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


Mathematical models: functional form and coefficients 
A model is a mathematical function that relates the response Y
to the factors X_{1} to X_{k}. A model
has a


Predicted values and residuals 
For given settings of the factors X_{1} to
X_{k}, a fitted model will yield predicted values. For
each (and every) setting of the X_{i}'s, a
"perfectfit" model is one in which the predicted values are identical
to the observed responses Y at these X_{i}'s.
In other words, a perfectfit model would yield a vector of predicted
values identical to the observed vector of response values. For these
same X_{i}'s, a "goodfitting" model is one that yields
predicted values "acceptably near", but not necessarily identical to,
the observed responses Y.
The residuals (= deviations = error) of a model are the vector of differences (Y  \( \small \hat{Y} \)) between the responses and the predicted values from the model. For a perfectfit model, the vector of residuals would be all zeros. For a goodfitting model, the vector of residuals will be acceptably (from an engineering point of view) close to zero. 