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Table 4 Comparison of linear and non-linear regression analysis of changes in swimming speed across years to determine which model is the best

From: Analysis of sex differences in open-water ultra-distance swimming performances in the FINA World Cup races in 5 km, 10 km and 25 km from 2000 to 2012

Swimming speed Kind of regression Sum of squares DOF AICc Best regression AIC-Test Best regression F-Test Delta Probability Likelihood
Annual fastest men 5 km Polynomial 0.26 5 -16.81 Linear Linear 20.03 4.4 e-05 99.9%
Linear 0.45 10 -36.85
Annual fastest women 5 km Polynomial 0.33 0 -21.12 Linear Undetermined 16.50 0.00026 99.9%
Linear 0.42 10 -37.63
Annual fastest men 10 km Polynomial 0.21 5 -21.46 Linear Linear 11.26 0.0035 99.6%
Linear 0.44 9 -32.72
Annual fastest women 10 km Polynomial 0.064 0 -36.51 Polynomial Undetermined 6.81 0.032 96.7%
Linear 0.59 9 -29.70
Annual fastest men 25 km Polynomial 0.98 0 -7.99 Linear Undetermined 17.78 0.00013 99.9%
Linear 1.14 10 -25.77
Annual fastest women 25 km Polynomial 0.49 0 -16.20 Linear Undetermined 15.16 0.00050 99.9%
Linear 0.71 10 -31.37
Annual 10 fastest men 5 km Polynomial 0.31 0 -21.52 Linear Undetermined 11.17 0.0037 99.6%
Linear 0.64 10 -32.69
Annual 10 fastest women 5 km Polynomial 0.26 5 -16.95 Linear Linear 22.44 1.33 e-05 99.9%
Linear 0.36 10 -39.39
Annual 10 fastest men 10 km Polynomial 0.15 0 -26.60 Linear Undetermined 6.11 0.044 95.5%
Linear 0.44 9 -32.71
Annual 10 fastest women 10 km Polynomial 0.12 4 -16.10 Linear Linear 12.82 0.0016 99.8%
Linear 0.63 9 -28.93
Annual 10 fastest men 25 km Polynomial 1.80 0 -0.72 Linear Undetermined 16.52 0.00025 99.9%
Linear 2.33 10 -17.24
Annual 10 fastest women 25 km Polynomial 0.78 0 -10.66 Linear Linear 20.74 3.12 e-05 99.9%
Linear 0.71 10 -31.41