Lecture 2, The truth about linear regression: Using Taylor's theorem to justify linear regression locally. Collinearity. Consistency of ordinary least squares estimates under weak conditions (non-Gaussian noise, non-independent noise, non-constant variance, dependent predictors). Linear regression coefficients will change with the distribution of the input variables: examples. Why \( R^2 \) is usually a distraction. Linear regression coefficients will change with the distribution of unobserved variables (omitted variable effects). Errors in variables. Transformations of inputs and of outputs. Utility of probabilistic assumptions; the importance of looking at the residuals. What it really means when coefficients are significantly non-zero. What "controlled for in a linear regression" really means.
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