You can give the bubbles different colors with the Background Color setting of the x-axis expression. See attached example.
If you want the quadrants themselves to have background colors you need to used colored textboxes and put the scatter chart on top of them and make the plot area transparent.
UN data.qvw 255.0 K
I checked the file, i wanted similar to that functionality,
but you have given the conditions in background color of expression like
if([Per capita GDP]>3000 and [Life expectancy]>60, blue(),
if([Per capita GDP]<3000 and [Life expectancy]<60, red(),
if([Per capita GDP]>3000 and [Life expectancy]<60, green(),
but in my case, [Per Capita GDP] is a huge expression and 3,000 value also is an expression stored in a variable.
The quadrants are dynamic based on selection.