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Table 1　Characteristic of the study participants (N = 53)Data in 6th grade of primary school Calendar Age (years) Bone age (years) Height (cm) Predicted height of Model 1 (cm)Data in adults (20-28years old) Age (years) Actual final height (cm) Father’s height (cm) Mother’s height (cm)224Mean (SD)12.2 (0.3)12.2 (1.2)149.2 (9.7)173.2 (4.5)23.9 (2.8)172.1 (6.8)173.5 (5.4)158.3 (5.3)same variables as Model 1 and developed a new equation by changing coefficients, to give Model 3. We then developed another prediction model with different variables (Model 4). To develop this final model, we used regression analyses, added or removed variables and calculated the accuracy. The final Model 4 included actual measured height, calendar age, father’s height, mother’s height and bone age.Statistical analysisMultiple regression analysis used the statistical software JMP® pro version 16. The significance level of the test was set at 5%.ParticipantsOf the 128 male players who belonged to the football club from 2006 to 2019, 53 men agreed to participate and were included in this study. The demographic characteristics of the participants are shown in Table 1. The mean (SD) bone age calcu-lated by the TW2 method was 12.2 (1.2). The mean difference (SD) between bone age and calendar age was 0.89 (0.75) years, and the mean difference between final height and measured height in 6th grade of primary school was 22.9 (8.2).Difference between predicted height and final heightWe assessed the accuracy of the conventional models by correlation analysis. For Model 1, the mean (SD) of the predicted heights was 173.2 (4.5) and the actual final height was 172.1 (6.8). The R-square was 0.33 (P < 0.0001) (Figure 1). For Figure 1　Correlation between final and predicted height (Model 1)R-square = 0.33, P < 0.0001Figure 2　Correlation between final and predicted height (Model 2) R-square = 0.52, P < 0.0001Model 2, the mean (SD) of the predicted heights was 172.4 (4.3) and the actual final height was 172.1 (6.8). The R-square was 0.52 (P < 0.0001) (Figure 2).New prediction modelsModel 2 was more accurate than Model 1. Model 1 was accurate at a final height of around 170–175cm. However, the difference was more prominent below 170cm or above 175cm. The difference between the predicted height and actual final height was linearly distributed, and the R-square was 0.56 (P < 0.0001) (Figure 3). The equation of Model 3 was final height = 0.63229313 × actual measured height − 8.2541327 × calendar age − 2.3009853 × bone age (TW2) + 206.627184. The R-square was 0.49 (P < 0.0001) (Figure 4).Results