= OLS Multivariate Derivation =

The model is constructed like:

{{attachment:model1.svg}}

where:

 * ''y'' and ''ε'' are vectors of size ''n''
 * ''β'' is a vector of size ''p''
 * '''''X''''' is a matrix of shape ''n'' by ''p''

This is estimated as:

{{attachment:model2.svg}}

with the constraint:

{{attachment:model3.svg}}

The [[Calculus/PartialDerivatives|partial derivative]] of this constraint with respect to ''b'' is calculated like:

{{attachment:b1.svg}}

{{attachment:b2.svg}}

Set this derivative to 0 to find the minimum with respect to ''b''.

{{attachment:b3.svg}}

{{attachment:b4.svg}}

{{attachment:b5.svg}}

{{attachment:b6.svg}}




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CategoryRicottone