Econometrics

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$\mathbf{b} = \left[\begin{array} {} b_0\\ b_1\\ \vdots\\ b_{p-1} \end{array}\right] = \mathbf{(X'X)^{-1}X^{\prime}y}$

Linear Algebra	Enter the Matrix
$\mathbf{y} = \mathbf{Xb}$	Linear Regression
$\mathbf{(X'y) =X^{\prime}Xb}$	Pre-multiply both sides of the equation by X’ in order to solve for b
$\mathbf{(X'X)^{-1}X'y =(X^{\prime}X)^{-1}(X^{\prime}X)b}$	Multiply (X’X)-1 by this inverse
$\mathbf{(X'X)^{-1}X'y = Ib}$	A matrix multiplied by its inverse is the identity matrix (I)
$\mathbf{(X'X)^{-1}X'y = b}$	OLS
$\mathbf{b} = \mathbf{(X'X)^{-1}X^{\prime}y}$	OLS

Linearity $Y_t = \alpha + \beta X_t + ε_t$
Expected value of error term is zero $E(ε∣X) = 0$
X is non-stochastic and fixed in repeated samples $Cov(X_s, ε_t) = 0$
Serial Independence $Cov(ε_s, ε_t) = 0$
Homoskedasticity $Var(ε_t) = \sigma^2 = constant$
No Multicollinearity $\sum_{t=1}^{T} (\delta_iX_{it} + \delta_jX_{jt}) \neq 0 \text{ and } i \neq j$
Normality of error term
$ε_t \sim N(\mu,\sigma^{2})$