Main Concept

The least-squares approximation to a set of data points $\left(x_i\, y_i\right)$ is the line $y\=a\cdot x\+b$ 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 $\sum _i^n{\left[y_i- \left(a\+b\cdot x_i\right)\right]}^2$ is minimal.

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MathApps/ProbabilityAndStatistics