Computational Engineering Modeling for Runner Athletes

Table 3

Model summary and parameter estimates for running time.

Equation	Model summary					Parameter estimates
	𝑅 square	𝐹	df1	df2	Sig.	Constant	𝑏1	𝑏2	𝑏3
Linear equation; 𝑦=𝑎0+𝑎1𝑥	0.006	0.110	1	18	0.744	16.410	−0.020
Quadratic; 𝑦=𝑎0+𝑎1𝑥+𝑎2𝑥^2	0.082	0.761	2	17	0.482	50.686	−1.328	0.012
Cubic; 𝑌=𝑎0+𝑎1𝑥+𝑎2𝑥^2+𝑎3𝑥^3	0.082	0.761	2	17	0.482	50.686	−1.328	0.012	0.00
Compound; 𝐴=𝑐𝑒^𝑘𝑡	0.005	0.083	1	18	0.776	16.240	0.999
Growth; 𝐴=𝑐𝑒^𝑘𝑡	0.005	0.083	1	18	0.776	2.787	−0.001
Exponential; 𝑦=𝑎𝑏^𝑥+𝑔	0.005	0.083	1	18	0.776	16.240	−0.001
Logistic; 𝑦=𝑎𝑥^𝑏+𝑔	0.005	0.083	1	18	0.776	0.062	1.001
Logarithmic; log𝑦=log𝑎+𝑏log𝑥	0.009	0.156	1	18	0.697	20.281	−1.242

𝑎: the independent variable (𝑚/𝑠) contains nonpositive values. The minimum value is 0.00. The logarithmic and power models cannot be calculated.
𝑏: the independent variable (𝑚/𝑠) contains values of zero. The inverse and S models cannot be calculated. Regression equation defined in stages (2-3-7-8) has been meaningless and stages (1-4-5-6-9-10-11) have been accepted, because the coefficients are meaningful.