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
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Advantages: perfect fit and comparable coefficients |
The linear model consisting of main effects
and all interactions has two advantages:
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Example | To illustrate in detail the above latter point, suppose the (-1, +1) factor X1 is really a coding of temperature T with the original temperature ranging from 300 to 350 degrees and the (-1, +1) factor X2 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 X1 (-1, +1) and X2 (-1, +1). The resulting coefficients are unit-invariant, 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 (X1 to T, X2 to t). The unit-invariant coded coefficients may be easily transformed to unit-sensitive original coefficients if so desired. |