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I placed a regression line through data purely as a visual aid:

enter image description here

The problem is there is a non-trivial risk that someone (especially non-statisticians) may interpret this regression line through the time series as predictive and hence assume it can be used to make estimations about the future (generally a bad idea).

What I know so far

I considered:

  • Avoiding the use of the word "trend", since it doesn't imply historical-only or future.
  • A disclaimer: "past trends do not predict future results" (similar to financial documents).

Question

Are there any better ways of placing a line through data such that it serves as a visual aid and is unambiguously not to be used for extrapolation?

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  • $\begingroup$ Best way to prevent a shark attack is to stay out of the water. If you are afraid people are going to interpret it one way, I would suggest just leaving it out and finding a better way to make your point. $\endgroup$
    – Demetri Pananos
    Commented Jan 29, 2022 at 5:16
  • $\begingroup$ @DemetriPananos that’s logical. Suppose that having it helps as a visual aid because it illuminates and smooths the historical data, making it obvious even just from a glance. Is there a way to have one’s cake and eat it too (or to go swimming and avoid the sharks)? $\endgroup$
    – stevec
    Commented Jan 29, 2022 at 5:22

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Unfortunately, people will tend to extrapolate if you slap a regression line on a time series, especially if it's about an intriguing topic. So I think your options are (from best to worst):

  1. Don't add a regression line at all. What is it intended to convey here, after all? We can see without it that salaries have been lower on average in the last couple of years. If anything, the regression line draws attention away from the possible return to previous salary levels in 2022. There's an interesting and possibly pandemic-related story to be told here, and the regression line hides that a bit.
  2. Use a different visual depiction that smoothes the line but is not a simple straight line. and s are both reasonable options that may incidentally highlight that increase in 2022.
  3. Add an explicit warning such as "The regression line is intended as a visual aid only and we do not advise using this to predict future salaries. Extrapolation of simple regression trends produces very poor results for most such time series'
  4. Get more serious about modelling the time series and account for autocorrelation, nonlinear change and uncertainty appropriately. One would hope then that the confidence (or prediction) intervals would accurately reflect uncertainty, instead of being inappropriately narrow because of using a poor model.
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