Least-squares line fitting - Revision history

A WASSERMANN at 18:16, 9 November 2010

2010-11-09T18:16:00Z

← Older revision		Revision as of 18:16, 9 November 2010
Line 1:		Line 1:
	This little JXSGraph application finds the line or the circle which is the best fit for given set of points.		This little JXSGraph application finds the line or the circle which is the best fit for given set of points.
			If the resulting line is green, it is a straight line. If the line is blue, it is a circle.

	<jsxgraph width="600" height="600">		<jsxgraph width="600" height="600">

A WASSERMANN at 18:14, 9 November 2010

2010-11-09T18:14:53Z

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A WASSERMANN at 18:12, 9 November 2010

2010-11-09T18:12:22Z

← Older revision		Revision as of 18:12, 9 November 2010
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	// Experiments with lines and circles:		// Experiments with lines and circles:
	~~if (false) {~~
	// Plot random points on a line disturbed by a random factor		// 1) Plot random points on a line disturbed by a random factor
	var i, p = [], angle, xr, yr, delta = 0.1;		var i, p1 = [], angle, xr, yr, delta = 0.1;

	// Random points are constructed which lie roughly on a line		// Random points are constructed which lie roughly on a line
Line 127:		Line 127:
	yr = 10*(Math.random()-0.5);		yr = 10*(Math.random()-0.5);
	xr = 0.yr+delta(Math.random()-0.5);		xr = 0.yr+delta(Math.random()-0.5);
	p.push(brd.create('point',[xr, yr], {withLabel:false}));		p1.push(brd.create('point',[xr, yr], {withLabel:false}));
	}		}
	~~} else {~~
	// Plot random points on a circle disturbed by a random factor		// 2) Plot random points on a circle disturbed by a random factor
	var i, p = [], angle, co, si, delta = 0.2;		var i, p2 = [], angle, co, si, delta = 0.2;

	// Random points are constructed which lie roughly on a circle		// Random points are constructed which lie roughly on a circle
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	co = 4Math.cos(angle)+delta(Math.random()-0.5);		co = 4Math.cos(angle)+delta(Math.random()-0.5);
	si = 4Math.sin(angle)+delta(Math.random()-0.5);		si = 4Math.sin(angle)+delta(Math.random()-0.5);
	p.push(brd.create('point',[co+2, si-1], {withLabel:false}));		p2.push(brd.create('point',[co+2, si-1], {withLabel:false}));
	}		}
	}
	brd.unsuspendUpdate();		brd.unsuspendUpdate();

			var bestFit = function(p) {
	//		//
	// From here on, the best-fitting circle or line is found by least-squares fitting.		// From here on, the best-fitting circle or line is found by least-squares fitting.
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	brd.create('circle',[[zm,xm,ym],radius]);		brd.create('circle',[[zm,xm,ym],radius]);
	}		}

			}; // end of bestFit()

			bestFit(p1);
			bestFit(p2);

	</source>		</source>

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Statistics]]		[[Category:Statistics]]

A WASSERMANN at 18:11, 9 November 2010

2010-11-09T18:11:31Z

← Older revision		Revision as of 18:11, 9 November 2010
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	}		}
	brd.unsuspendUpdate();		brd.unsuspendUpdate();

	~~bestFit(p1);~~
	~~bestFit(p2);~~

	var bestFit = function(p) {		var bestFit = function(p) {
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	}		}

	};		}; // end of bestFit()

			bestFit(p1);
			bestFit(p2);

	</jsxgraph>		</jsxgraph>

A WASSERMANN at 18:11, 9 November 2010

2010-11-09T18:11:00Z

← Older revision		Revision as of 18:11, 9 November 2010
Line 6:		Line 6:

	// Experiments with lines and circles:		// Experiments with lines and circles:
	// Plot random points on a line disturbed by a random factor
			// 1) Plot random points on a line disturbed by a random factor
	var i, p1 = [], angle, xr, yr, delta = 0.1;		var i, p1 = [], angle, xr, yr, delta = 0.1;

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	}		}

	// Plot random points on a circle disturbed by a random factor		// 2) Plot random points on a circle disturbed by a random factor
	var i, p2 = [], angle, co, si, delta = 0.2;		var i, p2 = [], angle, co, si, delta = 0.2;

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	}		}
	brd.unsuspendUpdate();		brd.unsuspendUpdate();

			bestFit(p1);
			bestFit(p2);

	var bestFit = function(p) {		var bestFit = function(p) {

A WASSERMANN at 18:10, 9 November 2010

2010-11-09T18:10:19Z

← Older revision		Revision as of 18:10, 9 November 2010
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	p2.push(brd.create('point',[co+2, si-1], {withLabel:false}));		p2.push(brd.create('point',[co+2, si-1], {withLabel:false}));
	}		}
	}
	brd.unsuspendUpdate();		brd.unsuspendUpdate();

A WASSERMANN at 18:09, 9 November 2010

2010-11-09T18:09:51Z

← Older revision		Revision as of 18:09, 9 November 2010
Line 6:		Line 6:

	// Experiments with lines and circles:		// Experiments with lines and circles:
	~~if (false) {~~
	// Plot random points on a line disturbed by a random factor		// Plot random points on a line disturbed by a random factor
	var i, p = [], angle, xr, yr, delta = 0.1;		var i, p1 = [], angle, xr, yr, delta = 0.1;

	// Random points are constructed which lie roughly on a line		// Random points are constructed which lie roughly on a line
Line 18:		Line 17:
	yr = 10*(Math.random()-0.5);		yr = 10*(Math.random()-0.5);
	xr = 0.yr+delta(Math.random()-0.5);		xr = 0.yr+delta(Math.random()-0.5);
	p.push(brd.create('point',[xr, yr], {withLabel:false}));		p1.push(brd.create('point',[xr, yr], {withLabel:false}));
	}		}
	~~} else {~~
	// Plot random points on a circle disturbed by a random factor		// Plot random points on a circle disturbed by a random factor
	var i, p = [], angle, co, si, delta = 0.2;		var i, p2 = [], angle, co, si, delta = 0.2;

	// Random points are constructed which lie roughly on a circle		// Random points are constructed which lie roughly on a circle
Line 33:		Line 32:
	co = 4Math.cos(angle)+delta(Math.random()-0.5);		co = 4Math.cos(angle)+delta(Math.random()-0.5);
	si = 4Math.sin(angle)+delta(Math.random()-0.5);		si = 4Math.sin(angle)+delta(Math.random()-0.5);
	p.push(brd.create('point',[co+2, si-1], {withLabel:false}));		p2.push(brd.create('point',[co+2, si-1], {withLabel:false}));
	}		}
	}		}
	brd.unsuspendUpdate();		brd.unsuspendUpdate();

			var bestFit = function(p) {
	//		//
	// From here on, the best-fitting circle or line is found by least-squares fitting.		// From here on, the best-fitting circle or line is found by least-squares fitting.
Line 101:		Line 101:
	brd.create('circle',[[zm,xm,ym],radius]);		brd.create('circle',[[zm,xm,ym],radius]);
	}		}

			};

	</jsxgraph>		</jsxgraph>

A WASSERMANN at 18:07, 9 November 2010

2010-11-09T18:07:40Z

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A WASSERMANN at 18:01, 9 November 2010

2010-11-09T18:01:21Z

← Older revision		Revision as of 18:01, 9 November 2010
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	var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5], keepaspectratio:true, axis:true});		var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5], keepaspectratio:true, axis:true});
	brd.suspendUpdate();		brd.suspendUpdate();
	if (~~true~~) {		if (false) {
	var i, p = [], angle, xr, yr, delta = 0.1;		var i, p = [], angle, xr, yr, delta = 0.1;

A WASSERMANN at 18:00, 9 November 2010

2010-11-09T18:00:45Z

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