The following is NOT legal advice. I am NOT an attorney. You should ALWAYS consult a competent attorney about any legal matters, including this matter.
Generally, raw data is not covered by copyright law in the US. I don't know exactly what the data you're using looks like, but if it's something akin to baseball statistics (a bunch of numbers), those can't be copyrighted (though their presentation can be). If it's just raw data, you don't even need the fair use exemption as there is no copyright protection.
As for images, those are almost certainly covered by copyright law.
Fair use is a four-prong test that is measured by a court. A good way to get a sense of whether or not your situation falls under the fair use exemption is to consult a competent attorney who can compare your situation to past rulings. Keep in mind, though, that an attorney can make an educated prediction, but cannot guarantee an outcome. The four factors considered, to give you an idea, are:
- the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
- the nature of the copyrighted work;
- the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
- the effect of the use upon the potential market for or value of the copyrighted work.
While all four prongs may be considered, you do not have to meet a specific requirement for all four. It's up to the court which of the criteria matter, or don't matter, in your situation and how much.
Keep in mind also, from a pragmatic standpoint, that copyright law would only be enforced if the publisher of the data decided to file a law suit. If that's unlikely, all this discussion is moot.
Finally, you can always just send in an email and ask. Given the nature of your work, they might just want a citation. And if they give your permission, you have nothing to worry about.
@Jacob added some more details about the situation.
What struck me as interesting in the added details was the statement This document is provided on the basis of strict confidentiality. If the data is truly in need of protection, like if it is a trade secret, it might be smart to exercise some extra caution here. Having posted the data on the open Internet, the company probably could not do much to keep you from using it. However, if it's truely valuable, they may fight to protect it which could create a huge headache, to say the least.
I think I outlined why you might be able to use the data with and without fair use above. I want to add however, that does not mean you should use it without permission. Even if the data is not protected by copyright, it would be best to ask permission if for no reason other than basic courtesy.
Being turned down does not change the law. If something was not protected by copyright before you ask, it will not be protected after you ask. If something falls under fair use before you ask, it will still remain under fair use after you ask. You really have very little to lose by asking. I can tell though that you are hesitant to ask so I will suggest you do so without revealing too much information about yourself and your work. Instead of diving in with a long, detailed explanation of your research, put your toe in the water with some basic details and see how they react.
For all you know, they might be interested in your work. Since it seems like your area of expertise, this might even lead to something more like a job interview. There is a lot of potential upside.
I don't want to say too much more about whether or not the specific data is covered by copyright because this is not a place to get legal advice and I am not someone to give it. But in general, if you put the raw coefficient numbers in the prose of your work, you are probably safe regardless of fair use. If you want to copy any photos, graphics, or detailed descriptions of the numbers, you'll have to do so under fair use and/or with permission.