Can regression analysis be applied to compute the synergy after "Firm A" aqcuires "Firm B"?

No. Two reasons:

1) Mathematics cannot be applied to corporate mergers. Simple reason: humans are involved. To think otherwise is to follow the same line of reasoning behind CDOs, etc.

2) The definition of “value” is highly subjective and not subject to quantification.

Synergy from corporate mergers derives from a lot of diverse sources, most of which are hard to measure separately, even more so in combination, (combining sales forces, their brand equities, manufacturing processes, distribution channels, etc, etc, etc,). I think it’s certainly possible to create a model that would mimic the synergy effect, but it would not be linear due to the huge number of factors involved, and the overwhelmingly complicated nature of the situation.