Deer jaw length and weight


The long tails to the residual distribution may be caused by a few outliers.


This page gives examples of residual probability plots. Explain that the crosses should be close to a straight line if all is well.

A simulation using data from the best-fitting normal linear model can be used to help assess whether the curvature in a probability plot is more than would be expected 'by chance' if the model is really OK.

Deer jaw length and weight

Select Random Normal Data then take several samples from the best-fitting normal linear model.

The probability plot from the data seems more curved than the random ones, suggesting that there is a problem. In the first example, the error distribution may be longer-tailed than a normal distribution or there may be a few outliers.

Warning:

If the other assumptions are violated, the probability plot of residuals will often be curved.

Antibiotic effectiveness

Again select Random Normal Data and take several samples from the best-fitting normal linear model.

Curvature in the probability plot here is probably caused by nonlinearity in the relationship between inhibition diameter and concentration — it makes the residual distribution seem to have tails that are too short.

British Airways share price

Again examine probability plots from the best-fitting normal linear model and observe that the curvature observe is greater than would be seen by chance.

The curvature in the probability plot suggests a skew residual distribution but is linked to non-constant variance in the scatterplot. If log(share price) is used as the response variable, the probability plot would be linear.

Deer jaw length and weight
Jaw lengths and body weights were recorded from 150 male deer that were shot in the Ruahine Ranges in New Zealand between November 1981 and November 1982.
Antibiotic effectiveness
An experiment was conducted to assess how well an antibiotic, polymyxin B, killed the bacterium, Brucella bronchiseptica. Petri dishes containing the bacterium (grown in agar) were used and different doses of the antibiotic were added. The diameter of the area cleared around the addition point were recorded. Each of 6 different doses of antibiotic was used 10 times.
British Airways share price
This data set gives the volume of British Airways shares traded in each of the first 57 trading days of 2002 — between 2nd January and 21st March — and the closing share price.