Least-Square Multiple Regression
engineering fundamentals Least-Square Multiple Regression
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Multiple Regression

Multiple regression estimates the outcomes (dependent variables) which may be affected by more than one control parameter (independent variables) or there may be more than one control parameter being changed at the same time.

An example is the two independent variables x and y and one dependent variable z in the linear relationship case:

z=ax+by

For a given data set (x1,y1,z1), (x2,y2,z2), ..., (xn,yn,zn), where n>=3, the best fitting curve f(x) has the least square error, i.e.,

Please note that a, b, and c are unknown coefficients while all xi, yi, and ziare given. To obtain the least square error, the unknown coefficients a, b, and c must yield zero first derivatives.

Expanding the above equations, we have

The unknown coefficients a, b, and c can hence be obtained by solving the above linear equations.

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