Multiple regression

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.