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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