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copied!<p>You can do a <a href="http://en.wikipedia.org/wiki/Simple_linear_regression" rel="nofollow">least-squares fit</a> of a line.</p> <pre><code>function LineFitter() { this.count = 0; this.sumX = 0; this.sumX2 = 0; this.sumXY = 0; this.sumY = 0; } LineFitter.prototype = { 'add': function(x, y) { this.count++; this.sumX += x; this.sumX2 += x*x; this.sumXY += x*y; this.sumY += y; }, 'project': function(x) { var det = this.count * this.sumX2 - this.sumX * this.sumX; var offset = (this.sumX2 * this.sumY - this.sumX * this.sumXY) / det; var scale = (this.count * this.sumXY - this.sumX * this.sumY) / det; return offset + x * scale; } }; function linearProject(data, x) { var fitter = new LineFitter(); for (var i = 0; i < data.length; i++) { fitter.add(i, data[i]); } return fitter.project(x); } </code></pre> <p><strong>Example:</strong></p> <pre><code>>>> linearProject([ 21410, 21886, 21837, 21895, 21564, 21714, 21571, 21324, 21310, 21390, 21764, 21598, 21493, 21352, 21478, 21058, 20942, 20825, 21321, 20950, 21039, 21117, 20733, 20773, 20929, 20900, 20687, 20999 ], 60); 19489.614121510676 </code></pre> <hr> <p>Doing something similar for a square polynomial is a little more complicated:</p> <pre><code>function SquareFitter() { this.count = 0; this.sumX = 0; this.sumX2 = 0; this.sumX3 = 0; this.sumX4 = 0; this.sumY = 0; this.sumXY = 0; this.sumX2Y = 0; } SquareFitter.prototype = { 'add': function(x, y) { this.count++; this.sumX += x; this.sumX2 += x*x; this.sumX3 += x*x*x; this.sumX4 += x*x*x*x; this.sumY += y; this.sumXY += x*y; this.sumX2Y += x*x*y; }, 'project': function(x) { var det = this.count*this.sumX2*this.sumX4 - this.count*this.sumX3*this.sumX3 - this.sumX*this.sumX*this.sumX4 + 2*this.sumX*this.sumX2*this.sumX3 - this.sumX2*this.sumX2*this.sumX2; var offset = this.sumX*this.sumX2Y*this.sumX3 - this.sumX*this.sumX4*this.sumXY - this.sumX2*this.sumX2*this.sumX2Y + this.sumX2*this.sumX3*this.sumXY + this.sumX2*this.sumX4*this.sumY - this.sumX3*this.sumX3*this.sumY; var scale = -this.count*this.sumX2Y*this.sumX3 + this.count*this.sumX4*this.sumXY + this.sumX*this.sumX2*this.sumX2Y - this.sumX*this.sumX4*this.sumY - this.sumX2*this.sumX2*this.sumXY + this.sumX2*this.sumX3*this.sumY; var accel = this.sumY*this.sumX*this.sumX3 - this.sumY*this.sumX2*this.sumX2 - this.sumXY*this.count*this.sumX3 + this.sumXY*this.sumX2*this.sumX - this.sumX2Y*this.sumX*this.sumX + this.sumX2Y*this.count*this.sumX2; return (offset + x*scale + x*x*accel)/det; } }; function squareProject(data) { var fitter = new SquareFitter(); for (var i = 0; i < data.length; i++) { fitter.add(i, data[i]); } return fitter.project(60); } </code></pre> <p><strong>Example2:</strong></p> <pre><code>>>> squareProject([ 21410, 21886, 21837, 21895, 21564, 21714, 21571, 21324, 21310, 21390, 21764, 21598, 21493, 21352, 21478, 21058, 20942, 20825, 21321, 20950, 21039, 21117, 20733, 20773, 20929, 20900, 20687, 20999 ], 60); 19282.85862700518 </code></pre> <p>I could do this for higher degree polynomials, but the expressions would get even longer. For arbitrary degree, you would have to look at matrices.</p>

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