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Use of prediction intervals / distribution in prediction profiler and simulator

As discussed many times with JMP representative over the last 10 years, a good improvement would be that the prediction profiler allows more model 'predictive checks', e.g comparing data to prediction intervals and visualizing the prediction intervals on the prediction profiler (because, really, to get an idea of the prediction of tomorrow's outcome for my process, the confidence interval usefulness is close to 0).

 

Similarly, when computing p(defect) in the simulator, this is a little sad to use a Normal approximation of the predictive distribution (i.e. normal(mean, RMSE) ) instead of the more correct form of a Student accounting for RSME but also for design uncertainty. This latter is completely forgotten now, and which makes it statistically wrong, especially with small d.f.. Unfortunately, small d.f. is the norm, when using DoE.

 

(I mean, the closed-form solution even exists for multivariate multiple linear regression (not much more computations), and then, instead of writing manually a correlation matrix, we could use the one computed from the data, right ?)...

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