interpreting parameter estimates

[#1]

I have to determine what terms appear most dominant to the response based on the parameter estimates table. I am a little confused because of the negative coefficients for some of the terms under the estimate column.

[#2]

The interaction terms represent an effect over and above the 'main effects,' 'linear effects,' or 'additive effects.' The negative parameter indicates an 'antagonistic' effect: this model predicts less of a positive change in the response than expected from the linear terms alone.

It seems that some of the parameters are not significantly different from zero, so these terms can be eliminated. The best practice is to remove the least significant term (highest p-value) and evaluate the new model. Remove one term at a time, and evaluate the new set of estimates and p-values.

I suggest that you use the Prediction Profiler once you have select the model to aid in the interpretation of the relationship between the factors and the response.

[#3]

In addition to Mark's explanation and recommendation, I have the following thoughts:

1. How much of a change in the response variable is of practical significance?  The estimates are indicators of how much the response will change for every "unit" of change in the Parameter.

2. I don't see the intercept in your parameter estimates table?  This is typically the average of the data.

3. Interactions can be difficult to understand and how to optimize them is dependent on both target value of the response and practical implications.  An interaction is when the effect of a factor depends on another factor.  For positive sign 2-factor interactions, the effect of the interaction is greater when those factors have the same sign (-,- or +,+), for negative interactions, the effect is greater when they have opposite signs ,(-,+ or +,-).  It is good practice to evaluate interactions before drawing conclusions about main effects.  Look at the interaction plots for evaluation.

[#4]

I think that this case is a mixture experiment. so the intercept is present but not explicit.