DOE coded values

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    What does coding values in a DOE do to the results? Does it make the regression coefficients just easier to calculate or does them make it more accurate?



    It is used for the sum of squares calculations


    Robert Butler

      When you center and scale your regressors you are guarding against roundoff errors which can completely invalidate your results.  Even with double precision and all of the other safeguards of the current computer systems roundoff error can wreak havoc.  The differences due to roundoff error will cause different regression programs to give wildly different estimates of parameter coefficients for the same set of data.
      There are two major causes of roundoff error.  The first is the situation where the numbers in the regression computations are of widely differing orders.  X1 for example is varied between .001 and .005 and X2 is varied between 200 and 300. 
      The second case occurs when the matrix to be inverted is very close to being singular.  This usually doesn’t happen in a DOE unless you have a situation where some of your experiments failed and you have to run the analysis without the benefit of all of your design points.
      If you wish to read more on this subject you can check pp.257-262 of Applied Regression Analysis, Second Edition by Draper and Smith.

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