Linear and non-linear regression model fitting of testicular three-dimensional growth in Miranda donkeys

Figures & data

Figure 1. Sample distribution. P25: value at 25% of observations; P50: value at 50% of observations and P75: value at 75% of observations.

Table 1. Models and model syntax.

Model	Initials	Model syntax/equation
Linear	LIN	Y = b0 + (b1 * t)
Logarithmic	LOG	Y = b0 + (b1 * ln(t)
Inverse	INV	Y = b0 + (b1 / t)
Quadratic	QUA	Y = b0 + (b1 * t) + (b2 * t**2)
Cubic	CUB	Y = b0 + (b1 * t) + (b2 * t**2) + (b3 * t**3)
Power	POW	Y = b0 * (t**b1) or ln(Y) = ln(b0) + (b1 * ln(t))
Compound	COM	Y = b0 * (b1**t) or ln(Y) = ln(b0) + (ln(b1) * t)
S-curve	SCRV	Y = e**(b0 + (b1/t)) or ln(Y) = b0 + (b1/t)
Logistic	LGI	Y = 1 / (1/u + (b0 * (b1**t))) or ln(1/y-1/u) = ln (b0) + (ln(b1) * t)
Growth	GRO	Y = e**(b0 + (b1 * t)) or ln(Y) = b0 + (b1 * t)
Exponential	EXP	Y = b0 * (e**(b1 * t)) or ln(Y) = ln(b0) + (b1 * t)

t represents time expressed in month units. Accessed from IBM Corp (2015)

Table 2. Summary of the results for determination coefficients, curve shape parameters, and peak for best fitting models for all the variables in the study.

Variable	Units	Model	R Square	F	df1	df2	Sig.	Intercept	a	b	c	R/Peak
Body Weight	Kg	S Curve	0.862	1340.95	1	215	0.000	5.707	–6.21			0.8250
Left Testicle Length	cm	Cubic	0.871	478.08	3	213	0.000	1.353	0.20	–0.001	0.000	9.4211
Right Testicle Length	cm	Cubic	0.922	838.74	3	213	0.000	1.261	0.20	–0.001	0.000	9.9544
Left Testicle Height	cm	Cubic	0.883	534.21	3	213	0.000	0.744	0.12	–0.001	0.000	5.9164
Right Testicle Height	cm	Cubic	0.825	333.91	3	213	0.000	1.034	0.09	–0.001	0.000	5.4259
Left Testicle Width	cm	Cubic	0.901	647.43	3	213	0.000	0.771	0.16	–0.001	0.000	6.9044
Right Testicle Width	cm	Cubic	0.894	600.67	3	213	0.000	0.741	0.17	–0.001	0.000	7.5141
Left Testicle Volume	cm^3	Cubic	0.817	307.153	3	206	0.00	–29.673	4.394	–0.026	0.000	192.6565
Right Testicle Volume	cm^3	Cubic	0.833	341.326	3.000	206.000	0.000	–24.232	3.761	–0.021	0.000	169.5926
Total Testicle Volume	cm^3	Cubic	0.830	334.944	3.000	206.000	0.000	–53.956	8.156	–0.047	0.000	362.2239
GSI	cm^3/Kg	Cubic	0.795	265.435	3.000	206.000	0.000	–0.160	0.031	0.000	0.000	1.3963

GSI- gonadosomatic index

Table 3. Summary of the measures for model fitness and flexibility criteria of the best fitting linear or nonlinear regression models for each particular trait.

Traits	SS	df	MS	F	Sig.	RSS	MSPE	MMSE	AIC	AICc	BIC
Body Weight in Kg	33.49	1.00	33.49	1340.95	0.00	5.37	0.03	0.00	–800.70	–800.70	–174180.10
Left Testicle Length in cm	1591.74	3.00	530.58	478.08	0.00	236.39	1.11	0.02	20.57	20.57	4035.32
Right Testicle Length in cm	1653.86	3.00	551.29	838.74	0.00	140.00	0.66	0.00	–93.10	–93.10	–20631.61
Left Testicle Height in cm	624.08	3.00	208.03	534.21	0.00	82.95	0.39	0.00	–206.69	–206.69	–45281.04
Right Testicle Height in cm	503.77	3.00	167.92	333.91	0.00	107.12	0.50	0.00	–151.19	–151.19	–33237.87
Left Testicle Width in cm	1022.12	3.00	340.71	647.43	0.00	112.09	0.53	0.00	–141.35	–141.35	–31101.39
Right Testicle Width in cm	978.36	3.00	326.12	600.67	0.00	115.64	0.54	0.00	–134.58	–134.58	–29631.53
Left Testicle Volume in cm^3	1020889.37	3.00	340296.46	307.15	0.00	228228.37	1107.91	0.00	1470.11	1470.11	308308.20
Right Testicle Volume in cm^3	819385.23	3.00	273128.41	341.33	0.00	164840.68	800.20	0.00	1362.00	1362.00	276086.19
Total Testicle Volume in cm^3	3661822.61	3.00	1220607.54	334.94	0.00	750708.15	3644.21	0.00	1669.76	1669.76	338560.58
Ratio Testicular Volume/Body Weight in cm^3/Kg	37.31	3.00	12.44	265.44	0.00	9.65	0.05	0.00	–673.44	–673.44	–146565.19

Table 4. Mean and Standard Deviation for Testicular biometric parameters in juvenile foal and mature Miranda donkeys.

Testicular biometric parameters	Juvenile		Mature
	Mean	Std. Deviation	Mean	Std. Deviation
Left testicle length (cm)	2.78	0.76	8.08	1.12
Right testicle length (cm)	2.76	0.62	8.00	1.28
Left testicle height (cm)	1.71	0.54	4.80	1.01
Right testicle height (cm)	1.71	0.49	4.47	0.72
Left testicle width (cm)	2.03	0.68	6.07	1.14
Right testicle width (cm)	2.10	0.58	6.05	1.25
Left testicle volume (cm^3)	5.92	4.58	132.08	61.16
Right testicle volume (cm^3)	5.89	4.50	120.24	51.88
Total testicular volume (cm^3)	11.75	8.92	252.32	111.50
GSI	0.08	0.05	0.89	0.33

Figure 2. Body weight (BW) modelling using a sigmoid curve function.

Figure 3. Left Testicle Length in cm modelling using a cubic function.

Figure 4. Right Testicle Length in cm modelling using a cubic function.

Figure 5. Left Testicle Height in cm modelling using a cubic function.

Figure 6. Right Testicle Height in cm modelling using a cubic function.

Figure 7. Left Testicle Width in cm modelling using a cubic function.

Figure 8. Right Testicle Width in cm modelling using a cubic function.

Figure 9. Left Testicle Volume in cm³ modelling using a cubic function.

Figure 10. Right Testicle Volume in cm³ modelling using a cubic function.

Figure 11. Total Testicle Volume in cm³ modelling using a cubic function.

Figure 12. Gonadosomatic index (GSI) modelling using a cubic function.

IBM Corp. 2015., Curve estimation models. In: SPSS Statistics 23.0.0. Armonk (NY): IBM Corp.

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Data availability statement

Data will be made available from the corresponding authors F.J.N.G. and A.M.B. upon reasonable request.