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Comment: Apparently mutlivariate regression ~= multiple regression
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| ## page was renamed from Econometrics/OrdinaryLeastSquares/Multivariate = OLS Multivariate Derivation = |
= OLS Multiple Regression Derivation = |
OLS Multiple Regression 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.
