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| = Ordinary Least Squares Multivariate Proof = | = OLS Multivariate Derivation = |
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| The partial derivative of this constraint with regard to ''b'' is calculated like: | The [[Calculus/PartialDerivatives|partial derivative]] of this constraint with respect to ''b'' is calculated like: |
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| {{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}} |
OLS Multivariate Derivation
The model is constructed like:
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:
with the constraint:
The partial derivative of this constraint with respect to b is calculated like:
Set this derivative to 0 to find the minimum with respect to b.
