Residuals (the difference between a model's prediction and the observed values) provide an essential tool for diagnosing assumption violations in regression models. Should the underlying data of a regression model not satisfy basic assumptions like independence of residuals, constant variance, and linear form, the results are potentially invalid. Fortunately, for almost every violation there exists a method to transform the data into an assumption-satisfying form. A least squares regression is one of the most basic and widely used models in statistics and we ought to use residual analysis to ensure correct usage. The scope of this notebook includes residual basics and calculation, error, residual plots, and tests and fixes for common regression assumption violations.
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