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I have recorded on a continuous scale (between 0 and 15) the strategy some players used in a video game and their associate payoff (also interval-ratio) in this game, so I have lots of couples of values like (2.34,12), etc.

I would now like to have an idea of what strategy brings the highest payoff in the game, or what would be the expected payoff for each strategy. It is difficult to see a clear relationship between strategy and payoff on a visual inspection. A 2D scatter plot gives this:

enter image description here

but there are lots of points stacked up on this plot. A 3D histogram gives a better idea of the distribution:

enter image description here

So I tried to do a loess regression on this data. Here is the smooth curve computed by loess:

enter image description here

but the R² of this regression is very low, 0.09.

Do you see a regression that would be best suited for this kind of data or should I stick with Loess regression?

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  • $\begingroup$ This sounds like a game theory problem. $\endgroup$
    – JenSCDC
    Sep 21, 2014 at 17:48
  • $\begingroup$ I imagine there are more variables involved than strategy that affect the payoff. $\endgroup$
    – Glen_b
    Sep 22, 2014 at 1:28
  • $\begingroup$ @Glen_b For now I only have the strategy as variable $\endgroup$
    – Sulli
    Sep 22, 2014 at 13:44

1 Answer 1

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Since strategy is continuous, you might start by considering a smooth regression relationship between payoff and strategy, perhaps something like a loess curve.

However, you might wish to consider whether leaving out an important predictor could mislead you. Firstly, it can make relationships much noisier than they would otherwise be, and secondly, it can bias your estimates of the relationships with the variables you do have, even changing their sign

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  • $\begingroup$ I've edited my post with data distribution and results from Loess regression. Do you still think it's the most adapted regression? $\endgroup$
    – Sulli
    Sep 23, 2014 at 10:22
  • $\begingroup$ Now I see your data, a single curve - of any kind - is not remotely suitable; there's a clear suggestion of an important, missing variable, making the marginal relationship uninterpretable. What do you mean "most adapted regression"? $\endgroup$
    – Glen_b
    Sep 23, 2014 at 10:53
  • $\begingroup$ I mean either try to fit the data to a predefined non-linear function, or use another type of smoothing like smoothing spline? Also, I have no idea as to what "span" smoothness parameter use for my loess smoothing. thanks $\endgroup$
    – Sulli
    Sep 23, 2014 at 11:01
  • $\begingroup$ Actually there is no missing variable in this specific dataset. It's just that if players play strategy "6" for example, they have half a chance to win 9, and half a chance to win 0. that's how I got this kind of distribution. Now is it possible to have an idea from this data what strategy brings the highest payoff on average? $\endgroup$
    – Sulli
    Sep 23, 2014 at 11:20
  • $\begingroup$ Yes so to make it more clear I'm not trying to get the best fit, I just want to have an idea from my data of what strategy brings the highest payoff on average. $\endgroup$
    – Sulli
    Sep 23, 2014 at 11:47

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