Two different statistical tests, each testing different hypotheses, do not have to agree.   The overall test tests the hypothesis (in layman's words) that the model has found a statistically significant effect. In this case, the effect is not significant.   The individual tests looks to see if the coefficient on a single parameter (Serum group 4) is zero, or not. It is different from zero. But we already know the effect of serum group is not significant, in other words the different serum levels are not statistically different from each other. So despite serum group being statistically different than zero, the serums are not different from each other, which is a different hypothesis. No difference between the serums, and no significant intercept; thus model is not significant. ... View more