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In a multiple linear regression, what is the reason for the most predictors to be non-significant ($p > 0.05$), but ANOVA shows significances? What could be some of the reasons? Or a calculation error?

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Any help is appreciated. I am trying to explain why majority of the coefficients are not significant, however obtained a significant regression model.

Igor F.
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0211
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    This is a typical symptom of multicollinearity between predictors, have you checked VIFs or the condition number? – Zhanxiong May 13 '23 at 01:47
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    @Zhanxiong: not really here, where the issue is the monthly dummy variables comparing to January. My guess is that this is something whose trend is slowly increasing over 5 years with a substantial December peak each year: that is enough to make the model better than a flat prediction even if there is little to distinguish some other months from January over the noise in the data – Henry May 13 '23 at 04:32
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    @0211 Welcome. Your Time variable is highly significant, which makes the regression highly significant compared to the model with just an intercept, making the regression F highly significant. For some fun, drop all the monthly expanators, rerun the regression and see what happens to R-squared, adjusted R-squared, and the value of F. Then it will be clear. – Graham Bornholt May 13 '23 at 05:11
  • Looks like sales data, with December being the strongest month. As others have pointed out, it seems that during most months the results are more or less the same as in January, but November and December differ significantly (February too, but not so strongly). – Igor F. May 13 '23 at 10:27
  • @Henry That's insightful and probably more pertinent to this problem. Multicollinearity was just my first reaction when I saw significant $F$-test but insignificant $t$-test outcomes. – Zhanxiong May 13 '23 at 19:42

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