How does the Analysis work?

The Volume Analysis page that opens during the creation of a project in MateCat shows you a global report of the volume to be translated: Standard weighted words, MateCat weighted words and Raw words.
For more detailed information, you can read here.

How are Internal Matches and repetitions calculated in a single project with more than one file?

When you import more than one file in a project, the files are considered as a single unit during the analysis, and the internal matches and repetitions are calculated on everything together. Read more details here.

I tried creating a project, but the Analyze button is inactive. Can you help me?

The first thing you have to do to create a project is upload a file; once the upload is finished, the analyze button will become active.

Where is the information about the analysis in the user guide?

The information can be found here.

How is the word count calculated?

The word count is performed through an analysis of the source files’ content against matches from the public translation memory, your private translation memories (if any) and machine translation suggestions. This is why you get more matches than with any other CAT tool, even if you don’t use a Private TM.
A detailed description can be found here.

What is considered a repetition? Are single words included?

A repetition is when the same sentence (segment) is repeated in the project, and can also be in more than one document.
Single words are not considered in the calculation of repetitions.

Is it possible to perform an analysis without using Machine Translation, Private TMs or Public TMs?

Machine translation can be easily disabled and having a Private TM is optional, but it is impossible to disable the Public TM matches. More information can be found here.

Is it possible to export the analysis in Excel?

The analysis can be exported in .txt format and with the API.