Are auto manufacturer lease promotions the same as money-factor promotions?

Car manufacturers often run lease promotions in which they quote a lease cost ($X down and $Y/month) for a particular vehicle model. We know that the total cost to lease a car is a function of three variables:

1. Purchase price
2. Residual value
3. Money factor (i.e., interest rate)

I’ve never approached a car dealer with one of those promotions so I can’t tell: Which of those variables, if any, is being promoted by the car manufacturer?

I gather that in general residual value and money factor are essentially fixed by the manufacturer’s leasing arm, so that the only variable that one can negotiate with a dealer is the purchase price. (It is to the buyer’s benefit to know which variable is being subsidized by a manufacturer promotion so that the dealer can’t hide that during negotiation.) So how does a buyer correctly incorporate the manufacturer’s lease promotion into the negotiation? Does the promotion show up as a reduced money factor? Or a credit on the purchase price? Or an elevated residual value?