Labelled dataset for NLP regression
I know of a good few NLP regression tasks, but these are usually not about a predicting an extrinsic value from the semantic description, but rather predict some numerical property of the text itself:

MT quality estimation: predict the quality of a translated sentence, usually as a score. Data available at the WMT QE Shared Task series. There are probably other similar datasets about predicting the quality of a sentence in general.
Author profiling: predicting the age of the author of a text. Some datasets exist in particular through the PAN workshop series.
Predicting a rating based on a comment - there's data everywhere on social media, Amazon etc. You could even use StackExchange posts and predict votes :)

I'm not aware of any data similar to your example (btw it would be a very challenging task). I know that there are some works on detecting fraud from the text of an insurance claim, so maybe there are datasets that you could use in this area.