If you could meaningfully slice the data by key1, key2 or key3 then you could make dimensions out of them. In that case you would have separate dimension tables that had all the values of each key, and any relevant attributes (even just a human-readable description of what the value represents) or groupings (roll-ups of the key values).
Each dimension table would have the key value and its attributes, and would link to the fact table on its key.
If your values (Var X) are additive across rows (i.e. all the values added together for Key1='Foo' mean something) then you can use the keys to slice the data.
I don't think that relationships between the Var columns are really relevant to dimensional modelling unless you want to unpivot them and indentify them by a 'variable type' dimension rather than separate columns
Beyond that, the question is a bit vague to really get a clear view of what you are trying to achieve and why you want to make a dimensional model of your data in the first place. Maybe if you can clarify your goals a bit we can give you a more meaningful answer.
EDIT:
Dimensional modelling is just identifying the axes by which you want to slice data in aggregate. Sometimes a dimension might be very simple - just a code. Sometimes it may be complex with lots of sub-attributes - such as an insurance policy. A dimension lets you slice data in aggregate, either by its key or by rolling up the data by some attribute of the dimension.
If the VarX columns are additive between rows - i.e it makes sense to aggregate (for example) var2 for two or more rows - then a dimensional structure might make sense for reporting. One key point of a dimensional model is that it tends to facilitate efficient queries in aggregate, and plays nicely with OLAP tools.
So, if I had values 'Foo', 'Bar', 'Wibble', 'Blarg' for key1 and values 'A', 'B', 'C' for key2 then I might have a few rows that looked a bit like:
Key1 Key2 Var1 [. . .]
--------- ---------- ---------- ----------
Foo A 10 . . .
Bar A 20 . . .
Foo B 50 . . .
If I wanted to see the total of Var1 for all Key2='A' then the reporting tool would allow me to slice on Key2 and add up all the rows. If I wanted to see the total of Var1 for Key1='Foo' then I could do something similar. In this instance the total of Var1 for Key2 = 'A' would be 30.
If this is the sort of thing you want to do the for data then a dimensional model could help, and would allow you to put up a statistical reporting facility with an off-the-shelf reporting tool such as Report Builder.
A dimension table for Key1 might look like
Key1 Key1Desc Key1Grouping
------- ------------------------ -------------
Foo Description of 'Foo' Group A
Bar Description of 'Bar' Group A
Wibble Description of 'Wibble' Group A
Blarg Description of 'Blarg' Group B
By joining this dimension table to the fact table you can then roll up by Key1Grouping and see stats for (say) 'Group A.' You can calculate ratios of Vars after the base additive measures have been aggregated.
Again - I'm still a bit unsure of quite what you want to know.
Best Answer
I would model this by storing both the date value and the SK back to the date dimension. Here is why storing that actual state value allows you to have ms level precision and can be useful when someone wants to see exactly when something happened. however for aggregates the SK can be a computed column if you are worried about the two values going out of sync
Repeat the pattern as needed for other dates.