5.
Process Improvement
5.5. Advanced topics 5.5.9. An EDA approach to experimental design 5.5.9.9. Cumulative residual standard deviation plot


Advantages: perfect fit and comparable coefficients 
The linear model consisting of main effects
and all interactions has two advantages:


Example  To illustrate in detail the above latter point, suppose the (1, +1) factor X_{1} is really a coding of temperature T with the original temperature ranging from 300 to 350 degrees and the (1, +1) factor X_{2} is really a coding of time t with the original time ranging from 20 to 30 minutes. Given that, a linear model in the original temperature T and time t would yield coefficients whose magnitude depends on the magnitude of T (300 to 350) and t (20 to 30), and whose value would change if we decided to change the units of T (e.g., from Fahrenheit degrees to Celsius degrees) and t (e.g., from minutes to seconds). All of this is avoided by carrying out the fit not in the original units for T (300,350) and t (20, 30), but in the coded units of X_{1} (1, +1) and X_{2} (1, +1). The resulting coefficients are unitinvariant, and thus the coefficient magnitudes reflect the true contribution of the factors and interactions without regard to the unit of measurement.  
Coding does not lead to loss of generality  Such coding leads to no loss of generality since the coded factor may be expressed as a simple linear relation of the original factor (X_{1} to T, X_{2} to t). The unitinvariant coded coefficients may be easily transformed to unitsensitive original coefficients if so desired. 