# Using MSE to determine prediction intervals?

I have a model that I've used MSE as the accuracy metric. After reading this article on calculating prediction intervals using MSE I looked around for other resources.

I then found this PDF from Wharton that suggests y_hat +/- 2 * RMSE forms a prediction interval for y. However it doesn't tell me what percent prediction interval this is. Is this the 95% prediction interval for y_hat?

As a result I'm a little confused on how to derive the right formula for a N% prediction interval given the RMSE or MSE of the model. Could anyone point me to the right resources, or show me how to derive the formula for this, so I can actually understand how they've arrived at what seems like two different formulas?

• That reference isn't quite right. It is making some (unstated) approximations, presumably to address an audience that might be confused by a full and accurate account of a prediction interval. Correct formulas are provided in several threads here, such as stats.stackexchange.com/questions/9131. They are needed in any situation where the fitted curve has appreciable uncertainty.
– whuber
Nov 25, 2016 at 20:37
• @whuber would you be willing to outline those unstated approximations in a comment or answer for completeness sake?
– user124589
Nov 25, 2016 at 20:46
• I already have: the approximation completely ignores uncertainty in the fitted curve.
– whuber
Nov 25, 2016 at 20:48