A numerical representation of distance from a regression line?

[Mark Richards]

Hello

Am a novice Stata user/ statistician. I have created a two way scatter of aggregated travel distances (y axis) and passenger counts (x axis) for suburbs of Cape Town. This I created from aggregated data bins from the original dataset using a collapse function (I think this was the correct method).I have a regression line. The data has non-normal distribution. I am trying to identify the 'worst outliers' for travel distance per capita. Is there a way to represent this in a numerical way? I can 'see' them on the graph, but for accuracy I would like to isolate the top 5 locations and describe them with more detail.

Many thanks. Mark

[Carlo Lazzaro]

Mark:
see Leverage statistics paragraph, -regress postestimation- entry, Stata .pdf manual.

[Nick Cox]

The appropriate measure of distance of any point from a regression line is the residual, obtainable through the predict command.

Working on log scale is surely indicated. Some bigger deviations from the regression line are likely to be just a side-effect of heteros{c|k}edasticity and would be moderated by working on log scale.

[Hemanshu Kumar]

Carlo Lazzaro aren't leverage statistics more a measure of how much of an outlier the predictor values are, rather than how far the predicted values are from the observed regressand? For what Mark has asked for, I am rather more inclined to suggest looking directly for large (absolute values of) residuals. You might want to

predict e, resid

and then look into outliers, perhaps using a boxplot, or less visually, using Nick's command:

extremes e

NB. The command is available from SSC, via

ssc install extremes

That said, the graph seems to show an almost canonical case of heteroskedasticity, with the variance of travel distance increasing in passenger count, and the suggestion in #3 of working with logs would mitigate this issue.

[Carlo Lazzaro]

Hemanshu:
I thought that Mark had already taken a look at his regression residuals.

[Mark Richards]

Many thanks everyone for your thoughts. Much appreciated.

Time to hit the books. Will also amend to logs and see that unfolds.

Mark