STAT W21 Lecture Notes - Lecture 11: Heteroscedasticity, Regression Fallacy, Homoscedasticity

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11 Sep 2017
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Rms: measure of the typical size of elements in a list well. Regression line is a horizontal line at height mean(y), so the rms of the vertical residuals is zero. If the scatterplot is football-shaped, the regression line follows the graph of averages reasonably. The sd of the values of y in the slice are thus approximately the rms of the residuals in. Football-shaped scatterplots are homoscedastic the vertical residuals of those values of y from their regression line the slice. When the scatterplot is not football-shaped, the rms error of regression is not a good measure of the scatter in a typical vertical slice. If a scatterplot is heteroscedastic and shows linear association. The rms error of regression will overestimate the scatter in some slices and underestimate the scatter in other slices. The rms error of regression will tend to overestimate the scatter in slices. If a scatterplot has outliers and is otherwise homoscedastic and shows linear association.

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