The 'E' in the regression is the inferred/predicted value of the E variable for that exercise, using no problem history from that exercise--only what's pulled in through the Bayes net. (Sorry that wasn't clear)
The 'T' variable is likely just a case of multicollinearity with the 'E' variable and should go away on a full-scale data set. If not it can easily be removed from the model. The 'E' variable is dominating because is additionally captures cross-sectional affects across the various exercises in the regression.
Ah, ok. So is this a sort of Markov model, where you are predicting the probability of getting an exercise right after observing (some subset of) the previous exercises? And E is not 1 or 0, but the expected probability of getting it right? I'm still confused where all the different E_i's fit in.
That would explain the magnitude, and I agree the negative weight on T would just be due to the direct correlation between E and T.
Edit: I just realized that an exercise consists of multiple problems, so you're predicting whether or not the student will get >= 85% of the problems right on an exercise.
The 'T' variable is likely just a case of multicollinearity with the 'E' variable and should go away on a full-scale data set. If not it can easily be removed from the model. The 'E' variable is dominating because is additionally captures cross-sectional affects across the various exercises in the regression.