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# Vaclav

Member Since 19 Jul 2012
Offline Last Active May 01 2015 08:59 AM

### #4974372[Solved] 2D linear regression problem

Posted by on 29 August 2012 - 03:44 AM

Edit: The problem has been solved, if anyone has the same problem see post #4.

I've been looking for a simple linear regression method, I've implemented one but it doesn't work the way I would like. Can someone either recommend me a free, easy to use C or C++ library which has least squares linear regression and tell me how to use it as well, or point out the mistake in my code?
At the moment my code doesn't use least squares, just a simple linear regression, but I don't think it should be a problem, should it?
This is the algorithm I've implemented: http://easycalculati...-regression.php

My problem with the current linear regression implementation:
The purple line fitted to the white points should be vertical, not horisontal:

However, if I swap x and y data, it works:

However, in the game where I use this function, I can't swap x and y, because the function must work every direction. Same problems in-game:
The purple line is fitted by my function to the white points inside the green box, but the correctly fitted line would be like the orange one which I have drawn by hand:

Here is my code:
(It's the algorithm from the link above, I've only added two checks not to divide by zero.)
[source lang="cpp"]//return: equation of line: y = *retA + (*retB)*x//p is a vector containing the points, CVector2 is my class containing two double values, x and yvoid gLinReg( std::vector< CVector2 >* p, double* retA, double* retB) { unsigned int i; std::vector<double> xy, x2; double sx=0.0, sy=0.0, sxy=0.0, sx2=0.0; //the number of values unsigned int n = p->size(); if( n == 0 ) { return; } //find X*Y and X^2 for all values for(i=0; i<n; i++) { xy.push_back( p->at(i).x*p->at(i).y ); x2.push_back( p->at(i).x*p->at(i).x ); } //find sumx, sumy, sumxy, sumx2 for(i=0; i<n; i++) { sx += p->at(i).x; sy += p->at(i).y; sxy += xy.at(i); sx2 += x2.at(i); } //get slope //B = (NSXY - (SX)(SY)) / (NSX2 - (SX)2) double denom = (n*sx2 - sx*sx); //the denominator //prevent dividing by 0 in the next step if( denom == 0.0 ) { *retB = signF((n*sxy - sx*sy))*100.0; //*100 instead of / (NSX2 - (SX)2) to get a big slope //signF is just a sign function returning 1 or -1 } else *retB = (n*sxy - sx*sy) / (n*sx2 - sx*sx); //get the interception point //Intercept(a) = (SY - b(SX)) / N *retA = (sy - (*retB)*sx) / n; }[/source]

And Here is how I use it:
[source lang="cpp"]//... std::vector< CVector2 > p; p.push_back(CVector2(60,10)); p.push_back(CVector2(60,20)); p.push_back(CVector2(60,80)); p.push_back(CVector2(60,90)); p.push_back(CVector2(60,100)); p.push_back(CVector2(55,30)); p.push_back(CVector2(45,40)); p.push_back(CVector2(40,50)); p.push_back(CVector2(40,60)); p.push_back(CVector2(50,70)); int c; double rA, rB; gLinReg( &p, &rA, &rB); drawLine( game.screen, rA, rB, 50); for(c=0; c < p.size(); c++) pixelRGBA( game.screen, p.at©.x, p.at©.y, 0xFF, 0xFF, 0xFF, 0xFF );//...//And here is how I draw the line for testing://px is the center of the linevoid drawLine( SDL_Surface* dest, double A, double B, int px) { CVector2 lineA, lineB; lineA.set( px-50, A+B*(px-50)); lineB.set( px+50, A+B*(px+50)); lineRGBA( dest, lineA.x, lineA.y, lineB.x, lineB.y, 0xFF, 0, 0xFF, 0xFF );}[/source]