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Simple question: I have a dataset, in which all the multivariate x variables (x0, x1, x2, x3..) are continuous, and all the y variables are categorical (distributed (equally) between 1-20 categories). Can this type of data be processed via multiple linear regression?

example:

data = [2.3, 4.5, 0.7, 2.1], [2]
       [3.4, 2.1, 0.7, 1.2], [5]
       [3.1, 1.2, 4.5, 4.1], [4]
       [4.1, 4.4, 3.2, 6.2], [11]
       ...

Thanks. :-)

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  • $\begingroup$ One approach would be to run a logistic regression but with a one-vs-all classification set-up. $\endgroup$
    – Steve S
    Commented Jul 15, 2014 at 8:54

1 Answer 1

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Instead of linear regression, use multinomial logistic regression.

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  • $\begingroup$ Yes sir, that's true. Yes, I can employ the multinomial logit for such data. But my question is, theoretically speaking, the y values are all continuous and independent from x. If I feed such a data to a multilinear regression model, will it be a valid step or not? Moreover, the fit that I will obtain, what do you think about its predictions? $\endgroup$
    – saifuddin778
    Commented Jul 15, 2014 at 15:38
  • $\begingroup$ @khan: If y is independent of x, then what are you doing? You're not going to discover a meaningful relationship. If you use linear regression, then you're essentially considering the order of ys (which is called "1", "2", etc.) to be meaningful, which is already wrong. You also make predictions like 2.5 or predictions that are outside the range of ys, neither of which is meaningful. How will you deal with these cases? I don't understand what you mean by whether such a model is "valid". It is definitely an inferior model. $\endgroup$
    – Neil G
    Commented Jul 15, 2014 at 17:03
  • $\begingroup$ I totally understand your point. I think i got it wrong. Can you please guide me or help me a bit with some numerical examples of multinomial regression, in such a case? At least some steps would be helpful. $\endgroup$
    – saifuddin778
    Commented Jul 15, 2014 at 17:49
  • $\begingroup$ @khan: why don't you read the wikipedia page and then do some research? $\endgroup$
    – Neil G
    Commented Jul 15, 2014 at 18:43

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