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say y is non-negative and continuous, I want to do regression on y=beta_0 + beta_1*x

then if I do prediction there would be some negative prediction, which is not valid.

What is the best way to fit the linear relationship between y and x?

(I know one simple way is to do log-transformation before regression, but I did some testing and found that the performance in natural scale is much better than log scale).

Mahali Sindy
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    You told us what $y$ isn't, but it would be more useful to know what it *is*. Could you tell us more? For example, if it is a count, you could use something like Poisson regression, but if it is continuous, the model would not make sense. – Tim Feb 15 '22 at 07:27
  • it is a continuous value – Mahali Sindy Feb 15 '22 at 09:01
  • Could you give us more details? Otherwise you're risking getting an answer that is irrelevant for the problem. – Tim Feb 15 '22 at 09:03
  • Do you really have to bother about negative predictions? If the reltionship is approximately linear, negative predictions will only be made for predictor values that do not occur practically. – cdalitz Feb 15 '22 at 09:58
  • [Gamma GLM?](https://stats.stackexchange.com/q/67547/247274) – Dave Feb 18 '22 at 23:15

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