The formulas for the models that are available in the Fit Curve red triangle menu are summarized in Table 14.1.
Model |
Formula |
---|---|
Polynomials |
where k is the order of the polynomial. These models can also be fit using the Fit Model and Fit Y by X platforms. |
Power Model |
a = Intercept b = Slope c = Power Available only when both the response values and the x values are nonnegative. |
Logistic 2P |
a = Growth Rate b = Inflection Point Available only when all response values are between zero and one. |
Logistic 3P |
a = Growth Rate b = Inflection Point c = Asymptote |
Logistic 4P |
a = Growth Rate b = Inflection Point c = Lower Asymptote d = Upper Asymptote |
Logistic 4P Rodbard |
a = Growth Rate b = Inflection Point c = Lower Asymptote d = Upper Asymptote Available only when the x values are positive. |
Logistic 4P Hill |
a = Growth Rate b = Inflection Point c = Lower Asymptote d = Upper Asymptote |
Logistic 5P |
a = Growth Rate b = Inflection Point c = Asymptote 1 d = Asymptote 2 f = Power |
Probit 2P |
a = Growth Rate b = Inflection Point Φ = Normal Distribution CDF Available only when all response values are between zero and one. |
Probit 3P |
a = Growth Rate b = Inflection Point c = Asymptote Φ = Normal Distribution CDF There is also an asymptote at zero. |
Probit 4P |
a = Growth Rate b = Inflection Point c = Lower Asymptote d = Upper Asymptote Φ = Normal Distribution CDF |
Gompertz 3P |
a = Asymptote b = Growth Rate c = Inflection Point |
Gompertz 4P |
a = Lower Asymptote b = Upper Asymptote c = Growth Rate d = Inflection Point |
Weibull Growth |
a = Upper Asymptote b = Growth Rate c = Inflection Point Available only when both the response values and the x values are nonnegative. |
Exponential 2P |
a = Scale b = Growth Rate |
Exponential 3P |
a = Asymptote b = Scale c = Growth Rate |
Biexponential 4P |
a = Scale 1 b = Decay Rate 1 c = Scale 2 d = Decay Rate 2 Available only when the response values are positive. |
Biexponential 5P |
a = Asymptote b = Scale 1 c = Decay Rate 1 d = Scale 2 f = Decay Rate 2 |
Mechanistic Growth |
a = Asymptote b = Scale c = Growth Rate |
Hybrid Exponential |
a = Maximum b = Scale c = Rate d = Power Available only when both the response values and the x values are nonnegative. |
Cell Growth 4P |
a = Peak value if mortality rate, d, is zero b = Response at time zero c = Cell Division Rate d = Cell Mortality Rate Available only when the response values are positive and the x values are nonnegative. |
Gaussian Peak |
a = Peak Value b = Critical Point c = Growth Rate |
ExGaussian Peak (Exponentially Modified Gaussian Peak) |
a = AUC (area under the curve) b = Location c = Scale d = Lambda φ = the standard normal pdf |
Lorentzian Peak |
a = Peak Value b = Growth Rate c = Critical Point |
One Compartment Oral Dose |
a = Area Under Curve b = Elimination Rate c = Absorption Rate Available only when the response values and the x values are all positive. |
Two Compartment IV Bolus Dose |
α = β = a = Initial Concentration b = Transfer Rate In c = Transfer Rate Out d = Elimination Rate Available only when the response values and the x values are all positive. |
Michaelis-Menten |
a = Maximum Velocity b = Michaelis Constant Available only when the response values and the x values are all positive. |
Inverse Michaelis-Menten |
a = Maximum Velocity b = Michaelis Constant Available only when the response values and the x values are all positive. |
First Order Rate |
a = Initial Value b = Rate Constant Available only if the x values are nonnegative. |
First Order with Limits |
a = Initial Value b = Limiting Value c = Rate Constant Available only if the x values are nonnegative. |
First Order with Equilibrium |
a = Initial Value b = Forward Rate c = Backward Rate Available only if the x values are nonnegative. |
Second Order |
a = Initial Value b = Rate Constant Available only if the x values are nonnegative. |
Second Order with Two Components |
a = Initial value b = Offset c = Rate Constant Available only if all x values are nonnegative. |
Antoine Equation |
a = Component Specific Constant b = Component Specific Constant c = Component Specific Constant Available only when the response values are greater than 0. The vertical asymptote is at 10a. The horizontal asymptote is at −c. |
Higuchi |
a = Release Constant Available only if all x and y values are nonnegative. |
Higuchi with Lag |
a = Release Constant b = Time Lag Available only if all x and y values are nonnegative. |
Higuchi with Burst |
a = Release Constant b = Burst Available only if all x and y values are nonnegative. |
Hixson-Crowell |
a = Release Constant Available only if all x and y values are nonnegative. |
Hixson-Crowell with Lag |
a = Release Constant Available only if all x and y values are nonnegative. |
Korsmeyer-Peppas |
a = Release Constant b = Diffusional Exponent Available only if all x and y values are nonnegative. |
Korsmeyer-Peppas with Lag |
a = Release Constant b = Diffusional Exponent c = Time Lag Available only if all x and y values are nonnegative. |
Korsmeyer-Peppas with Burst |
a = Release Constant b = Diffusional Exponent c = Burst Available only if all x and y values are nonnegative. |