Answer:
Speaker - Abraham Lincoln delivered the speech.
Abraham Lincoln delivered the speech and so was the speaker.
Occasion - Abraham Lincoln gave this speech in 1861, right before he moved to Washington, DC.
The occasion is the time and the place the event happened as well as why it happened, which are included in the above sentence.
Audience - The speech was directed to the people of Illinois.
The audience are those people the event or address was meant for which in this case is the people of Illinois.
Purpose - Lincoln wanted to thank the people of his home state before he moved away.
Why the address was had is what this attempts to explain and in this case that would be President Lincoln thanking his home state.
Subject - Lincoln’s farewell from the state of Illinois was the topic of discussion.
The subject is the topic of discussion in the address and as stated above, it was Lincoln's farewell to Illinois.