Table 4.

Transformation of the nonlinear regression and linear regression.

Types	Nonlinear Function	Do Transformation	Linear Function
Hyperbolic function	$Y=a+b\frac{1}{x}$	$x\text{'}=\frac{1}{x}$	$Y\text{'}=a+bx\text{'}$
Power function	$Y=a{x}^b$	$Y^{\prime }=\ln Y x=\ln x A=\ln a$	$Y\text{'}=A+bx\text{'}$
Exponential function	$Y=a{e}^{bx}$ or $Y=a{e}^{\frac{b}{x}}$	$Y^{\prime }=\ln Y, A=\ln a$ or $Y^{\prime }=\ln Y, x=\frac{1}{x} , A=\ln a$	$Y\text{'}=A+bx\text{'}$ or $Y\text{'}=A+bx\text{'}$
Logarithmic function	$Y=a+b\ln x$	$x\text{'}=\ln x$	$Y\text{'}=a+bx\text{'}$
S curve type	$Y=\frac{1}{a+b{e}^{-x}}$	$Y^{\prime }=\frac{1}{Y}, x=e^{-x}$	$Y\text{'}=a+bx\text{'}$
Parabolic type	$Y=a+bx+c{x}^2$	$x_1=x,x_2=x^2$	$Y^{\prime }=a+b{x}_1+c{x}_2$