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I am wondering if I can estimate a regression, if the dependent variable y has duplicates, whereas all the independent variables (more than 15) are continuous and do not have any duplicates.

In other words, it is possible to have multiple x observations for a single y observation.

I have a lot of data and typically, x does not vary a lot around y, so I expect the model to be good.

However, I still wonder if from a statistical perspective such a setup is ok, or if there is any bias. Any recommendations and tips are welcome.

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  • $\begingroup$ To be clear, you have a vector y which looks like ${1,2,3,1,4,2,4}$ or something? and associated vectors X which are continuous? $\endgroup$ Mar 7, 2019 at 20:34
  • $\begingroup$ @user5957401 principally yes, but y is not categorial/ just in integers. It is continuous, but with duplicates. Something like 12.31,15.87,15.87,12.31,14.99,19.98, 20.23... $\endgroup$
    – Talik3233
    Mar 7, 2019 at 20:36
  • $\begingroup$ Edit: sorry I believe continuous is the wrong word in stats. What I mean is in decimals. $\endgroup$
    – Talik3233
    Mar 7, 2019 at 20:44
  • $\begingroup$ Consider if a logistic regression could be interesting, where you model each y as it's own class. You will get better advice if you provide a frequency count for each y and plot of y and x. $\endgroup$ Mar 7, 2019 at 20:47
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    $\begingroup$ In general, having Y values that are the same for different observations isn't a huge problem. However, it may indicate that the underlying model should be something other than the standard linear model. You may want to consider logistic or poisson regressions. $\endgroup$ Mar 7, 2019 at 20:53

1 Answer 1

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First, you don't have multiple x observations for a single y observation, as far as I can tell. You have observations of x and y, where some y are duplicated. E.g. something like this:

x     y  
1    31.02
2    27.25
1.5  31.02
1.9  27.25

Second, I would be curious as to what led to this. What is y? Why does it get this sort of duplication? Is this due to some kind of rounding? Is it data entry error (which happens a LOT more than people think it does?) Or what? It isn't necessarily wrong, it's just that when I see something odd I get suspicious.

Third, to answer your question, there is no assumption, in OLS regression, that the dependent variable has to be different for each observation.

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