   Linear                           2  3207.12   553.195  276.597  125.26  0.000

   Quadratic                        3    91.95    91.948   30.649   13.88  0.004

     Emmentha*Gruyere               1     0.00    22.500   22.500   10.19  0.019

     Emmentha*Wine                  1    82.03    17.586   17.586    7.96  0.030

     Gruyere*Wine                   1     9.91     9.914    9.914    4.49  0.078

  Component* Temperature

   Linear                           3   294.55    53.799   17.933    8.12  0.016

     Emmentha*Temperature           1   250.09    36.033   36.033   16.32  0.007

     Gruyere*Temperature            1    37.66    50.654   50.654   22.94  0.003

     Wine*Temperature               1     6.79    34.487   34.487   15.62  0.008

   Quadratic                        3    99.42    99.419   33.140   15.01  0.003

     Emmentha*Gruyere*Temperature   1    24.46    32.400   32.400   14.67  0.009

     Emmentha*Wine*Temperature      1    47.96    35.703   35.703   16.17  0.007

     Gruyere*Wine*Temperature       1    26.99    26.995   26.995   12.23  0.013

Residual Error                      6    13.25    13.249    2.208

Total                              17  3706.28

Interpretation

For the fondue data, the analysis of variance table shows the following:

·    Regression: This tests whether the terms in the model have any effect on the response. The regression model is significant (p = 0.000). That is, at least one of the terms in the regression equation has an impact on the mean response.

Regression is further broken into Components only and Components and Process Variable (Temperature), and then into the different orders of terms in the model - linear and quadratic.

-     Components only

-     Linear: The p-value for all linear terms is 0.000, indicating that at least one linear term has an impact on the mean response.

-     Quadratic: The p-value for all quadratic terms is 0.004, indicating that at least one of the quadratic terms has an  impact on the mean response. The Emmentha*Wine term (p-value = 0.030) and Emmentha*Gruyere term (p-value = 0.019) are significant.

-     Component *Temperature

-     Linear: The p-value for all linear terms is 0.016, indicating that at least one term has an impact on the mean response. The p-values for all of the individual linear terms are less than 0.05.  

-     Quadratic: The p-value for all quadratic terms is 0.003, indicating that at least one of the quadratic terms has an  impact on the mean response. The p-values for all of the individual quadratic terms are less than 0.05.

·    Residual Error: The residual error measures amount of variation in the response left unexplained by the model.