# How can model be significant if no predictors are significant?

Here is my model and output:

plants_lm <- lm(weight ~ group, data = plants)

summary(plants_lm)

Call:
lm(formula = weight ~ group, data = plants)

Residuals:
Min      1Q  Median      3Q     Max
-1.0710 -0.4180 -0.0060  0.2627  1.3690

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)        5.0320     0.1971  25.527   <2e-16 ***
groupFertlizer_A  -0.3710     0.2788  -1.331   0.1944
groupFertlizer_B   0.4940     0.2788   1.772   0.0877 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6234 on 27 degrees of freedom
Multiple R-squared:  0.2641,    Adjusted R-squared:  0.2096
F-statistic: 4.846 on 2 and 27 DF,  p-value: 0.01591


I don't understand how the predictors (levels of "group") are both insignificant, yet the model is somehow significant. I found this post: Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?

But none of this seems to apply here. The answers on that post say it can happen if the predictors are correlated (in my case they can't be, they are separate treatments) or if two or more predictors are close to significant. That doesn't seem to be the case here as Fertilizer A is not close. Or is it? What is "close"? Any insight appreciated.

• Remember what the tests on the individual coefficients are testing as opposed to the overall test. If that does not help try changing the reference category and refit the model. Oct 5 '21 at 14:17
• But my reference is the control. Surely I want that to be the reference? Oct 5 '21 at 14:18
• And can you elaborate on your statement? Sorry, I am a stats beginner and trying to learn R at the same time and it's a bit overwhelming. What is it that the individual coefficients are testing compared to the overall test? If I am trying to determine if Fertilizer A or B have an impact on plant growth rates, which is more important? Oct 5 '21 at 14:19
• Similar questions: stats.stackexchange.com/questions/155459/…, stats.stackexchange.com/questions/94441/… (see answer by @gung:), stats.stackexchange.com/questions/549815/… and many more ... Nov 11 '21 at 11:57
• To the original question, lots of small "insignificant" effects can add up to a bigger effect. Nov 11 '21 at 12:49