STAT W21 Chapter Notes - Chapter 11: Heteroscedasticity, Homoscedasticity, Scatter Plot
Chapter 11: Errors in Regression
● The regression line generally doesn’t go through all of the data
● The vertical amount by which the line misses a datum is called a residual
● The RMS of the residuals have a simple relation to the correlation coefficient and SD of
Y is (1-r^2)^0.5 * SD(Y)
The RMS Error of Regression
● Regression line doesn't pass through all of the data points on the scatterplot exactly
unless the correlation coefficient is +/- 1
● If the scatterplot is football shaped the mean of the values in a thin vertical strip will be
able the same as the height of the regression line and the SD of the values in a vertical
strip will be able the same as the rms vertical error of regression
● Football shaped scatterplots are homoscedastic
○ The SD of the values of Y in every vertical slice is about the same
○ It also shows nonlinear association
● If the scatter plot is heteroscedastic and hows liberal association the rms error of
regression will overestimate the scatter in some slices and overestimate in other slices
Example:
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