Duc's 2nd Information Analysis - Money and Games

[Cassie 1,226 / 23,060]

So, it's been 2 days, I'd say that's long enough to get results. How many did we get? Well, 15. Not as many as last time. That's okay. I'll admit this topic was considerably less interesting. In fact, there aren't much things I find more interesting than traps.

 

Ahem.

 

More to the point, let's look at the data. 15 individuals responded to the voluntary survey. Two questions were asked: "How many games do you own?" and "What is your average monthly income?". As these are both clear quantitative variables, we can find the correlation between the two using the formula for r, the correlation coefficient. The equation is:

 

 

r will always be a value between -1 and 1. A positive value for r means the two variables have a positive relationship, aka, as one increases, the other increases, and as one decreases, the other decreases. A negative value for r means the two variables have a negative relationship, aka, as one increases, the other decreases, and as one decreases, the other increases. If you ignore the sign on r and look only at the number, you can see how strong the correlation is. Values for r that are closer to 1 indicate a stronger correlation. The closer you get to 0, the weaker the correlation is. Also, in this case, X is the explanatory variable, the variable that causes a change in the other variable, and y is the response variable, the variable that is changed. The X and y with lines over them are the average for x and y, respectively, and the S_x and S_y are the standard deviations for x and y, respectively.

 

Confused yet? Sorry. That's probably too much for most people.

 

tl;dr r is a number that tells you how clustered together the data is and in which way the relationship is. I'll explain it after we get our r (which I'll use excel to calculate because plugging 15 values for x and y into that equation is not fun).

 

For the explanatory (the x) variable, I used average monthly income, and for the response (the y) variable, I used number of owned games. Putting all our values on a scatter plot, this is what it looks like:

 

 

For the time being, we'll assume that the person with an income of 10,000 isn't trolling, as I have no idea if they are or aren't.

 

Anyways, now that we have them on the scatter plot, we want to do 2 things: get a line of best fit (Least Squares Regression Line for you Statistics nerds out there) and get the correlation. The line of best fit has a few formulas for it, but I don't feel like going over them and that would confused more people. tl;dr the line tries to predict y based on x, i.e. in this case it would predict owned games based on average monthly income. So here's the line:

 

 

The equation for the line is y = -0.0055x + 119.03. Let's say we wanted to guess how many games someone who made $1000 per month had. We would plug 1000 in for x to get a predicted value of 113.53 games (114 since you can't have .53 a game unless it was made by Bethesda). Is this value a good prediction?

 

This is where the R² value you see in that graph comes into play. R² is just R... squared. But it tells us the percent of the variation in the response variable (owned games) that can be accounted for by the best fit line. In this case, R² is 1.8%. What this means is that the line is a terrible predictor of the games owned. Why? Because the actual correlation here is very low.

 

If you look at those points, they are spread out a lot. If we take the square root of R², we get r, which is .14 (hah, I avoided using the formula). Also, we know the correlation is negative because the slope of the best fit line is negative, so r is actually -.14. What do we know?

 

We know that the correlation is incredibly weak and negative.

 

AKA, the higher your income, the fewer games you're likely to own, except not really because the correlation between the two is weak. Just look at all those people who get $0 per month and own a few games.

 

Ok, so what did we learn here? Not much. It was cool to see an actual negative correlation, meaning that maybe people are as bad with money as me, seeing as it suggests people with less money buy more games, but the weakness of the correlation makes it moot.

 

Some possible errors within this: well, for starters, the person who makes -$58 for month, unsure if they were a troll, and the one who made $10000 a month, unsure for them to. Maybe y'all are that poor and that rich. Also, the data isn't all that linear, so correlation may not be that appropriate here, and more importantly, the data consists of a lot of people who make $0 per month, which I guess I should've expected. It means that it's basically all over the place, and so there really isn't much correlation. If we removed Mr. Moneybags making $10k, the correlation would probably disappear entirely.

 

Welp, that was nice. It's difficult to get good data, seeing as I need volunteers (which biases it) and people don't visit here that often. So yeah, the data was probably biased and the findings not very significant, but I don't care, at least I've found other people who buy a bunch of games on very little a month. See ya!

 

I haven't bought any games in months and I've barely played any too. Actually, now I'm buying anime figures, but I guessed that I would get even less data if I asked how many figures people owned. Oh well.

[Joshy 4,364 / 44,940]

The results aren't too surprising.  You did learn something: There's no correlation.  People who make money are just as likely to be gamers as people who make little to nothing  interesting results although too bad you didn't give it more time.  Maybe you'll see more correlation if you start binning it into other categories like age or general area they live in.

 

Bragging about about how much your parents make even if they make a lot is very silly.

 

edit:

 

I thought of something that you could do to improve this study and possibly answer your question.  Maybe a linear correlation is difficult, but you could probably get the probability that someone who has lower or higher income will have a certain number of games.  Make it a matrix and load each cell with a probability instead.

 

 

I would imagine the contour graph would be the most fun and easiest to interpret.  Then you can find hot spots to see if a certain income is more likely to buy games.

 

 

I think you're already seeing a hot spot with $0.  If you could filter it by age you might get less noisy results.

 

I'm picturing something like this, which I just stole from mathworks website.  I think you already have enough information and might be able to use a z-table although I'm not sure I admit my statistics has always been shaky (http://www.z-table.com/) I think I can kind of see the form of Z in your formula for r.

 

Edited October 21, 2020 by Joshy

[SpaZBoT 9 / 569]

If your a true gamer....like most here that are members of GFL....which is why I joined RE....TF2 servers just had best bunch of players ...high skill level....not spamming / flaming / cheat-botting /hacking whateva, which does my headin,  because they just love online multi enough to want to play whatever it is they play CS, TF2, etc I like them all but nothing beats a fragg on a GFL 2fort after a stressful day in IT land..... :)))

Oh yeah right my original point.....i dont think there would be a correlation anyways coz gamers here are not gaming for Status or Whos making the big dollars etc they end up finding a particular game that rocks there world so i guess a true gamers probably got know spare free time to purchase new games despite " maybe " having the income".....:)

But I do appreciate the answer and the figures and graphs, thoughts  and the trippy awesome chart above LoL :)) nice work .....flashbaks