3. More depth - the normal scores plot

Most model diagnostics (here the model is the normal distribution for the error terms) compare reality (what we observe) to theory (what we expect). In general OBSERVED versus EXPECTED.

This is how the normal scores plot is constructed.

On the X-axis is what we expect.

On the Y axis is what we observe.

The idea is simple: say there were 100 observations (n = 100) and therefore 100 residuals.

The model says that the residuals come from an approximate normal distribution.

Now order the residuals from lowest to highest.

Where would you expect the smallest of 100 observations from a normal distribution to lie?

Plot where you expect it to be against where it actually is.

Repeat for the other 99 points.

If the model is correct than theory and reality should coincide, ie observed equals expected and the points should roughly (because there's inherent variability) lie along a line.

Extension.

There is no reason why for the X-axis we have to use the normal distribution, perhaps the data has a gamma distribution (useful for life length data). You just calculate where you EXPECT the data to be if a gamma distribution is true. These more general plots are called Quantile-Quantile or Q-Q plots.