At what age are people being described as being old? I saw the figure below getting a lot of attention on Twitter with the description: ‘As a kid my dad told me “The age you consider ‘old’ is the square-root of your age times 10”. At 9 you think 30 is old, at 16 you think 40, etc. Turns out he was wrong. It’s the square-root of your age times 8.’
That is a great fit, i.e. the overlap between the blue and the orange line, but is it true? A follow-up tweet describes that the figure shows the answers from ~200 people. That is not a lot.
I always tell my students that they should never go out and collect low-quality data if they can download high-quality secondary data for free. Luckily, the European Social Survey (round 4) provides data on this exact question for more than 50,000 respondents. Using this data, I replicated the figure:
In this figure we do not see as great a fit as in the other figure. For 18-year-olds the average answer is 57 years. For 25-year-olds the average answer is 60. This is far from the estimates we get with the square-root of the respondent’s age times 8.
The lesson? Do not overfit your model (especially not to your N≈200 sample).