This time, I have received 30 months of monthly data from "kowenicki" (thanks!), and the results are quite different this time, although still interesting. The correlations are as follows:

Wii - X360 : -0.55
Wii - PS3 : - 0.63
X360 - PS3 : -0.30

First of all, all the signs are negative as it should be, meaning all systems are competing with each other! In other words, any rise in any system steals from the market shares of the other systems.

Secondly, unlike the previous result, the correlations between X360 and Wii, and between PS3 and Wii are not statistically significant, which means, Wii competes with both consoles more or less the same.

The third point, which is quite interesting, is that the least of the competitions is between PS3 and X360. Their users are apparently exclusive most of the time, from which we can judge that many non-hardcore PS2 users went to Wii, while hardcore ones chose between 360 and PS3, considering their tastes, and competition didn't affect their decision much.

Last but not Least, we can see that the main competition is between the HD consoles and the wii! Those who are interested can take a look at the excel file below :
http://rapidshare.com/files/288962580/console_correlation.xls

Edit:

The site has gone on some updates with the data, which had a slight impact. With the latest data, the correlations are:

Wii - X360 : -0.52
Wii - PS3 : - 0.66
X360 - PS3 : -0.30

The difference is that the negative correlation between Wii & PS3 has increased, while decreasing between Wii & X360, and remaining the same between X360 & PS3. The essence of the analysis that the real competition is between HD consoles and the Wii does not change, however, now that the gap between Wii-PS3 and Wii-X360 correlation is significantly larger, we can say that Wii is in stiffer competition with PS3 than with X360. In other words, Wii is stealing more sales from PS3 than from X360 (in terms of percentages).

For those who are interested the link above is also updated.

- UPDATE (24 Sept. 2009)

Now that PS3 has the new slim model and seen a drop in its price, we would expect the sales of its competitors to fall, right? And the higher competition the more they should fall. Well, when we look at the sales figures of 360 and Wii, we do see a drastic decrease in wii sales but NOT in 360 sales. That again is a proof that the real war is between Wii and the HD consoles, rather than between 360 and PS3 (which doesn't mean there is no competition between 360 and ps3 however).

Wait, there's a war going on? Wow! Wait, I'm going to get my hatchet and everything!

Rofl! - Win!

On Topic: No wai!

On Futher Topic: Gonna grab mah...

The Eidelweiss sucks. You should've used the shamrock lol.

Actually if there is a war, its between the Wii and the PSP, who knows with the PSP GO! Maybe the psp will overtake the Wii!

This thread is actually the continuation to thread :
http://www.vgchartz.com/forum/thread.php?id=80378&page=8

isint that the only war?

Oh, damn, I left my picket sign in my other profile!

I can't decipher the tables, so what is the given correlation when combined Xbox 360 and PS3 sales are taken against the Wii?

Well, there really isn't anything to decipher in the tables. One of them is the table you provided while the other is the market share in percentage for each case.

It doesn't make sense to find the combined correlation of the HD consoles versus wii because the whole market is composed of only 2 products then, and it will naturally be complementary (the increase in one HAS TO decrease the other one), which is demonstrated by a perfect negative correlation (-1). But it doesn't work that way, invalid in that form.