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I created a multivariate regression following the scheme $$y = \beta_0 + \sum^n_{i=1}\beta_i*x_i$$ and got an average deviation ofaround 5%.

When I tried the regression without the $\beta_0$ I got a more approximate accuracy now on ca. 3%.

I am creating a model where certain factors (in the 9th grade) have an impact on the students' performance (PISA Questionnaire).

Would it make sense to neglect the $\beta_0$ term? I could imagine it means something like starting performance in the beginning of the year, which is then impacted during the year. If one assumes such a starting point does not make sense, when setting it up as a 'total-school experience factors' meaning the factors have been present over the total in-school time, and thus one could say it does not make sense, to have some performance level before coming to school, as there is no entry performance test...

What do you think?

Nick Cox
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thebilly
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    The term _multivariate_ here is best omitted. It is only helpful if you have multiple responses or outcomes, not the case here. Having several predictors doesn't make a regression multivariate. You could say multiple, but that term is fading away slowly. Having several predictors is not special any more, as it was say in the 1930s or 1950s. – Nick Cox Dec 14 '18 at 09:52
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    It appears that you're missing existing threads on leaving out the intercept. That major point aside, what specific implementation are you using that makes you talk of _average deviation_ (that is necessarily zero, always, in plain regression if deviation means residual and you're using least squares) and what do you mean by _accuracy_ here? – Nick Cox Dec 14 '18 at 09:56
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    $\beta_0$ as a matter of algebra is just what is predicted when **all** your predictors $x$ are 0. You don't say what your predictors are but that doesn't sound like performance at the "beginning of the year", whatever that means. (Please bear in mind that the PISA data mean essentially nothing to most people here.) – Nick Cox Dec 14 '18 at 10:01

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