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Regression Analysis (Manually fitting data)

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FCS Express has the ability to perform regression analysis on your data through manual formulas and custom data grids or at a click through Scatter with Regression plots.

FCS Express provides the user with many mathematical functions to create custom tokens and custom data sets. These functions operate similar to functions within Microsoft Excel™. When it comes to regression analysis there are four basic functions that apply to all of the available equations that a regression can be performed on. In the table below the functions are listed with the red italic, xxx, representing the FCS Express Function name for a particular equation (The FCS Express Function names can be found in the Available Equations.). A description of the function argument is given in the right side of the table.

Regression Function Type	Description	Arguments	Result
PerformxxxFit	Performs a fit of the specified X-Y values to a particular equation.	([X Values],[Y Values],[SD],[Fixed Parameters]) Where X Values is a comma delimited list of X values, generally specified by a series of tokens. Where Y Values is a comma delimited list of Y values, generally specified by a series of tokens. Fixed Parameters allows you to specify variables that should not be fit, but will be forced to use the value that you specify. The format of the Fixed parameters is a comma delimited list of var=value where var is one of the available variables for that equation and value is the value to fix it to. SD, or Standard Deviation, allows you to specify a standard deviation for each list of the Y values, generally specified by a series of tokens. The SD value assigns a "weight" to each associated X and Y value with a lower SD value resulting in a higher weight and a higher SD value resulting in a lower weight. If the SD is not specified, an SD of zero is assumed for each Y value.	Comma delimited list of all of the fit variables and their fit values
ExtractxxxResults	Extracts a particular variable from the result of a PerformxxxFit custom token.	ExtractxxxResults([modelParameters], "Variable 1" \| "Variable 2" \| "Variable 3") Where xxx represents an equation (ie. Linear, Sigmoidal, Exponential, etc...). Where modelParameters represents a comma delimited list of all of the fit variables and their values, generally specified by a token result of the PerformxxxFit function. Where Variable represents a variable defined by the PerformxxxFit function and "\|" represents "or" . Each PerformxxxFit function will define a unique set of variables that will replace the example of "Variable 1, Variable 2, Variable 3" when the function is used: ie... "m" \| "b" \| "r2" or "A" \| "B" \| "C"\| "r2" for Linear and Sigmoidal equations respectively. Unwanted variables must be deleted to return a result. For example: ExtractLinearResults([modelParameters], "m") will return the fit value result of the "m" variable associated with the equation.	The value of the specified variable.
xxxXtoY	Uses the X values of a given data set and the "Model Parameters" or "Fit" of a regression to return an unknown Y Value.	xxxXToY(X, [modelParameters]) Where xxx represents an equation(ie. Linear, Sigmoidal, Exponential, etc...). Where X is a comma delimited list of X values, generally specified by a token. Where modelParameters represents a comma delimited list of all of the fit variables and their fit values. Generally specified by a token result of the PerformxxxFit function.	Comma delimited list of all of the Y values calculated from the associated equation, X value, and fit variables.
xxxYtoX	Uses the Y values of a given data set and the "Model Parameters" or "Fit" of a regression to return an unknown X Value.	xxxYToX(Y, [modelParameters]) Where xxx represents an equation (ie. Linear, Sigmoidal, Exponential, etc...) Where Y is a comma delimited list of Y values, generally specified by a token. Where modelParameters represents a comma delimited list of all of the fit variables and their fit values. Generally specified by a token result of the PerformxxxFit function.	Comma delimited list of all of the X values calculated from the associated equation, Y value, and fit variables.

To view a list of all possible equations please see the topic of Available Equations. To see an example of using these equations please see the topic of Regression Analysis Example or visit the Linear Regression Analysis tutorial.