• NLR 

Function : NLR

{ NLR Function WAV 11/28/03

NonLinear Regression Analysis
y = A + B*X + C*X*X (2nd order)

y price
x bar (time)
A,B,C coefficients to determine

Standard deviation (S) of price from
calculated price for length data is returned

price for desired bar (either a past or future one)
is returned

}
InPuts: Length(NumericSimple), price(NumericSeries),
DesiredBar(NumericSimple),oNLRPrice(NumericRef),oStdDev(NumericRef);

vars: AvgX(0),AvgY(0),N(0),XM(0),YM(0),XM2(0),SXX(0),SXY(0),SYY(0),
SSYY(0),SXX2(0),SX2X2(0),SYX2(0),ACoeff(0),BCoeff(0),CCoeff(0),
X(0),Y(0), MaxLength(100),s(0),TX(0),TY(0),RV(0),ERR(0);

array: YValue[100](0),XValue[100](0);

if BarNumber = 1 then
begin
N = length;
{ be sure array size is protected }
if N > MaxLength then
N = MaxLength;
if N < 2 then
N = 2;
end;

{ fill arrays }
for value1 = 1 to N
begin
XValue[value1] = value1-1;
YValue[value1] = Price[value1-1];
end;

{ calc averages of x,y pairs }
AvgX = 0; AvgY = 0;
for value1 = 1 to N
begin
AvgX = AvgX + XValue[value1];
AvgY = AvgY + YValue[value1];
end;
if N <> 0 then
begin
AvgX = AvgX / N;
AvgY = AvgY / N;
end;

{ do regression and calc 3 coefficients }
SXX = 0; SXY = 0;SYY = 0;SXX2 = 0;SX2X2 = 0;SYX2 = 0;
for value1 = 1 to N
begin
XM = XValue[value1] - AvgX;
YM = YValue[value1] - AvgY;
XM2 = XValue[value1]*XValue[value1] - AvgX*AvgX;
SXX = SXX + XM*XM;
SXY = SXY + XM*YM;
SYY = SYY + YM*YM;
SXX2 = SXX2 + XM*XM2;
SX2X2 = SX2X2 + XM2*XM2;
SYX2 = SYX2 + YM*XM2;
end;

value99 = SXX*SX2X2 - SXX2*SXX2;
if value99 <> 0 then
begin
BCoeff = ( SXY*SX2X2 - SYX2*SXX2 ) / value99 ;
CCoeff = ( SXX*SYX2 - SXX2*SXY ) / value99;
end;

ACoeff = AvgY - BCoeff*AvgX - CCoeff*AvgX*AvgX;

{calc estimated price for desired bar
DesiredBar: use + for past and - for future
eg., for next bar in future:
DesiredBar = -1 }
oNLRPrice = ACoeff + BCoeff*DesiredBar+
CCoeff*DesiredBar*DesiredBar;

{calc std dev}
S = 0; AvgY = 0;
for value1 = 1 to N
begin
TY = YValue[value1];
TX = XValue[value1];
RV = ACoeff + BCoeff*XValue[value1]+
CCoeff*XValue[value1]*XValue[value1];
ERR = TY - RV;
AvgY = AvgY + TY;
S = S + ERR*ERR;
end;
if N-1 <> 0 then
if S /(N-1) > 0 then
S = SquareRoot(S /(N-1));

oStdDev = s;

NLR = 1;

 Indicator : NLR1 

{ NLR1 Indicator WAV 11/26/03

NonLinear Regression Analysis
y = A + B*X + C*X*X (2nd order)

y price
x bar (time)
A,B,C coefficients to determine

modified 11/29
utilize NLR function
added price input
removed mult input
plots only last bar from curve

}
InPuts:
Length(20), price(close);

vars: S(0),oNLRPrice(0);

value1 = NLR(length, price, 0, oNLRPrice, S);

plot1(oNLRPrice, "NLR");