Table 3 Parametric coefficients of the GAM model for dependent variables and approximate significance of smooth terms.

Parametric coefficients	VO₂max		Handgrip_strength		Vertical_jump		Fat_mass		Muscle_mass		MFR		HBMI
Parametric coefficients	Estimate	Std Error	Estimate	Std Error	Estimate	Std Error	Estimate	Std Error	Estimate	Std Error	Estimate	Std Error	Estimate	Std Error
(Intercept)	48.43**	1.05	7.47**	1.16	6.34**	1.35	35.40**	1.22	60.94**	1.15	0.84**	0.16	0.42**	0.06
general_sport (individual modality)	0.80	0.67	0.79	0.71	0.28	0.73	− 0.13	0.54	0.17	0.52	0.03	0.08	0.05	0.03
general_sport (invasion modality)	0.95**	0.28	− 0.06	0.30	0.09	0.31	− 0.24	0.23	0.24	0.22	0.05	0.03	− 0.01	0.01
general_sport (combat modality)	− 1.31*	0.55	0.17	0.58	0.50	0.60	− 0.41	0.45	0.37	0.43	0.09	0.07	0.00	0.03
skill_sport (closed modality)	− 0.20	0.66	− 0.50	0.70	− 0.40	0.72	0.19	0.54	− 0.17	0.51	0.01	0.08	− 0.04	0.03
Sex	− 2.76**	0.24	− 1.55**	0.26	− 1.59**	0.26	3.60**	0.20	− 3.25**	0.19	− 0.32**	0.03	− 0.08**	0.01
Age	− 0.58**	0.11	0.98**	0.11	1.35**	0.12	− 0.69**	0.09	0.66**	0.08	0.05**	0.01	0.05**	0.01
age_group (10–13)	2.42**	0.64	1.61**	0.57	1.31	0.89	− 4.26**	1.00	4.11**	0.94	0.05	0.12	0.07*	0.04
age_group (14–17)	0.85	1.27	0.17	1.19	1.11	1.83	− 3.20*	1.47	3.13*	1.40	0.19	0.16	− 0.04	0.09
hours_per_week	0.25**	0.04	− 0.01	0.04	0.16**	0.05	− 0.08*	0.03	0.08*	0.03	− 0.01	0.01	− 0.01	− 0.01
years_of_practice	0.26**	0.04	0.06	0.04	0.11**	0.04	− 0.04	0.03	0.04	0.03	0.01*	− 0.01	− 0.01	− 0.01
kidmed	0.10**	0.04	0.07	0.04	− 0.03	0.04	0.02	0.03	− 0.02	0.03	− 0.01	− 0.01	− 0.01*	− 0.01

Aproximate significance of smooth terms	F	edf	F	edf	F	edf	F	edf	F	edf	F	edf	F	edf
s(weight):age(6–9)	1.63**	0.97	1.55**	1.61	7.41**	1.00	39.48**	3.86	38.86**	3.80	6.18**	2.43	0.01	0.15
s(weight):age(10–13)	0.09	0.99	1.48**	1.58	0.58**	2.28	5.96**	4.95	5.92**	4.95	8.36**	0.99	0.54**	2.53
s(weight):age(14–17)	1.5**	3.86	1.00**	0.97	1.10**	3.07	0.26	1.94	0.28	2.01	0.11	0.92	0.82**	3.41
s(height):age(6–9)	2.01**	2.15	0.61**	0.88	4.45**	2.21	17.37**	4.70	17.49**	4.68	3.24**	2.39	4.34**	1.79
s(height):age(10–13)	1.94**	3.39	1.31**	3.38	3.05**	2.22	7.13**	0.99	7.36**	0.99	10.22**	2.25	1.96**	3.27
s(height):age(14–17)	1.00**	2.79	6.68**	5.88	0.89**	1.69	2.63**	2.98	2.74**	3.01	1.77**	2.74	9.00**	5.73
s(bmi):age(6–9)	0.47**	1.75	− 0.01	− 0.01	− 0.01	− 0.01	0.15	1.52	0.14	1.48	0.06	0.68	5.86**	0.99
s(bmi):age(10–13)	14.54**	3.80	1.49**	4.10	6.15**	3.77	3.86**	4.64	3.88**	4.68	1.61**	2.49	2.94**	2.54
s(bmi):age(14–17)	2.75**	5.77	1.04**	2.68	1.65**	6.00	18.37**	3.07	17.35**	3.14	8.32**	3.53	1.10**	3.23

VO₂max maximal oxygen uptake, MFR Muscle-fat-ratio, HBMI handgrip strength to body mass index, Estimate regression coefficients, Std Error Standard Error, F statistic; *Significant differences (p < 0.05); **Significant differences (p < 0.01), edf Effective degrees of freedom. The reference intercept of the general_sport group corresponds to the court/net modality, while the intercept of the skill_sport corresponds to the opened modality. The intercept of the sex corresponds to the girls group, and the intercept of the age corresponds to the 6–9 group. Regarding the hour_per_week, years_of_practice, and kidmed groups, the intercept is set at 0.

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