# Econometric Theory/Multiple Regression Analysis

Our first regressions (MLE and OLS) were bivariate. Our lines were simple, two variable lines. However, in most economic data, there are a multitude of possible independent things that can effect a dependent variable. So we can expand our explanatory functions to allow multiple independent variables.

Instead of our functions looking like $Y_=\alpha + \beta X_i + \epsilon_i$, our functions look like $Y_i = \beta_0 + \beta_1 X_{1,i} + \beta_2 X_{2,i} + \cdots + \beta_n X_{n,i} + \epsilon_i$

By adding more variables and data to our model, we can hopefully get a better fit and understanding of the dependent variable. However, with the added variables come added problems that will misguide our model.

## Goodness of FitEdit

$\bar{R^2} = 1 - (\frac{\hat{var(\epsilon)}} {\hat{var(Y)}})$