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Can I conclude I have outliers when no coefficients are significant but f-test is significant in the linear regression?

 Call:
 lm(formula = co[, 12] ~ co[, 2] + co[, 3] + co[, 5] + 
     co[, 7] + co[, 8] + co[, 9] + co[, 11] + co[, 2] * 
     co[, 11])

 Residuals:
     Min      1Q  Median      3Q     Max 
 -5.0542 -1.6286 -0.2886  1.1572 24.6327 

 Coefficients:
                        Estimate Std. Error t value Pr(>|t|)
 (Intercept)           3.7720074  9.0737734   0.416    0.679
 co[, 2]            -0.3272521  0.3601090  -0.909    0.366
 co[, 3]            -0.1776742  0.8922504  -0.199    0.843
 co[, 5]            -0.0507871  0.2318475  -0.219    0.827
 co[, 7]            -0.0415144  0.0633719  -0.655    0.514
 co[, 8]            -0.0001058  0.0005771  -0.183    0.855
 co[, 9]            -1.0555060  7.6677272  -0.138    0.891
 co[, 11]           -0.4332281  1.4533123  -0.298    0.766
 co[, 2]:co[, 11]  0.1683719  0.1859764   0.905    0.368

 Residual standard error: 3.74 on 92 degrees of freedom
 Multiple R-squared:  0.1731,    Adjusted R-squared:  0.1011 
 F-statistic: 2.407 on 8 and 92 DF,  p-value: 0.02095

Then the VIF test to check multicolinearity shows below:

            co[, 2]            co[, 3]            co[, 5] 
           131.188424             1.264675             1.684113 
            co[, 7]            co[, 8]            co[, 9] 
             1.638692             1.356281             1.145669 
           co[, 11]            co[, 2]:co[, 11] 
            49.944243           180.188574 
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  • $\begingroup$ I think this could happen if you have a highly significant constant term but no relationship with any of the predictor variables. $\endgroup$ – Michael R. Chernick May 5 '17 at 23:58
  • $\begingroup$ Actually not even the constant term is significant $\endgroup$ – Eric May 5 '17 at 23:59
  • $\begingroup$ Can you show me an example with a significant F value and no significant relationship between the dependent variable and the regressors? $\endgroup$ – Michael R. Chernick May 6 '17 at 0:03
  • $\begingroup$ Please check above now. $\endgroup$ – Eric May 6 '17 at 0:06
  • $\begingroup$ I would suspect (multi)collinearity. When the predictor variables have linear relationships with one another, the individual standard errors are inflated, but the overall model fit can still be strong. $\endgroup$ – Matt Tyers May 6 '17 at 0:17