What do parallel lines in a fitted values vs. residual plot mean? How should I transform my data?

Question

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Parallel lines on residual vs fitted plot

I'm regressing the time it took for an event to happen on another, normally-distributed predictor.

When I plot the fitted values against the residuals, the data line up in a series of parallel lines (with negative slopes).

The Q-Q plot is sigmoidal, but not too too bad.

Any suggestions for what I should do to my data?

Transform the response variable? Use a generalized linear model (glm) instead? If the latter, what family of error distribution should I use?

Many, many thanks!

Answer 1

You said the qq-plot has a sigmoidal shape but not too bad. If it's not too bad then just use what you have. Your series of parallel lines with negative slopes is hard to imagine as well. It does sound like there's some pattern happening in the data that your regression isn't explaining. Without seeing your actual figures it's hard to tell if you have any problem at all.

Time variables often have tails out to the right. Often a useful transform is rate. Right now you might have the time it took something to occur in seconds. Let's say it took 2s for something to occur. The rate would be 0.5 occurrences / second. The transform is just 1/t. That might fix your qq-plot but it would just change the parallel lines, not eliminate them.