# How to tell that a reciprocal relationship exists by a residual plot?

I'm following an example from the book "R by Example", where they talk about two-way ANOVA.

The database used in poison. The analysis is:

L <- aov(Time ~ Poison * Treatment, data = poison)


Further on, the book says:

The residual plots suggest a reciprocal transformation of the response (poison survival time) (The dependent variableTime)...

That is, a more appropriate variable would be 1/Time.

Here is the residual plot, using plot(L):

I guess that the reciprocal relationship is evident by the gradually increasing residuals. Why is this correct?

When making the reciprocal model using L <- aov(1/Time ~ Poison * Treatment, data = poison), the residual plot no longer has this property:

So my questions is how could I've known that the special pattern in the first residual plot suggests a reciprocal relationship?

• Use a spread-vs.-level plot. I explain and illustrate their use at stats.stackexchange.com/a/74594/919 and you can find more about them by searching our site. With a little practice one can eyeball a residuals vs. fitted plot and imagine the resulting spread-vs.-level plot (although many people have been fooled by the visual variation that occurs when residuals are clustered within horizontal bands).
– whuber
Dec 9, 2014 at 20:01