The spread-location plot was suggested in [1] and the version in this Demonstration in [2], which used

*Mathematica* to derive the optimal symmetrizing transformation for

for a variety of error distributions.

In this Demonstration, the linear regression

is fitted to data generated with

,

and

is t-distributed on four degrees of freedom,

is uniformly distributed on

, and

is set to

. So the linear regression model is mis-specified and a log transformation of the response variable is needed. The purpose of the spread-location plot is to detect this type of mis-specification. The loess smoother, shown in red, helps to show if there is a relationship between the variance as measured by

and the location as measured by

.

Snapshot 1: using a log-transformation,

, improves the visualization in the plot of

versus

for the data shown in the thumbnail, with

; the box-whisker chart confirms that

is more symmetrically distributed

Snapshot 2: referring again to the data used in the thumbnail, Snapshot 2 shows that

does not work as well

Snapshots 3 and 4: a smaller sample,

, is used; the effect of the skewness of

when

is less dramatic and so is the improvement in using

[1] W. S. Cleveland,

*Visualizing Data*, Summit, NJ: Hobart Press, 1993.

[2] A. I. McLeod, "Improved Spread-Location Visualization,"

*Journal of* *Computational and Graphical Statistics,* **8**(1), 1999 pp. 135–141.

doi:10.1080/10618600.1999.10474806.