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?