RMSE versus parameter estimate

Dear all,

A basic question about the comparison of RMSE value and parameter estimate. I got the point that RMSE value and parameter estimate are not correlated to each other and that a parameter estimate smaller in value than the RMSE value can still be significant for the model.

But still, I am wondering if we can consider a parameter with a parameter estimate value (let's say 2) lower than the RMSE (let's say 2.5) ?

Could we conclude that a parameter estimate lower than the RMSE value is a negligible effect on response ?

I think my confusion starts with the fact that I consider these two values as being a part of the same dimensionality (the response dimensionality - Y)... So, I consider these two values as to be comparable.

Many thanks,
Hi Dason,
Sorry I do not get your question... This post rises in the context where I built a model, and let's say two predictors are significant, but one of these predictors has a parameter estimate value lower than the RMSE value.


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So to answer the question directly. In general the answer is no. Especially talking about estimated slopes in a model. You can change the slopes just by changing the scale you measure the predictor on so a direct comparison doesn't make any sense.