# question on GAM p-value in summary output

mod_gam1 <- gam(Overall ~ s(Income, bs="cr"), data=d)
summary(mod_gam1)
##
## Family: gaussian
##
## Formula:
## Overall ~ s(Income, bs = "cr")

## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Income) 6.9 7.74 16.4 2e-14 ***


It significant p-value<0.05 mean that smooth component use for income was correct or that independent variable income had significant effect on overall?

I'm new to GAM. I read several comment, paper and lecture not on it but i'm still confuse.

It means that given the smoothing function that was applied, there is a significant association between $$income$$ and $$Overall$$. There is no way to judge from the output whether the specific spline you chose via bs="cr" is "correct". This rather depends on which type of model works best for your goal and application.
You can check the spline that was fit via plot(model_gam1) and employ some critical reasoning whether this makes sence. If the only "problem" with $$income$$ is that it is right-skewed, which is quite usual, a simple log-transformation might be sufficient, which avoids some interpretability issues of GAMs.