I wanted to play around with probability theories and see if I find any statistical inferences from the Powerball lottery history going back to 11/1/1997. What theories could I apply besides simple linear and multiple regression analysis?
I have broken the numbers down based on Wikipedia description of the game with a simple console program.
Studying the statistical properties of the Powerball draws is likely not going to turn up anything interesting. I wouldn't play Powerball, but I would bet on the fact that the numbers are uniformly drawn.
However, there might be something interesting to learn about how people play Powerball. If one knew about how people tend to select numbers, it would be possible to take advantage of this by playing combinations that are less likely to end in a shared prize. The ideal data-set for this would be the actual combinations selected by people.
However, short of this, it would be possible to extract some information about patterns-of-play using the actual draws from the data set you have provided along with any data you can get on number of matches, prizes paid, etc. (tickets sold or at least jackpot size would be useful here as well).