Spread-Location Regression Diagnostic Check

random seed

4511

sample size n

100

λ

1

The spread-location plot from a linear regression shown on the left is a plot of

(λ)



e

i



versus



y

i

, where

i=1,…,n

,

(λ)



e

i



is the power transformation of the absolute residual, and



y

i

is the fitted value.

The red line is a nonparametric smoother used to enhance the visualization. The purpose of this plot is to check for possible model mis-specification caused by monotonic change in variance related to the level as estimated by the fitted values. On the right, the box-whisker chart of the

(λ)



e

i



is shown. By adjusting the power transformation parameter

λ

to make the distribution of the

(λ)



e

i



more symmetric, the visualization of the spread-location relationship is improved. Some popular software programs fix

λ=0.5

, but this Demonstration illustrates that this might not always be the best choice. Vary the sample size,

n

, and the random seed to see the impact of sample size and randomness. See Details for further discussion.