Considering all parameters included in the model, the parameter showing the highest correlation with body weight was determined as body length according to all sample sizes. As indicated in Table 2, the highest correlation was found in 50 sample sizes (r:0.95). This was followed by sample sizes of 30, 20 and 10, respectively. The highest correlations for the BW parameters between BL were found 0.95, 0.90, 0.83 and 0.81 respectively. In addition, the lowest correlation values are BW between HW (r:0.46), BW between HG (r:0.51) and BW between PW (r:0.48). Considering all sample sizes, body length was included as an independent variable in nonlinear models.
As shown in Table 3, the results of nonlinear models, in which five different models for estimate best-fitted model for relationship between body length and body weight of Morkaraman sheeps at different sample sizes.
R2 and MSE values for models estimated by five different models and sample sizes have been used to determine the best fit models.
Considering the sample sizes; the lowest R2 and the highest Mean Square Error values occurred in the group with sample size 10. According to this group, the highest R2 value (0.64) was determined in Logistic and the lowest MSE value (14.76) was determined in Saturation growth models. Topal and Macit (2004) were reported that in their study on 66 Morkaraman sheep, as a result of multiple regression analysis, the R2 value of body length affecting body weight was 0.282 and MSE value was 31.702 respectively. When we take into the group with a sample size of 20, the highest R2 value (0.71) and the lowest MSE value (13.44) was detected in Saturation growth models. Rather et al. (2021) were emphasized that the coefficient of determination (R2) is succesful to estimate body weight from body measurements in Kashmir Merino sheeps. Considering the sample sizes of 30 and 50, the highest R2 values (0,82-0,92) and the lowest MSE values (11,88-11-94) were found in the Incomplete gamma model, respectively. In Dağlıç and Kıvircik male lambs, Akbaş et al. (1999) and in Morkaraman and Awassi, Bilgin et al. (2004), reported that Brody is the best model for describing as unfit between body weight and age in sheeps.
Considering the different sample sizes, the results of the linear regression model are given in Table 4. According to these results, the R2 value was 0.66 and the MSE value was 17.16 in the model with a sample size of 10, and the R2 value was 0.69 and the MSE value was 15.44 in the model with a sample size of 20. In addition, the R2 value was 0.81 and the MSE value was 13.11 in the model with a sample size of 30, and the R2 value was 0.90 and the MSE value was 11.08 in the model with a sample size of 50. According to these obtained values, it was found that as the sample size increased, the R2 value increased and the MSE value decreased. According to different sample sizes, these coefficients showed that, there are more similarity between the (linear and nonlinear) methods. Barragan et.al 2020 reported that according to all nonlinear models R2 value is calculated higher than 0.75 for estimate body weight from body measurements.
In Table 5, the results of the evaluators of goodness of fit (R2aj, AIC, BIC, MEP) for each model. Considering the R2aj value, the highest value was obtained as Incomplete gamma (0.8464), Logistic (0.7921), Allometric (0.7744) and Exponential (0.7744) with sample size 50. The low MEP values, the lowest values were obtained as Incomplete gamma (10.9096), Exponential (11.0864) and Logistic (11.3212), respectively. The lowest R2a value was obtained as Allometric (0.3481), Exponential (0.3600), Saturation growth (0.3721) and Incomplete gamma (0.3969) with sample size 10. Considering the high MEP values, the highest values were obtained as Incomplete gamma (24.8530), Exponential (24.2070) and Allometric (20.6392), respectively. Considering the AIC value, the lowest value was obtained as Incomplete gamma (175.3682), Logistic (187.7116), Allometric (188.9002) and Exponential (189.4751) with sample size 50. The lowest BIC value were obtained as Incomplete gamma (182.4006), Exponential (198.6672) and Logistic (202.1524), respectively.