respectively

My advice: don't use this word.

This word can be confusing to many people. Really, it is quite simple. There is only one way to use it correctly. 

In the sentence: 

A and B relate to 1 and 2, respectively. 

A relates to 1. B relates to 2. This means that A does not relate to 1 and 2. A and B do not both relate to 1.


Example:

Increasing greenhouse gas emissions correlate with increasing and decreasing sea levels and polar ice coverage, respectively. 

The currencies of Japan and Russia are the yen and rouble, respectively.

Better still: don't use it!
Example:

Increasing greenhouse gas emissions correlate with increasing sea levels and decreasing polar ice coverage.

The currency of Japan is the yen and the currency of Russia is the rouble.

Origin of the confusion

1) It sounds good and people want to use it but they don't know how. 
2) In some languages a similar word (e.g.  "beziehungsweise" in German) means and/or. "Respectively" cannot be used to mean "and/or" in English.

E.g. 
"I will be late to the party, I should be there at 20:30 or possibly 21:00." 
"Ok, but don't forget to bring beer and/or wine!"