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Regression: RASE vs. Standard Error

In the Fit Model platform when I do a multivariate "fit least squares", the platform lets me save three values to columns:

• Std Error of Predicted
• Std Error of Residual
• Std Error of Individual

I am interested in knowing how the modeling error changes across the predictor variables, instead of just using one flat RMSE value for the whole model (For example, I might see high variation at low voltage)

 

So these 3 StdError values are interesting to me, but I don't know how to interpret them. Stderr Residual/Individual are very close to my RMSE number, but there is very little variation - the values are very similar across the whole table (in my table RMSE is ~32MHz.... "StdErr of Residual" varies from 30.2 to 32.1, and "StdErr of Individual" varies from 32.3 to 34.0)

 

However, the "Stderr of Predicted" seems to be quite interesting and the trend makes sense to me - the variation is smaller where I have more data points (suggesting the model is more confident there) ... however the magnitude of numbers don't make sense. It varies from 2.66 to 11 MHz. Not sure how to square that with the overall RMSE of 32.

 

Can anyone help me understand this?

 

Thanks,
Charles

Re: Regression: RASE vs. Standard Error

I think I understand better now, after deep-diving into this subject. StdError of Individual seems to be the basis of a confidence interval, which is that se, scaled by a t-multipler:

 

Re: Regression: RASE vs. Standard Error

Hi Charles,

Thanks for answering your own question.  I was looking into it but found myself learning the topic to answer your question as I didn't have additional insight beyond what the JMP Help online documentation provided.

Plotting those 3 error types against each other, it looks like there are formulaic relations between all 3 and they are used to determine the confidence levels of the model fit parameters. 
What I find useful from these errors is to see if the residuals show any systematic variation.  If they do, that is an indicator that your model is underfitting and missing some key effect.

Mark