data_plot <- qplot(x_test, y_test_obs) + 
  geom_line(aes(y=y_test_fit))+
  theme_bw()
print(data_plot)

linear_model_test <- gam(y_test_obs~x_test)
nested_gam_model_test <- gam(y_test_obs~s(x_test)+x_test)
print(anova(linear_model_test, nested_gam_model_test, test="Chisq"))

summary(nested_gam_model_test)$s.table