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The Truth About Linear Regression

The Truth About Linear Regression

陈傲天
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Linear regression is optimal linear (mean-square) prediction; we do this because we hope a linear approximation will work well enough over a small range. What linear regression does: decorrelate the input features, then correlate them separately with the response and add up. The extreme weakness of the probabilistic assumptions needed for this to make sense. Difficulties of linear regression; collinearity, errors in variables, shifting distributions of inputs, omitted variables. The usual extra probabilistic assumptions and their implications. Why you should always looking at residuals. Why you generally shouldn't use regression for causal inference. How to torment angels. Likelihood-ratio tests for restrictions of nice models.
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