# August 2017: Regression between reputation rank and log reputation

Coming out of mini-hibernation, I thought it might be fun to do this little regression again. The original can be found here.

I used the top 400 users to do these regressions. (Still profiles above 101 points.) If you would like a copy of the dataset, just look here.

I also recorded additional stats for the top 108 users: reach, the approximate number of people reached, and member_months which is the amount of time the user has had a profile in months; both of these stats can be found on the user profiles. I did not use any of these extra variables for my regressions below.

. regress rank reputation

Source |       SS           df       MS      Number of obs   =       400
-------------+----------------------------------   F(1, 398)       =     93.00
Model |  1010207.04         1  1010207.04   Prob > F        =    0.0000
Residual |  4323092.96       398  10862.0426   R-squared       =    0.1894
Total |     5333300       399  13366.6667   Root MSE        =    104.22

------------------------------------------------------------------------------
rank |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
reputation |  -.0336321   .0034874    -9.64   0.000    -.0404882    -.026776
_cons |   221.1348   5.633239    39.26   0.000     210.0602    232.2094
------------------------------------------------------------------------------


The regression is still trash without the log transformation.

. regress rank ln_reputation

Source |       SS           df       MS      Number of obs   =       400
-------------+----------------------------------   F(1, 398)       =   1327.50
Model |  4103132.34         1  4103132.34   Prob > F        =    0.0000
Residual |  1230167.66       398  3090.87351   R-squared       =    0.7693
Total |     5333300       399  13366.6667   Root MSE        =    55.596

-------------------------------------------------------------------------------
rank |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
ln_reputation |  -114.0159   3.129309   -36.43   0.000     -120.168   -107.8639
_cons |   858.4509   18.27098    46.98   0.000     822.5312    894.3706
-------------------------------------------------------------------------------


$R^2 = 0.77$ is really good.

. regress rank ln_reputation in 15/200

Source |       SS           df       MS      Number of obs   =       186
-------------+----------------------------------   F(1, 184)       =   2729.31
Model |  502355.538         1  502355.538   Prob > F        =    0.0000
Residual |  33866.9618       184  184.059575   R-squared       =    0.9368
Total |    536222.5       185      2898.5   Root MSE        =    13.567

-------------------------------------------------------------------------------
rank |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
ln_reputation |  -81.27982   1.555809   -52.24   0.000    -84.34934    -78.2103
_cons |   614.4555    9.75469    62.99   0.000       595.21    633.7009
-------------------------------------------------------------------------------


Removing the cluster of low rank profiles (bottom 200) at the end and outliers (top 15) at the top still improves the results. $R^2 = 0.94$

The regressions with log reputation were both improved since the last time I did this mini study. Notably, without removing the 215 users from the regression, it is still very good and a sizable improvement from last time I ran it $(R^2 = 0.77 > 0.67)$. So this tells me that as more time passes, we get a more stable picture of how users flesh out over time, and whaddya know, they better fit the predicted pattern.

The coefficients from the older study to this one...pretty much stay the same. More points aren't any more or less likely to raise your rank than they were one and a half years ago. I guess that is not surprising since all the incentives have stayed the same. Even if we have more people to dole out points, they are being doled out amongst more people. So I guess our community has a pretty boring culture. :P

I guess I will end by asking, "Do you have any statistical ho-hums you'd like to see for our site, and additionally, any suggestions for making this model more interesting/elucidating for our community?"

• Nice stuff. One question though. What is the research question? (haha joking) Commented Aug 20, 2017 at 7:57