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OLS Multivariate Derivation

The model is constructed like:

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:

model2.svg

with the constraint:

model3.svg

The partial derivative of this constraint with respect to b is calculated like:

b1.svg

b2.svg

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

b3.svg

b4.svg

b5.svg

b6.svg

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Statistics/OrdinaryLeastSquares/Multiple (last edited 2025-09-24 13:43:06 by DominicRicottone)