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Using Input Variable Transformations to Improve Model Fit and Reduce Experimental Test Size (on Some Models!)

Gerald Fish, President, Experistats

The Custom DOE design platform in JMP is an excellent tool for laying out an experiment, applying constraints, etc. However, the platform assumes that the data will be modeled with some sort of N-degree polynomial fit. Some systems (such as the ideal gas law: P=nRT/V) may be better fitted if we could use an equation of factor multiples, rather than polynomial additions. This paper will show how we can make a transformation of input factors prior to using the Custom Designer to design the experiment. This transform can actually reduce the size of the experiment (compared to a full quadratic model). We will show how to estimate the form of the modeling equation (using dimensional analysis); how to transform the input factors; what kind of systems this might work on (and what kind it doesn’t); typical results for this method; and what to do if you try the transform, but it doesn’t work for you.

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