## In regression, we assume noise is independent of all measured predictors. What happens if it isn't?

A number of key assumptions underlie the linear regression model - among them linearity and normally distributed noise (error) terms with constant variance In this post, I consider an additional assumption: the unobserved noise is uncorrelated with any covariates or predictors in the model.
In this simple model:
\[Y_i = \beta_0 + \beta_1X_i + e_i,\]
\(Y_i\) has both a structural and stochastic (random) component. The structural component is the linear relationship of \(Y\) with \(X\).
[Read More]