Lotteries vary on the amount of sales money they devote to jackpots. In the Powerball and Megamillions cases, 32.7% and 31.7% of sales are devoted to the cash value of the jackpot: This is the money used to buy the annuity value for each drawing. If the lottery rolls over, that money, of course is placed in the next 1st prize pool. Thus if you compare the two cash values with a projected Megamillions jackpot and multiply it by 0.317% you will have the lottery's estimate of ticket sales. They in turn make these estimates based on the history of sales (which of course they know) and other data they have collected.
Note that the annuity jackpot depends on interest rates, which vary considerably. Thus the annuity value is NOT the most consistent way to estimate sales.
If you graph jackpot jump sizes vs the number of rollovers, you will see a curve that visually suggests an exponential curve, particularly, if you go out towards higher numbers of rollovers. I am sure that the lottery uses pretty sophisticated curve fitting procedures in their estimations, and this is where they come from. They are not "linear regressions" necessarily, but they probably use the same type of minimization techniques in predicting the upcoming jackpot. Usually they are pretty accurate, as you can see from the powerball prize listings on their website, where they report the ultimate prize value to the nearest $100,000 for historical prizes. (There is generally a lag of a few weeks while they collect the data). They were inaccurate in the recent MegaMillions only because they were in territory with which they were not familiar: The MM game had never been this large, nor had the population base (now including Texas and other states) been this large. Thus they started their estimate out small $217 million and actually produced a jackpot of $239 million.
Over many years of reviewing data, keeping notes on published data, seeking out data, etc relating to sales vs. jackpots, I have come up with a procedure that I think is pretty painless and easy to use for estimating sales. After each drawing, the lotteries post on their websites the number of winners. I take these numbers of winners and divide them by the probability of winning a prize overall. Thus if, for a particular jackpot, there has been 839,469 winners I divide this by 1/36.06, since your odds are 1 in 36.06 that you will winsome lottery prize from $2 to millions of dollars on each ticket. In the present case I see that based on this probability, I can estimate $31,271,000 represented the sales for that particular drawing. (The drawing in this example was the one from last Oct 18's Powerball.)
I have checked this approach against other measures including announced figures, the published financial reports of lotteries, etc, etc, and I believe that the averages so derived give excellent agreement, although the standard deviation is high, owing to understandable local fluctuations. My cash value calculations converge very closely to the lottery's published values. Since I have confidence in this approach, I use it almost exclusively these days, averaging data over extended periods to avoid eras derived from a particularly popular set of numbers that may from time to time come up. To correct for systematic variances, I typically use a running average of 25 drawings to generate sales estimates for the numbers I post here. I would think that my estimates are probably within a few percent of the true situation, as the announcement by the head of MM confirmed in the last big drawing. (A comment on this is earlier in this thread.)
I hope you find this useful KyngeRichard.
Good luck!