More on GDP (PPP) and life expectancy

I've reworked my charts illustrating life expectancy as a function of Purchasing Power Parity per capita for about 220 countries. I've used a scatter chart this time. It looks like this:

When we add a linear regression trendline, it fits like this:

When we apply a 2nd order polynomial trend line, it fits like this:

Neither trendline fits great and I don't know enough about fitting lines to data to know what to make of them. The linear regression line seems particularly off the mark for the high end PPPs. The polynomial looks to my eyes like it fits better, though the highest PPP (Luxembourg) looks left out.

Anyone know anything about these trendlines and how you know if they mean something?

As I mentioned earlier, all the data is from the CIA World Factbook: https://www.cia.gov/library/publications/the-world-factbook/docs/rankorderguide.html.