"It's how perfectly you can fit a straight line to them."
You can be mathematically accurate without being mathematically precise. Better imprecise but correct than incorrect but precise.
If you're trying to give a quantitative lay picture of what exactly 0.56 linear correlation means, you need to still be quantitatively right, while the above are quantitative. Pictures and examples can help. "For perspective, 0.56 is about the correlation between <example> and <example>"
Saying there is a quantitative strength to a relationship is, to a regular person, meaningless. Am I .56 in love with my wife?
Can I fit in a straight line to her?
These are not good descriptions. Of course HN is full of data scientists who wildly object to oversimplifying statistical relationships -- luckily you are here to give the detailed mathematical context. But these are not simplified descriptions for a general audience.
> Saying there is a quantitative strength to a relationship is, to a regular person, meaningless.
That the average person would not understand a particular accurate description of a subject does not, in and of itself, make a completely inaccurate alternative description less wrong or even a good simplification.
