2变量线性回归的方程式 [英] Equations for 2 variable Linear Regression

问题描述

我们使用的编程语言中没有线性回归函数.我们已经实现了一个变量线性方程:

y =轴+ B

，并使用类似于此堆栈溢出答案.

我知道，随着变量的添加，这个问题在几何上会变得更加困难，但是出于我们的目的，我们只需要再添加一个:

z =轴+ By + C

在给定x，y和z数组的情况下，是否有人拥有封闭形式的方程式或使用任何语言可以求解A，B和C的代码?

解决方案

因此您拥有三个线性方程式

k = aX1 + bY1 + cZ1
k = aX2 + bY2 + cZ2
k = aX3 + bY3 + cZ3

您可以做的是将其重写为matriz

| x1 y1 z1 | | a |   | k |
| x2 y2 z2 | | b | = | k |
| x3 y3 y3 | | c |   | k |

计算[a b c ]做以下矩阵运算

| a |              | x1 y1 z1 |     | k |
| b | =  inverse(  | x2 y2 z2 | )   | k |
| c |              | x3 y3 y3 |     | k |

可以在此处找到3x3矩阵逆的公式>

We are using a programming language that does not have a linear regression function in it. We have already implemented a single variable linear equation:

y = Ax + B

and have simply calculated the A and B coefficents from the data using a solution similar to this Stack Overflow answer.

I know this problem gets geometrically harder as variables are added, but for our purposes, we only need to add one more:

z = Ax + By + C

Does anyone have the closed form equations, or code in any language that can solve for A, B and C given an array of x, y, and z's?

解决方案

so you have three linear equations

k = aX1 + bY1 + cZ1
k = aX2 + bY2 + cZ2
k = aX3 + bY3 + cZ3

What you can do is rewrite it as matriz

| x1 y1 z1 | | a |   | k |
| x2 y2 z2 | | b | = | k |
| x3 y3 y3 | | c |   | k |

to work out [a b c ] do the following matrix operation

| a |              | x1 y1 z1 |     | k |
| b | =  inverse(  | x2 y2 z2 | )   | k |
| c |              | x3 y3 y3 |     | k |

The formula for a 3x3 matrix inverse can be found here

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