|
Size: 797
Comment: Killing Econometrics page
|
← Revision 11 as of 2025-09-24 13:43:06 ⇥
Size: 730
Comment: Updated link
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| ## page was renamed from Econometrics/OrdinaryLeastSquares/Multivariate = OLS Multivariate Derivation = |
= OLS Multiple Regression Derivation = |
| Line 22: | Line 21: |
| The [[Calculus/PartialDerivatives|partial derivative]] of this constraint with respect to ''b'' is calculated like: | The [[Calculus/PartialDerivative|partial derivative]] of this constraint with respect to ''b'' is calculated like: |
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.
