Least Squared Error Solution

Learn about approximating the solution of an inconsistent linear system through least squares.

Squared error

Squared distance is also known as squared error. Consider a linear equation in wiw_i's:

w1a1+w2a2+...+wnan=bw_1a_1+w_2a_2+...+w_na_n=b

The squared error (squared distance) on a given point, (w^1,w^2,...,w^n)(\hat w_1,\hat w_2,...,\hat w_n), is defined as:

SE(w^1,w^2,...,w^n)=(w^1a1+w^2a2+...+w^nanb)2SE(\hat w_1,\hat w_2,...,\hat w_n)=(\hat w_1a_1+\hat w_2a_2+...+\hat w_na_n-b)^2

Note: In the case of w=w^w=\hat{w}, the sum of squared errors=0. This implies that we’re able to find an exact solution.

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