{ Linear Regression multiple-output function, verified as series for backward 
  compatibility; all outputs of this function are identical to the LinearReg function 
  except for the LRValueRaw output, which in not adjusted for ExecOffset here (series 
  functions cannot be adjusted this way); also MULTIPLE-OUTPUT FUNCTIONS note below }

inputs: 
	Price( numericseries ), 
	Length( numericsimple ), { Length > 1 }
	TgtBar( numericsimple ), { use negative integer for future, positive for past }
	oLRSlope( numericref ), 
	oLRAngle( numericref ), 
	oLRIntercept( numericref ), { left intercept, at vertical through 
	 Price[ Length - 1 ] }
	oLRValueRaw( numericref ) ;

variables: 
	SumXY( 0 ), 
	SumY( 0 ), 
	SumX( 0 ), 
	SumXSqr( 0 ), 
	OneSixth( 1 / 6 ), 
	Divisor( 0 ) ;

if Length > 1 then
	begin 
	SumX = Length * ( Length - 1 ) * .5 ;
	SumXSqr = Length * ( Length - 1 ) * ( 2 * Length - 1 ) * OneSixth ;
	Divisor = Square( SumX ) - Length * SumXSqr ;
	SumXY = 0;
	for Value1 = 0 to Length - 1 
		begin
		SumXY = SumXY + Value1 * Price[Value1] ;
		end ;
	SumY = Summation( Price, Length ) ;

	oLRSlope = ( Length * SumXY - SumX * SumY) / Divisor ;
	oLRAngle = ArcTangent( oLRSlope ) ;
	oLRIntercept = ( SumY - oLRSlope * SumX ) / Length ;
	oLRValueRaw = oLRIntercept + oLRSlope * ( Length - 1 - TgtBar ) ;
	LinearRegFC = 1 ;
	end 
else 
	LinearRegFC = -1 ;

{
MULTIPLE-OUTPUT FUNCTIONS

A multiple-output function has two types of parameters or "inputs" - input parameters 
and input/output parameters.  The values of the input parameters are passed into the 
multiple-output function, but not modified by the function.  The values of the input/
output parameters are passed into the multiple-output function, modified by it, and 
the modified values are then inherited by - or output to - the calling routine.

The input/output parameters are often used for output purposes only, i.e., the 
incoming values are ignored.  The outputs are in addition to the function return.  In 
multiple-output functions, the function return is generally used to return an error 
code, though sometimes the return may simply be a dummy value.

The input/output parameters are declared with a "ref" suffix (such as "numericref") in 
the multiple-output function's declaration statements.  For further clarity, the names 
of the input/output parameters are generally prefixed with an "o" in the function as 
well as in all the routines that call the function.

The built-in single-return WRAPPER FUNCTIONS that call the multiple-output functions 
are specialized calling routines designed to offer simplified, alternate pathways to 
the functionality of the underlying multiple-output functions.  In the wrapper 
functions, the input/output parameters are declared as local variables and generally 
initialized to zero.  They are passed through to the multiple-output function without 
further modification.  After the call, the wrapper function picks out the single 
output of interest and assigns it as the return of the wrapper function.
}

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  ** TradeStation reserves the right to modify or overwrite this analysis technique 
     with each release. ** }