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Least Squares Approximation
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Main Concept
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The least-squares approximation to a set of data points ![x[i], y[i]](/support/helpjp/helpview.aspx?si=8451/file02288/math32.png) is the line  that comes closest to going through all the points, in the following sense:
The sum of the squares of all the errors (the difference in the y-value between the data point and the closest point on the line) is minimized.
The problem is to find values  and  such that the sum ![(∑)[y[i]- (a+b*x[i])]^(2)](/support/helpjp/helpview.aspx?si=8451/file02288/math60.png) is minimal.
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Click on the graph to create the set of data. The total area covered by all the purple squares represents the error that should be minimized.
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