The top chart shows that the relationship between unemployment and wage growth isn't as strong as you'd think. Recent research highlighted by Fed President Bullard made the same observation. But the bottom chart -- now that's what a tight correlation looks like!
I ran a quick, down-and-dirty calculation from FRED data using simple correlation analysis, but I used the employment to population rate and the Y/Y percentage change in average hourly earnings of all employees. Here's the scatterplot:
The correlation was .68 -- pretty high.
Here's a chart of the prime age employment ratio:
It's still low; it only just attained levels seen at the low of the last recession, meaning this analysis could be on to something.