The fraction of variance that is not explained by the proxies is associated with the residuals, and their variance is one part of the mean
squared prediction error, which determines the width of the error band.
If you would like your modeling result to be taken seriously as a guide to future planning (I don't mean to presume to know your motives), then keep track of
the squared prediction error, the sum of the squared prediction errors (CUSUM), and the square root of the mean prediction error (RMSE) over the next 20 years.
Not exact matches
This flexibility suggests finding a lower bound on the mean
square error for linear
prediction of from factors based on test scores.
Some results on mean
square error for factor score
prediction.
Cross-validation skill, measured by the correlation between two - month lead
predictions and observations of September ice extent, is 0.82, while the RMS
error of
predictions is 0.72 million
square km.
The average of the
squared resulting
prediction errors will start to rise when too many PLS components are used.
The
prediction mean
squared error is the
square of the standard
error and is the sum of two terms.