Here's a linear regression that uses 5 parameters (6 including an intercept) to capture more than 5/6 of the variance while using up less than half of the degrees of freedom. This should be viewed as a descriptive dimensional reduction, i.e. an attempt to describe the data well with reasonably few parameters; when I'm doing something like inference or forecasting I have a stronger prejudice towards using fewer parameters and preserving more degrees of freedom (or at least regulating the fit somehow), but this is sufficiently pseudoscientific that I feel I might as well include the interaction terms that seem to pull their weight:
robust.se intercept 63437.5 1489.285 42.60 E 1375.0 2183.031 0.63 F -1875.0 2183.031 -0.86 J 6100.0 1815.196 3.36 EJ 7450.0 2944.699 2.53 FJ -5450.0 2944.699 -1.85
To try to get useful data reduction, I have refused to use any cubic (or higher) interaction term; including the first- and second-order terms that I've left out only explains 20% of the variance that is left in this fit, so I feel the clarity of parsimony here is more valuable than a slightly better fit. The first thing to note is that I've dropped the S/N axis entirely; it doesn't do much. Also, the P types have very little variance (a standard deviation of $2700 versus $6100 for the J types); they're largely in the low sixties.
The J types are a bit more interesting. Their mean is very close to $70,000, but EJs make about $9000 a year more than IJs, and TJs make about $7000 more than FJs. The IFJs are right in the middle of the P's; it's the other J types that do well.
The linked article suggests some problems with this; some of the things it raises as problems don't really bother me, but it doesn't mention that these are household incomes, which means that you're conflating income effects, family size effects, and effects from affinities of people from personality types for spouses of other personality types.