Prediction from predicted/residual values compare to standard error of the estimate

[yumi]

Hello.

I have to indicate how good prediction is, by looking at the actual, predicted, and residual values, compare to the standard error of the estimate.

I understand that the smaller standard error of the estimate is more accurate, and is a better prediction. But when “Residual score of 27.82” is very close to “the standard error of the estimate of 34.45”, is it the good prediction, too? Actual Value is 10. I'm confused.

THANK YOU for your assistance!

 

[Junes]

Re: Prediction from predicted/residual values compare to standard error of the estima

Hi, welcome. I'm not sure I understand your question entirely, but I'll try to help you on your way.

The residual of 27.8 is for that particular point. It shows the error of your model for that case. So, whatever you are trying to predict for the United States, your model undershoots by 27.8.

The standard error of the estimate is a summary statistic for all residuals. It's the standard deviation of the residuals:

\(s = \sqrt{\frac{\sum(Y - Y')^2}{N-2}}\)

Where \(s\) is the SEE, \(Y'\) is the predicted value and \(Y\) is the actual value (each \(Y - Y'\) is one residual). Note that we have to divide by \(N-2\) instead of \(N\) because it's a sample estimate (unless of course you are actually dealing with a population). For more info, see here.

It has the same units as your residuals, and usually you can think of the standard error of the estimate as a "typical" or "average" residual (though it's not a mean in the mathematical sense). Some individual residuals may be higher, some may be lower.