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I would like to use a linear regression model for prediction. That is, given a value for the dependent variable, I would like to use the coefficients obtained to calculate the predicted independent variable. Now, I have run the regression and obtained a non-zero intercept, but it is insignificant at even a 10%-level. Should I ignore the term? Or leave it in? The beta (that is, the $x$-coefficient) is highly significant.

I am aware of the theoretical meaning of this insignificance - we do not have sufficient information to say that the intercept differs from $0$. But am unsure how to go about predicting values with all this.

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    $\begingroup$ You should include all coefficients when making prediction, just because it is insignificant does not mean it's useless. $\endgroup$ Dec 20, 2021 at 7:25
  • $\begingroup$ Could you elaborate on that? I think I get the intuition, but not 100% sure $\endgroup$
    – Student
    Dec 20, 2021 at 7:46
  • $\begingroup$ If you do expect that the intercept is non zero, then I would suggest subtracting the mean from all your independent variables (which are the ones you use to predict the dependent variable) and then running your regression routine. $\endgroup$
    – seanv507
    Dec 20, 2021 at 7:47
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    $\begingroup$ I have the feeling that this is a prractical question: You seem to be interested in the coefficients in order to state something about the raletionship of $x$ and the target (an increase of one unit in $x$ increases the value of the target by $\beta$). If you want to say anything about that you need to be 'sure' about this relationship i.e. the model. You can run statistical tests but in the end, reality might kick in and you/many people might make varying assumptions (which might or might not hold) and/or misinterpret statistical assertions. So how to be sure? Just split the dataset... $\endgroup$ Dec 20, 2021 at 9:55
  • $\begingroup$ into train and test set, train the model on the training set and let it predict on the test set and compare the actual target vs the prediction (RMSE or MAE or quantiles of errors, whatever you are interested in). Do these metrics "make sense" (i.e. the error is "not too big")? If so, then you have found a good model and you can rely on the parameters. You could also repeat this procedure mutliple times and see whether all the errors are small and the parameters are more or less the same... this is the ultimate proof because this means that the model works in reality. $\endgroup$ Dec 20, 2021 at 9:57

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