More Information

Pre-Defined and User-Defined Curve Fitting


Regressions Concerning Two Continuous Variables (Pre-Defined)

In the context of Citrin, the regression methods grouped under this title deal with finding the relationship between one outcome (dependent) variable and one predictor (independent) variable.

The pre-defined functions include:

  • Linear (X on Y): Y = aX + b (the equation is calculated by minimizing the deviations between the dependent variable and the regression line)
  • Linear (thru zero): Y = aX (regular linear regression where the intercept is forced through zero)
  • Polynomial: Y = aX + bX2... + c (the equation is calculated by minimizing the deviations between the dependent variable and the regression curve. The order of the equation can be from 2 to 6)
  • Exponential: Y = b*e(a * X) (the equation is calculated by minimizing the deviations between the dependent variable and the regression curve
  • Logarithmic: Y = a * log(x)+b (the equation is calculated by minimizing the deviations between the dependent variable and the regression curve
  • Power: Y = b * Xa (the equation is calculated by minimizing the deviations between the dependent variable and the regression curve

Options for Applying Pre-Defined Functions

The pre-defined functions can be applied dynamically (as you change plot variables on the fly) or linked to specific variable pairs.

Linear Regression and Confidence Belt
Applied to Groups of Data Objects

    Applying Predefined Functions Dynamically:

  • With this option, when you change the plot variables on the fly, Citrin will dynamically analyze and update the regression curve, based on the chosen regression type and options.

    Applying Predefined Functions to a Variable Pair:

  • With this regression option, you can apply a pre-defined function to specific pairs of variables. You can also apply different functions to different variable pairs.
  • The right-hand side image displays a double-Y scatter series graph, in which linear regression is applied to Y1-X variable pair and polynomial regression to Y2-X variable pair.

Cubic Spline Interpolation

A cubic spline is made from piece-wise third-order polynomials that pass through the control points provided.

  • You can apply a cubic spline interpolation to a displayed chart, or generate a specified sequence of interpolations (using the Stats Analyzer) and save them in a worksheet for other uses.

Applying Different Regression Functions
to Different Variable Pairs

User-Defined Non-Linear Regression

The user-defined regression uses Levenberg-Marquardt "full Newton-type" method.