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Table 2 Comparison of linear and non-linear regression analysis of changes in running speeds across years in the annual fastest women and men to determine which model is the best

From: Will women outrun men in ultra-marathon road races from 50 km to 1,000 km?

Running speed Kind of regression Sum of squares DOF AICc Best regression Best regression Delta Probability Likelihood
AIC-Test F-Test
Annual fastest men 50 km Polynomial 45.22 29 17.22 Polynomial Polynomial 12.99 0.0015 99.8%
Linear 77.31 31 30.22
Annual fastest women 50 km Polynomial 33.46 30 4.86 Polynomial Polynomial 6.30 0.041 95.9%
Linear 43.38 31 11.16
Annual fastest men 100 km Polynomial 29.45 44 -16.02 Polynomial Polynomial 45.56 1.27 e-10 100%
Linear 85.81 47 29.54
Annual fastest women 100 km Polynomial 14.83 37 -33.57 Polynomial Polynomial 38.62 4.10 e -09 100%
Linear 47.05 42 5.04
Annual fastest men 200 km Polynomial 3.30 0 4.15 Linear Undetermined 22.70 1.17 e -05 99.9%
Linear 4.99 15 -18.54
Annual fastest women 200 km Polynomial 0.011 0 -27.78 Polynomial Undetermined 26.48 1.77 e -06 99.9%
Linear 2.92 4 -1.30
Annual fastest men 1,000 km Polynomial 1.65 0 1.39 Linear Undetermined 2.24 0.24 75.4%
Linear 5.15 6 -0.84
Annual fastest women 1,000 km Polynomial 1.08 0 -4.19 Linear Undetermined 9.72 0.0076 99.2%
Linear 1.93 8 -13.92