Table 1 Equations of 10 curve estimation models between DNW and CMI

Linear equation

y = 81.9 + 16.6x

0.618

434.6

< 0.001

Quadratic equation

y = 92.3 + 4.8x + 2.4x²

0.627

225.1

< 0.001

Cubic equation

y = 64.8 + 52.8x − 20.1x² + 3.0x³

0.636

155.5

< 0.001

Logarithmic equation

y = 99.3 + 32.3 log(x)

0.568

354.1

< 0.001

Reciprocal equation

y = 148.9 − 44.0/x

0.455

224.9

< 0.001

Exponential equation

y = 85.6  exp(0.14x)

0.617

433.5

< 0.001

Growth curve

y = exp(4.45 + 0.14x)

0.617

433.5

< 0.001

Composite curve

y = 85.6 + 1.14^x

0.617

433.5

< 0.001

Power function

y = 98.6x^0.27

0.581

373.7

< 0.001

S-curve

y = exp(5.00 − 0.37/x)

0.479

246.8

< 0.001