Least Squares Approximation
The least-squares approximation to a set of data points xi, yi is the line y=a⋅x+b 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 a and b such that the sum ∑inyi− a+b⋅xi2 is minimal.
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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