Currently, I am modelling the results of game theory experiments where two parties negotiate to divide a fixed sum of money between themselves. Y is recorded as the percentage of the money which the first party takes (e.g. when Y = 40, the first party takes 40% and the second party is implied to take 60%).
When applying a simple linear regression model to this problem, the outputs of the model does not make sense. For instance, Y may be predicted to be 110, but there is no 110% of that fixed sum in reality.
I understand that logistic regression outputs a range which may be interpreted as between 0 - 100. But my understanding is that logistic regression does not apply here because:
- this is not a classification problem, and
- logistic regression requires the values of Y in the training set to be binary (which is not the case here)
Hence, what should I do to constrain the linear regression model to output a range between 0 to 100, or are there other models that I should be looking at? Also, is there a name for this problem I am facing? My vocabulary is lacking here.