Data Modeling Equations

There are two types of curve fitting used by CurveExpert. The first group falls under the category of regression curves (which can be further subdivided into linear and nonlinear), which attempt to minimize the difference between themselves and the data points. The second group, interpolations, ensure that the curve fit passes exactly through each data point.

In CurveExpert, the regression models are divided into families according to their typical behavior. Of course, you are not limited to only these models in CurveExpert! If the model that you would like to use does not appear below, simply define a custom model and let CurveExpert apply that model to your data set.

Regressions

Linear Family

  • Linear Fit, y=a+bx
  • Quadratic Fit, y=a+bx+cx^2
  • nth order Polynomial Fit, y=a+bx+cx^2+...

Exponential Family

  • Exponential Fit, y=a*exp(bx)
  • Modified Exponential Fit, y=a*exp(b/x)
  • Logarithm Fit, y=a+b*ln(x)
  • Reciprocal Logarithm Fit, y=1/(a+b*ln(x))
  • Vapor Pressure Model, y=exp(a+b/x+c*ln(x))

Power Law Family

  • Power Fit, y=a*x^b
  • Modified Power Fit, y=ab^x
  • Shifted Power Fit, y=a*(x-b)^c
  • Geometric Fit, y=ax^(bx)
  • Modified Geometric Fit, y=ax^(b/x)
  • Root Fit, y=a^(1/x)
  • Hoerl Model, y=a*(b^x)*(x^c)
  • Modified Hoerl Model, y=a*b^(1/x)*(x^c)

Yield-Density Models

  • Reciprocal Model, y=1/(a+bx)
  • Reciprocal Quadratic, y=1/(a+bx+cx^2)
  • Bleasdale Model, y=(a+bx)^(-1/c)
  • Harris Model, y=1/(a+bx^c)

Growth Models

  • Exponential Association Fit, y=a*(1-exp(-bx))
  • Three-Parameter Exponential Association Fit, y=a*(b-exp(-cx))
  • Saturation-Growth Rate Model, y=a*x/(b+x)

Sigmoidal Models

  • Gompertz Relation, y=a*exp(-exp(b-cx))
  • Logisitic Model, y=a/(1+exp(b-cx))
  • Richards Model, y=a/(1+exp(b-cx))^(1/d)
  • MMF Model, y=(ab+cx^d)/(b+x^d)
  • Weibull Model, y=a-b*exp(-cx^d)

Miscellaneous Models

  • Sinusoidal Function, y=a+b*cos(cx+d)
  • Gaussian Model, y=a*exp((-(b-x)^2)(2*c^2))
  • Hyperbolic Fit, y=a+b/x
  • Heat Capacity Model, y=a+bx+c/x^2
  • Rational Function, y=(a+bx)/(1+cx+dx^2)

Interpolations

  • Lagrangian Interpolation, y=a+bx+cx^2+...
  • Linear Spline, y=a+bx, piecewise
  • Quadratic Spline, y=a+bx+cx^2, piecewise
  • Cubic Spline, y=a+bx+cx^2+dx^3, piecewise
  • Tension Spline