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In a football manager game, there are many players as in this screenshot:

football player

My y is the average rating of a player, my sample size N is big enough, and x1,x2,x3,...,x30 are the attributes like finishing, acceleration and pace (which can take values from 1 to 20). No attribute has a negative effect.

Can I use regression or another technique to find parameters such as:

y=f(x1)+f(x2)+...+f(x30)

In other words, after sampling N players, I want to know which attribute has the most effect in average rating, and which the least, and a scale to know how much more important is one attribute compared to the least important one.

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  • $\begingroup$ When you write f(x1), what kind of function f do you have in mind? $\endgroup$ – Silverfish Aug 13 '16 at 19:09
  • $\begingroup$ I have tried giving the text a brief copyedit and improved some of the formatting. Please feel free to revert any of my changes that you disagree with. $\endgroup$ – Silverfish Aug 13 '16 at 19:11
  • $\begingroup$ @Silverfish I would think the most simple form of f(x1) would be a parameter, say a1, f(x1) = a1*x1. And f(x2) = a2*x2. Eventually what I am looking is a way to rank a1, a2,....,a30 and find out the least important a, and see how much the rest scale compared to it. $\endgroup$ – n17n Aug 13 '16 at 19:24
  • $\begingroup$ If every $f$ is a linear function, this is a linear regression problem. $\endgroup$ – Sycorax Aug 13 '16 at 19:41
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    $\begingroup$ You could do non-negative linear least squares, i.e.. linear least squares in which the coefficients being estimated are constrained to be non-negative. Or you could try something other than a linear model. $\endgroup$ – Mark L. Stone Aug 13 '16 at 20:17
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First you should graph the correlation between the average rating and each of the variables separately to get an idea of the data. You also want to check the amount of variation in your Y variable (you don't want too much) and the variation in your X variable (you want a lot).

Next run a linear regression. You said in the comments that the coefficients were negative, but what were the standard errors? I am guessing the variables are correlated so you may suffer from multicollinearity making inference about specific coefficients difficult. Just because the coefficients aren't what you ``want'' at first glance doesn't mean the functional form is wrong.

Next, consider grouping the categories into larger categories and doing tests of joint significance for the larger categories. Or you could try other kinds of functional forms like squaring your variables to bring out more variation.

Also check the R^2 to see if your RHS is getting at most of the variation in Y. If it is low, while the marginal effects may be meaningful, there is much more determining Y than what you are estimating.

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  • $\begingroup$ I don't yet understand what the negative coefficients mean and the multicollinearity is and how to deal with it. I am going to try to increase x variety by squaring x. Finally I strongly suspect that there is much more determining Y than what I am estimating. $\endgroup$ – n17n Aug 13 '16 at 21:18
  • $\begingroup$ @n17n That's why I said you should do some graphs/basic analysis to get an idea of how your variables are varying. If you go straight to regressions before any basic summary statistics, you will likely not understand the output. Mutlicollinearity just means the variables on the right hand side are strongly related. If that is the case then you may want to try running the regression but remove some of them. $\endgroup$ – VCG Aug 13 '16 at 21:24
  • $\begingroup$ Regarding multicollinearity i could just get more data? Because there are some rows, where X is not varying at all. $\endgroup$ – n17n Aug 13 '16 at 21:45
  • $\begingroup$ Multicollinearity is about the relationship between Xs. So if the 2 Xs are measuring a very similar attribute, then they will stay highly correlated even with more observation, but yes, more data will likely lead to more variation, so that should help.Do some summary statistics to see how much variation there is in each X variable. Don't include those that barely have any (or square them). $\endgroup$ – VCG Aug 13 '16 at 21:49
  • $\begingroup$ I did a linear regression giving negative coefficients. the standard error is .137 and the Collinearity VIF is less than 3000 $\endgroup$ – n17n Aug 14 '16 at 2:20

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