Multiple regression
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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:
Compute the vector using ordinary least squares regression using the following equation:
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>