Re: [amibroker] The linear trend calculations

["Tomasz Janeczko" <amibroker@xxxxxx>]

Dimitris,
 
The linear (Least-Squares ) regression model 
postulates that 
Y= a+bX+e
Where the "residual" e is a random variable with mean zero.  
The coefficients a and b are determined by the 
condition that the sum of the square residuals is as small as possible. 

So error is SUM OF THE SQUARE of residuals.
 
You are not using sum of squares of residuals as error estimate.
 
For more info see:
<A 
href="">http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm
Best regards,Tomasz Janeczkoamibroker.com
<BLOCKQUOTE 
>
  ----- Original Message ----- 
  <DIV 
  >From: 
  Dimitris 
  Tsokakis 
  To: <A title=amibroker@xxxxxxxxxxxxxxx 
  href="">amibroker@xxxxxxxxxxxxxxx 
  Sent: Monday, March 15, 2004 12:17 
  PM
  Subject: [amibroker] The linear trend 
  calculations
  
  I tried to duplicate the LinRegIntercept( ARRAY, periods ) 
  example from the 4.50 users guide.I used as example the 
  C1=MA(RSI(50),200).The error was calculated from 
  Cum(abs(y-C1)).
   
  C1=MA(RSI(50),200);Plot(C1,"C1",1,1); x = 
  Cum(1);lastx = LastValue( x ); Daysback = 
  LASTX-ValueWhen(Cum(IsTrue(C1))==1,X); aa = LastValue( LinRegIntercept( 
  C1, Daysback) );bb = LastValue( LinRegSlope( C1, Daysback ) );y = Aa + 
  bb * ( x - (Lastx - DaysBack) ); Plot( IIf( x >= (lastx - Daysback), y, 
  -1e10 ), "LinReg", colorRed,8 ); 
  Title=Name()+"\nLine="+WriteVal(aa,1.1)+"+"+WriteVal(bb,1.3)+"*(t-t1)"+"\nError="+WriteVal(Cum(abs(y-C1)),1.0);start=Cum(IsTrue(C1))==1;PlotShapes(shapeUpTriangle*start,colorWhite);
   
  My analytic 
  codet=Cum(1)-1;tmax=LastValue(t);C1=MA(RSI(50),200);Plot(C1,"C1",1,1);C1max=1.5*LastValue(ceil(Highest(C1)));C1min=0.5*LastValue(floor(Lowest(C1)));start=Cum(IsTrue(C1))==1;t1=ValueWhen(start,t);PlotShapes(shapeUpTriangle*start,colorWhite);C10=ValueWhen(start,C1);d0=Param("d0",-0.03,-0.03,-0.005,0.005);Line0=C10+d0*(t-t1);d1=-d0;Line1=C10+d1*(t-t1);Error0=LastValue(Cum(abs(C1-Line0)));Error1=LastValue(Cum(abs(C1-Line1)));Err=Max(Error0,Error1);Title=Name()+"\nInitial 
  Error="+WriteVal(err,1.0);stepi=0.1;stepj=0.001;j1=d1;j0=d0;for(i=C1min;i<=C1max;i=i+stepi){for(j=j0;j<=j1;j=j+stepj){Line=i+j*(t-t1);err1=LastValue(Cum(abs(C1-Line)));if(err1<err)err=Min(err,err1);}}Title=Title+"\nMinError="+WriteVal(err,1.0);iA=0;jA=0;for(i=C1min;i<=C1max;i=i+stepi){for(j=j0;j<=j1;j=j+stepj){Line=i+j*(t-t1);err1=LastValue(Cum(abs(C1-Line)));if(err1==err){Plot(Line,"\n"+WriteVal(j,1.4),colorRed,8);Title=Title+"\n\nLine="+WriteVal(i,1.1)+"+"+WriteVal(j,1.3)+"*(t-t1)";iA=i;jA=j;}}}Title=Title+"\nFirst 
  Approx [iA,jA]=["+WriteVal(iA,1.1)+","+WriteVal(jA,1.3)+"]";
   
  gave, in many cases, smaller error.Is there any 
  explanation ?Dimitris Tsokakis
   
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