The sentence is too long. Break it into two.
Not only does it provide a visual representation of the data; it also makes analyzing the data easier and more efficient. This is especially true in examining the relationships between certain variables in terms of proportionality.
The problem with putting a semicolon between efficient and especially is twofold:
First, the clause that would follow the semicolon is not independent. "Especially when examining the relationships between certain variables in terms of proportionality." cannot stand on its own.
A semicolon may be used to join related, shorter independent clauses or in the place of commas when you use dependent clauses as the items in a series.
Secondly, this is inappropriate because the sentence is long and confusing. There's nothing inherently better about writing long sentences over writing shorter, more concise ones.