Multiple regression

Multiple regression
You are encouraged to solve this task according to the task description, using any language you may know.

Given a set of data vectors in the following format:

$y=\{y_{1},y_{2},...,y_{n}\}\,$

$x_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,$

Compute the vector $\beta =\{\beta _{1},\beta _{2},...,\beta _{n}\}$ using ordinary least squares regression using the following equation:

$y_{i}=\beta \cdot x_{i}\,$

You can assume y is given to you as an array, and x is given to you as a two-dimensional array.

Ruby

Using the standard library Matrix class:

<lang ruby>require 'matrix'

def regression_coefficients y, x

 y = Matrix.column_vector y.map { |i| i.to_f }
 x = Matrix.columns x.map { |xi| xi.map { |i| i.to_f }}

 (x.t * x).inverse * x.t * y

end </lang>

Testing: <lang ruby> regression_coefficients([1, 2, 3, 4, 5], [ [2, 1, 3, 4, 5] ]) # => Matrix0.981818181818182 </lang>