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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Mathematical models: functional form and coefficients |
A model is a mathematical function that relates the response Y
to the factors X1 to Xk. A model
has a
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Predicted values and residuals |
For given settings of the factors X1 to
Xk, a fitted model will yield predicted values. For
each (and every) setting of the Xi's, a
"perfect-fit" model is one in which the predicted values are identical
to the observed responses Y at these Xi's.
In other words, a perfect-fit model would yield a vector of predicted
values identical to the observed vector of response values. For these
same Xi's, a "good-fitting" 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 perfect-fit model, the vector of residuals would be all zeros. For a good-fitting model, the vector of residuals will be acceptably (from an engineering point of view) close to zero. |