Linear Equations
Linear Group Function Numbers
- y=a0+a1*x
- y=a0+a1/x
- y=a0+a1*sqrt(x)
- y=a0+a1*sqrt(x)
- y=a0+a1/x^2
- y=a0+a1*exp(x)
- y=a0+a1*exp(–x)
- y =a0+a1*ln(x)
- y=a0+a1/ln(x)
- y=a0+a1*(ln(x))^2
- 1/y=a0+a1*x
- 1/y=a0+a1/x
- 1/y=a0+a1*sqrt(x)
- 1/y=a0+a1/sqrt(x)
- 1/y=a0+a1/x^2
- 1/y=a0+a1*exp(x)
- 1/y=a0+a1*exp(–x)
- 1/y=a0+a1*ln(x)
- 1/y=a0+a1/ln(x)
- 1/y=a0+a1*(ln(x))^2
- y^2=a0+a1*x
- y^2=a0+a1/x
- y^2=a0+a1*sqrt(x)
- y^2=a0+a1/sqrt(x)
- y^2=a0+a1/x^2
- y^2=a0+a1*exp(x)
- y^2=a0+a1*exp(–x)
- y^2=a0+a1*ln(x)
- y^2=a0+a1/ln(x)
- y^2=a0+a1*(ln(x))^2
- sqrt(y)=a0+a1*x
- sqrt(y)=a0+a1/x
- sqrt(y)=a0+a1*sqrt(x)
- sqrt(y)=a0+a1/sqrt(x)
- sqrt(y)=a0+a1/x^2
- sqrt(y)=a0+a1*exp(x)
- sqrt(y)=a0+a1*exp(–x)
- sqrt(y)=a0+a1*ln(x)
- sqrt(y)=a0+a1/ln(x)
- sqrt(y)=a0+a1*(ln(x))^2
Exponential Group Function Numbers
- ln(y)=a0+a1*x
- ln(y)=a0+a1/x
- ln(y)=a0+a1*sqrt(x)
- ln(y)=a0+a1/sqrt(x)
- ln(y)=a0+a1/x^2
- ln(y)=a0+a1*exp(x)
- ln(y)=a0+a1*exp(–x)
- ln(y)=a0+a1*ln(x)
- ln(y)=a0+a1/ln(x)
- ln(y)=a0+a1*(ln(x))^2
Power Group Function Numbers
- y=a0+a1*x^2
- y=a0+a1*x^3
- y=a0+a1*x^4
- y=a0+a1*x^5
- y=a0+a1*x^6
- 1/y=a0+a1*x^2
- 1/y=a0+a1*x^3
- 1/y=a0+a1*x^4
- 1/y=a0+a1*x^5
- 1/y=a0+a1*x^6
- y^2=a0+a1*x^2
- y^2=a0+a1*x^3
- y^2=a0+a1*x^4
- y^2=a0+a1*x^5
- y^2=a0+a1*x^6
- sqrt(y)=a0+a1*x^2
- sqrt(y)=a0+a1*x^3
- sqrt(y)=a0+a1*x^4
- sqrt(y)=a0+a1*x^5
- sqrt(y)=a0+a1*x^6
- ln(y)=a0+a1*x^2
- ln(y)=a0+a1*x^3
- ln(y)=a0+a1*x^4
- ln(y)=a0+a1*x^5
- ln(y)=a0+a1*x^6
Polynomial Group Function Numbers
- y=a0+a1*x+a2*x^2
- y=a0+a1*x+a2*x^2+a3*x^3
- y=a0+a1*x+a2*x^2+a3*x^3+a4*x^4
- y=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5
- y=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6
- 1/y=a0+a1*x+a2*x^2
- 1/y=a0+a1*x+a2*x^2+a3*x^3
- 1/y=a0+a1*x+a2*x^2+a3*x^3+a4*x^4
- 1/y=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5
- 1/y=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6
- y^2=a0+a1*x+a2*x^2
- y^2=a0+a1*x+a2*x^2+a3*x^3
- y^2=a0+a1*x+a2*x^2+a3*x^3+a4*x^4
- y^2=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5
- y^2=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6
- sqrt(y)=a0+a1*x+a2*x^2
- sqrt(y)=a0+a1*x+a2*x^2+a3*x^3
- sqrt(y)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4
- sqrt(y)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5
- sqrt(y)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6
- ln(y)=a0+a1*x+a2*x^2
- ln(y)=a0+a1*x+a2*x^2+a3*x^3
- ln(y)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4
- ln(y)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5
- ln(y)=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6
Notes:
- Equations 11-20, 56-60, 81-85: 1/y=f(x) corresponds to fitting data to y=1/(f(x))
- For example, 1/y = a0+a1ln(x) is the linearized version of the nonlinear equation y = 1/(a0+a1exp(x)).
- Equations 11-20, 56-60, 81-85: 1/y=f(x) corresponds to fitting data to y=1/(f(x))
- For example, 1/y = a0+a1ln(x) is the linearized version of the nonlinear equation y = 1/(a0+a1exp(x)).
- Equations 21-30, 61-65, 86-90: y^2=f(x) corresponds to fitting data to y = sqrt(f(x))
- For example, y^2 = a0+a1x^2 is the linearized version of the nonlinear equation y = sqrt(a0+a1x^2).
- Equations 31-40, 66-70, 91-95: sqrt(y)=f(x) corresponds to fitting data to y=(f(x))^2
- For example, sqrt(y) = a0+a1x+a2x^2+a3x^3 is the linearized version of the nonlinear fitting equation y = (a0+a1x+a2x^2+a3x^3)^2
- Equations 41-50, 71-75, 96-100: ln(y)=f(x) corresponds to fitting data to y = exp(f(x))
- For example, ln(y) = a0+a1x is the linearized form of nonlinear equation y = exp(a0+a1x)
- Note this corresponds to the familiar exponential equation y = a0′exp(a1′x) where a0′ = exp(a0) and a1′ = a1.
Nonlinear Equations
Standard Functions
Power
y=a0+a1*x^a2
Exponential
y=a0+a1*exp(-x/a2)
Peak Functions
Gaussian
y=a0+a1exp(-0.5((x–a2)/a3)^2)
Lorentzian
y=a0+a1/(1+((x–a2)/a3)^2)
Logistic Peak
y=a0+a14n/(1+n)^2 n = exp(-(x–a2)/a3)
Erfc Peak
y=a0+a1*erfc(((x–a2)/a3)^2)
Log-Normal
y=a0+a1exp(-0.5(ln(x/a2)/a3)^2)
Transition Functions
Sigmoidal
y=a0+a1/(1+exp(-(x–a2)/a3))
Cumulative
y=a0+a10.5(1+erf((x–a2)/(sqrt(2)*a3)))
DoseRspLgstc
y=a0+a1/(1+(x/a2)^a3)
pH Activity
y=(a0+a1*10^(x–a2))/(1+10^(x–a2))
1-Site Ligand
y=a0*x/(a1+x)
Photosynthesis Rate
y=a0a1x/(a0+a1*x)
Waveform Functions
SineWave
y=a0+a1sin(2pi*x/a3+a2)
SineWaveSquared
y=a0+a1(sin(2piπ*x/a3+a2))^2