Table 4.

Summary of linear and nonlinear regression equations and Kendall’s tau correlation coefficients (r) for the relationship between each long bone measurement and stature in the upper limb. The p-values for all coefficients were statistically significant, with p < 0.001

Long Bone	Measurement Type	Kendall’s Tau Correlation (r)	Model Type	Equation	Residual Standard Deviation (in cm)	Kolmogorov–Smirnov Test Statistic (D)	Test Accuracy (in %)	Mean Absolute Deviation (MAD)
Humerus	Length	0.905	Linear	$y=0.46x+25.3$	5.56	0.0833	95.8	5.54
			Nonlinear	$y=337-329e^{-0.00214x}$	4.60	0.0476	95.8	3.99
	Proximal Breadth	0.830	Linear	$y=3.97x-3.93$	8.84	0.0544	96.6	8.31
			Nonlinear	$y=\frac{231}{\left(1,+,9.81,e^{-0.0758x}\right)}$	8.27	0.0544	95.9	7.75
	Midshaft Breadth	0.820	Linear	$y=8.22x-6.71$	13.5	0.114	97.2	10.2
			Nonlinear	$y=\frac{211}{\left(1,+,12.2,e^{-0.184x}\right)}$	12.1	0.0909	94.3	9.98
	Distal Breadth	0.854	Linear	$y=2.88x-2.21$	9.02	0.0838	93.9	8.22
			Nonlinear	$y=\frac{198}{\left(1,+,10.6,e^{-0.0716x}\right)}$	7.30	0.0503	95.0	7.03
Radius	Length	0.895	Linear	$y=0.610x+24.4$	6.23	0.0888	98.8	6.14
			Nonlinear	$y=297-295e^{-0.00352x}$	4.77	0.0533	97.0	4.39
	Proximal Breadth	0.826	Linear	$y=8.16x+1.01$	10.5	0.0686	94.9	7.57
			Nonlinear	$y=\frac{196}{\left(1,+,11.6,e^{-0.021x}\right)}$	8.38	0.0629	91.4	7.84
	Midshaft Breadth	0.808	Linear	$y=12.1x-13.3$	13.6	0.0994	94.2	12.3
			Nonlinear	$y=\frac{208}{\left(1,+,13.9,e^{-0.273x}\right)}$	12.5	0.0819	93.0	11.9
	Distal Breadth	0.810	Linear	$y=5.41x+1.37$	11.7	0.100	93.3	9.04
			Nonlinear	-	-	-	-	-
Ulna	Length	0.895	Linear	$y=0.581x+21$	5.64	0.0702	97.7	5.71
			Nonlinear	$y=338-336e^{-0.00268x}$	4.62	0.0585	96.5	3.88
	Midshaft Breadth	0.759	Linear	$y=13.1x-18.3$	17.3	0.124	94.7	15.4
			Nonlinear	$y=\frac{209}{\left(1,+,15.7,e^{-0.295x}\right)}$	16.3	0.101	95.3	15.9
Upper Limb (Humerus + Radius)	Length	0.904	Linear	$y=0.262x+24.8$	5.52	0.0864	99.4	5.52
			Nonlinear	$y=325-319e^{-0.00129x}$	4.44	0.0494	96.9	3.93