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    <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 &lt; data.length; i++) { fitter.add(i, data[i]); } return fitter.project(x); } </code></pre> <p><strong>Example:</strong></p> <pre><code>&gt;&gt;&gt; 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 &lt; data.length; i++) { fitter.add(i, data[i]); } return fitter.project(60); } </code></pre> <p><strong>Example2:</strong></p> <pre><code>&gt;&gt;&gt; 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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    1. COI'd seriously suggest finding a curve-fitting library in some other language and translating what you need to JavaScript rather than trying to directly implement textbook formulas. The problem is that textbook formulas are often numerically unstable, which is to say that they're really sensitive to the difference between floating-point representations of numbers and actual mathematical numbers. For example, any calculation that potentially involves subtracting one large number from another large number is likely to be overcome with rounding errors if the two numbers are close to each other.
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