I am currently working on a multiple linear regression in order to evaluate the impact of some variables on a contract's length, which can only take integer values (years). As I am only interested in which variables have a significative effect on the length and in the difference in magnitude between the two, but not really on the value itself (basically on the qualitative effect), is it ok to interpret the predictor as a continuous variable despite the fact that it is discrete? It obviously changes the R-squared interpretation, but other than that, is there any major difference in interpretation if I use a OLS or a quantile regression? And what if the duration is bounded?

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    $\begingroup$ OLS regression predicts the conditional mean of the dependent variable, while quantile regression predicts the conditional median. However, it seems that is your dependent variable (the number of years) which can only takes integer values, rather than your predictors? In this case, why not using a model suited for discrete count variables such as a Poisson regression? $\endgroup$ – matteo Dec 3 '16 at 16:19
  • $\begingroup$ Hi, thanks for your answer. The problem is that it is part of a project in an introduction class in which we have not seen Poisson regression. Would using a quantile regression flaw that much the interpretation if I'm only interested in seeing which variables have an impact on the regressor? $\endgroup$ – allo Dec 3 '16 at 16:43
  • $\begingroup$ Also, the model is not stochastic, the number of years in the contract is negotiated and I'm evaluating the effect of some characteristics of the bargainers. Not sure if Poisson processes assume a Poisson distribution. The number of years is more of an outcome than a counting process. $\endgroup$ – allo Dec 3 '16 at 16:48
  • $\begingroup$ You should fix your question, there must be some errors in terminology. Number of years length of contract cannot be the result of some poisson process, so poisson regression and the like are irrelevant here. Probably you should just ignore that the variable only can take integer values! See stats.stackexchange.com/questions/249290/… $\endgroup$ – kjetil b halvorsen Dec 3 '16 at 16:53
  • $\begingroup$ You mean that I should just run my regressions as if the variable was continuous to see which indep variable has a significative impact? Is there any changes to be made in interpretation? By countable in the question, I meant that the values had numerical interpretation, not that it was obtained from a counting process. I have edited it. $\endgroup$ – allo Dec 3 '16 at 17:47

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