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LASSO workflow for cross validation and final model

Please check my understanding of how CV is working in JMP for LASSO (or any other regularization method).  Suppose I choose 5-fold CV.  Here is what I think happens...

 

 

We loop through all the lambdas.  For each lambda we generate 5 errors and average these.  At the end we use the minimum error to identify the optimal lambda_star.  Now we use all the data, along with lambda_star to find the final model (the set of coefficients).

 

My understanding is that the in-sample error is what we calculate with the final model on all the data.  What about the out-of-sample error?  I've seen leave-one-out used to estimate this.  Does JMP calculate this and show it in the report, and if so, how is that done?  Also can lambda_star be displayed.  I saw a related discussion for retrieving the tuning parameter but I'm hoping to avoid JSL if I can.

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