Prediction variance and prediction interval

[#1]

Can someone please explain the difference between prediciton variance and prediction interval?  I know they are the errors invovled when making a predction for a new response.  But I don't know the difference.  Is the prediction band shown in the prediction profiler the prediction variance or prediction interval?  Thanks!

[#2]

The prediction variance is the variance of observations. It is a combination of the variance of the response (standard deviation squared) and the variance of the predicted mean (standard error squared). The prediction interval represents a specified amount of coverage. The prediction interval is a multiple of the prediction variance.

The prediction profiler does not display the prediction interval. Per the JMP Help:

"The black lines within the plots show how the predicted value changes when you change the current value of an individual X variable. In fitting platforms, the 95% confidence interval for the predicted values is shown by solid blue curves surrounding the prediction trace (for continuous variables) or the height of an error bar (for categorical variables). For continuous variables, the confidence interval region is shaded."

So the shaded area and the interval shown on the left is the confidence interval of the mean response.

[#3]

Thank you for the explanation of prediction variance.  I have gotten a lot of questions in terms of how to translate it to something meaningful so one can compare two designs.

Is the prediction interval you are describing the same thing as the individual confidence interval that you can save out from a model?  (Side bar, it would be nice to be able to plot the individual CI's in the prediction profiler as well...I have not figured out if this is possible. Does not appear to be.)