interpreting SSYhat for N=1

[rparker]

I have a question about SEYhat in time-series regression for N=1 subject....  

I want to know whether the StdError of the fitted score (SEYhat) can be legitimately interpreted normally for N=1 subject, with only one plotted Y score for each X value.......  

I am interested in using the Y-hat score as a proxy for N=1 student progress.  It has some desirable attributes, including small size. I've looked at the SEest (or SEprediction), and its not what I'm after because it refers to error around an individual predicted score.  

All examples I've found using SEYhat include at least 2 datapoints per X predictor value.  Yet when I look at the SE Yhat formula, it seems to include nothing that requires multiple datapoints per X value. Its ingredients are Xvar, MSErr, SEslope, SEintcept, and X-Xbar deviation score.  None of these require deviation of Ys around a Yhat for a particular value of X.  
Do you have an opinion on this question?

Thanks, RParker