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I ran a regression and the intercept is statistically insignificant (the p-value is greater than 0.05). I tried to look in some textbooks as to how to handle this scenario but I am still unsure. One textbook I looked at 'Basic Econometrics'by Gujarati and Porter says that if the intercept is insignificant then we have a regression through the origin and that if we remove the intercept, in this case, the model will be more precise. On the other hand, 'Introductory Econometrics'by Chris Brooks says that even if the intercept is insignificant, we should not remove it from the model.

Which one of these textbooks is correct? Should I leave the insignificant intercept in the model or run a regression through the origin?

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    $\begingroup$ It bears mentioning that failure to detect a nonzero intercept is not the same thing as inferring that the intercept is actually zero. $\endgroup$ – heropup Nov 26 '18 at 7:32
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    $\begingroup$ Why do you think this is a problem? $\endgroup$ – kjetil b halvorsen Nov 26 '18 at 9:16
  • $\begingroup$ I don't think its a problem sorry. I re edited the question. Rather its a scenario I haven't encountered before. $\endgroup$ – user198848 Nov 27 '18 at 0:19
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If the true data generating process implies that Y=0 whenever X=0, then exclude the intercept, otherwise keep the intercept, even it is not significant. One example of this: response variable (Y) is distance the can run, and the covariate (X) is volume of gasoline consumed by the car. When X = 0, Y = 0.

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  • $\begingroup$ There are many reasons not to follow this advice. See stats.stackexchange.com/questions/102709/… $\endgroup$ – kjetil b halvorsen Nov 26 '18 at 9:16
  • $\begingroup$ Thanks for the link. I read and saw that it was pointed out that the insignificance of the intercept is not enough to remove it from the model. So is it that we remove the intercept only when we have strong theoretical reason to believe that when x=0, y must also equal 0? $\endgroup$ – user198848 Nov 27 '18 at 0:26

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