Residual & forecast error

[sweetie]

The residual in chapter 3 of the book is defined to be Y - Y_hat. Why is the forecast error in chapter 8 = Y_hat - Y, which is negative of what was defined in chapter 3?

Thanks for your help.

[NewTubaBoy]

Don't you usually square them... so it doesn't matter which it is?

[sweetie]

I agree, but it is not a square here. That's why I'm confused.

[Peter Lemonjello]

Interesting.

Just a guess -- the error is the actual minus expected. For a forecast, Yhat is the "actual" in that the forecasted event hasn't happened yet.

[Abraham Weishaus]

Exactly.

The residual is the excess of the actual over the estimate. It is the amount of the actual which the suggested regression model doesn't capture.

The forecast error is the excess of the forecast over the actual. The expected value of the forecast error is the difference between the forecast and the expected value of the actual, which is the model (Y).

[sweetie]

Thank you.