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I'm trying to create a prediction model for estimation of continuous variable based on about 35 Independent variables.My data set has circa 27k observartions. Here is the summary of the the targeted continuous variable:

              Frequency Percent
(0,5]              2706  10.053
(5,10]             5226  19.415
(10,25]            4397  16.335
(25,100]           7142  26.533
(100,1e+03]        6465  24.018
(1e+03,1e+05]       981   3.645
Total             26917 100.000

I tried (by using R) Random Forest (RandomForest package),Linear regression, Conditional Inference Trees (ctree function in party package) but all of them have results that have a significant overestimation. Here are the results of the prediction where I counted number of observations by thier distance from the actual values: Any idea how can i balance the results?

enter image description here

Here are some views on the data: The target variable is LTV for a user, I would like to predict LTV value after 180 days based on users behavior of the first 7 days. Here Is a summary fot the target variavle:

  vars     n   mean     sd median trimmed   mad  min      max    range skew kurtosis   se
1    1 26917 178.35 622.29  33.49   66.63 39.28 0.03 22103.73 22103.71 14.1   325.08 3.79

UPDATE: Here are the distributions of the targeted variable (first)and the prediction (secound)results: targeted variable prediction results based on the linear regression model that was the best

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    $\begingroup$ 1. Could you show prediction $\hat y$ over true outcome $y$ plots? 2. Your $y$ covers orders of magnitude. Is there reason to assume that the $y$ should be modeled basically in a linear fashion over such a dynamic range? Or would a transformation like $\log y$ make sense? 3. What is the meaning of your target value ($y$)? $\endgroup$ – cbeleites Jan 14 '15 at 18:01
  • $\begingroup$ Thanks cbeleites, I updated the problem desc.I'm not sure that there is "a reason to assume that the y should be modeled basically in a linear fashion over such a dynamic range" but linear regression gave the best results so far.The log transformation is not helpfull in prediction as long as I don't have an interaction variables.Thanks for your help.. $\endgroup$ – user49422 Jan 15 '15 at 7:59
  • $\begingroup$ OK. So no log: I was asking because you basically present us a log axis here with your binning. With plot prediction over true/reference value I actually meant a scatter plot with $\hat y$ on the ordinate and $y$ as abscissa. $\endgroup$ – cbeleites Jan 15 '15 at 9:33
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    $\begingroup$ Tess us more about your actual problem! Without that we can hardly advance! How did you reach the conclusion about overestimation? Based on a holdout sample? Otherwise? Tell us! $\endgroup$ – kjetil b halvorsen Jan 15 '15 at 12:38
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    $\begingroup$ ok, thank you.. I'll try to figure out how to present the data more clearly. $\endgroup$ – user49422 Jan 15 '15 at 16:22

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