Ask a calvinist: What about Acts 16:31?

I've been trying to write about faith preceding regeneration, and have been trying to collect, from multiple sources, other possible meanings of the verse "Believe on the Lord Jesus Christ and you will be saved. If "saved" includes regeneration, which seems apparent from other Scriptures, then the verse reads "Believe on the Lord Jesus Christ and you will be [regenerated]" Many people don't believe this, and so I have been trying to understand how they interpret that verse. As of this moment, I have not gotten very far with this.

Here is my most recent frustrating interchange on the topic:

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I posted this on a overwhelmingly Calvinistic discussion site:

Does Faith Precede Regeneration?

I know that reformed theologians will say that it does. I have heard many reasons given, including, of course, the logic that because man is dead in sin, he cannot have faith until he is regenerated.

My question is this:

Acts 16:31
So they said, “Believe on the Lord Jesus Christ, and you will be saved, you and your household.”

This verse, some will say, clearly states that faith precedes salvation, and that salvation includes justification, regeneration, sanctification, and finally glorification. Hence, faith biblically precedes salvation.

What do the respected reformed theologians say about this? (IE Calvin, Spoul, Spurgeon, Piper)
What do you think about this?

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Response by X 40 minutes ago

If you believe on the Lord Jesus Christ you will be saved.

The (Calvinist) Doctrines of Grace teach that exact thing.
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Reply by Me 31 minutes ago

Yes, but supposing that regeneration is part of salvation,
If you believe on the Lord Jesus Christ you WILL be regenerated.

"Will" implies it being in the future... after faith...
Does faith, then, logically precede regeneration?

Or does "salvation" not include regeneration?
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Response by X 23 minutes ago

This has already been explained. You hear, the Spirit quickens you and you are given faith (faith is a gift and not from yourself Ephesians 2:8,9). Simultaneously in time, but there is a logical sequence.
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Reply by Me 18 minutes ago

I still don't understand your interpretation of that particular verse.

Of course reformed theologians believe that you are regenerated, and then you are given faith - at the same time, but that regeneration logically precedes faith.

I realize that. However, I am trying to respond to those who put forward that particular verse, in which faith logically precedes salvation.

Is regeneration, then, separate from salvation?
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Response by X 12 minutes ago

My interpretation is what the verse says. If you believe on the Lord Jesus Christ, you will be saved. It seems what is confusing you about it is that you are reading your theological baggage into a very straight-forward verse.
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Response by Y 8 minutes ago

Does faith precede regeneration?
Yes
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Reply by Me 1 minute ago

Rev - How do Calvinists interpret this verse? I just don't get it

Xulon - You claim that this "has already been explained" - Where?
If your interpretation is all so straight-forward, then why have you not answered my clarifying questions?
IE Is regeneration, then, separate from salvation?
Does faith, then, logically precede regeneration?
Or does "salvation" not include regeneration?