Least Square Method(Least Mean Square)

• Least Square Method(Least Mean Square)

 

 

The way how to obtain parameters to minimize the sum of data and residual(error).

In other words, to obtain parameters(a, b) with minimum E.

 

- y = f(x) : Linear

- ei : Residual(Error)

- (xi, yi) : Data

- a, b : Parameters

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• y = f(x) : Linear Regression

 

It can be expressed as below.

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• Error

 

Distance between the point and y.

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• Sum of the square errors 

 

 

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• Matrix Equation

 

 

Y : Data y.

A : Data x, Column vectors with all elements 1.

X : The goal, a coefficient of 'y = ax + b'.

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1. 

 

ax + b = y is same as below.

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2. Get X.

 

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Example.

 

1) Data

 

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2) Set the Y, A, X

 

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3) Get X.

 

 

4) Get the Linear Regression

 

 

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