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Table 3 Comparison of linear and non-linear regression analysis of changes in running speeds across years in the annual ten 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 ten fastest men 50 km Polynomial 29.00 16 61.73 Linear Linear 33.98 4.16 e-08 100%
linear 71.73 31 27.75
Annual ten fastest women 50 km Polynomial 5.87 22 -31.64 Polynomial Polynomial 8.34 0.015 98.5%
Linear 9.02 23 -23.30
Annual ten fastest men 100 km Polynomial 3.08 39 -107.90 Polynomial Polynomial 88.13 7.28 e-20 100%
Linear 26.76 42 -19.77
Annual ten fastest women 100 km Polynomial 9.57 32 -41.00 Polynomial Polynomial 34.71 2.89 e-08 100%
Linear 27.52 33 -6.29
Annual ten fastest men 200 km Polynomial 0.36 0 -6.75 Linear Undetermined 0.27 0.46 53.4%
Linear 1.12 4 -7.02
Annual ten fastest women 1,000 km Polynomial 1.32 e-20 0 -136.61 Polynomial Undetermined 135.24 4.27 e-30 100%
Linear 0.25 1 -1.36