So here is just a general response, beginning with a note on the regressive method.
I learn the basics of regression analysis one day and forget it the next partially because I am sure the critique of positivism in general launched by Roy Bhaskar and his student Andrew Sayer (Method in Social Science) is devastating. Compare them to Verba and Keohane' book on methods and you will see that bourgeois thought is very weak on quesions of method. But critical realism is making inroads.
But I will speak in a non statisical language:
Since those who have a college degree may lack unobserved skill, any unexpected weakness in the correlation between educational attainment and income level need not be taken as proof that skill or cognitive ability accounts for little of the variance in income. That is, educational attainment is a poor proxy for skill/underlying cognititve ability and we cannot determine its power to account for income outcomes by reference to educational attainment.
Plenty of low skilled people could have college degrees and unsuprisingly fare badly as income earners while those who truly have unobserved skill or cognitive ability do really tend to make big bucks.
That lawyers remain the highest paid profession makes a joke out of the idea that high income is accounted for by the skill of its recipient (unless skill means ability to enter a corrupt profession for the sole purpose of making money); meanwhile companies use H-1 visas to get the very best foreign programmers and engineers at basically working class wages which should shoot down any hypothesis about the positive relation between unobserved skill/cognitive ability/IQ and income.
Why do process engineers make less than design engineers make less than lawyers? It's not because each has a higher IQ or more unobserved skill than the other. It's simply because each is successively removed from the production process and closer to the bourgeoisie which devalues the contribution of production and productive labor generally, That is the primary task of bourgeois ideology and the ruling ideas are those of the ruling class. And this seems to be reflected practically in the income structure of even so called skilled workers. As labor economist Rosemary Crompton once argued, there is no other way to understand the basically arbitrary hierarchy in the wages of lawyers to design engineers to process engineers.
Another note: since there has been greater intra class variance (that is, income inequality among those who have college or high school degrees or no degrees), unobserved skill can be invoked to account for greater intra group variance as well.
Yet I think the most important thing to remember is the actual social and material construction of unskilled labor. Tasks are simplified in order on the one hand to lower training costs and to give bite to threats to replace unruly worker and on the other hand to make possible the automation of tasks which have been simplified.
Labor is thus trained to carry out simplified tasks and inculcated with the disposition to do so from an early age. This is key to the power capital has over labor, and has studied by Harry Braverman and David Noble. Yet as productivity expands and industries grow more slowly or even contract or perhaps simply move abroad and new industries emerge, labor has never enjoyed the broad technical education to enjoy free rotation and variability in tasks.
Of course it may be that no new industries are emerging (the world is not buying much of skill intensive capital goods nowadays) and this actively de-skilled labor has no where to go but the badly paid, pure service industry. But even if new industries demanding new skills are emerging and growing quickly, capital so actively deforms labor that it undermines labor's mobility even as industrial development depends on it. The bourgeois ideologues blame the sinking of the dispossessed and the immobility of labor on the IQ and race of the proletariat but these horrors of unemployment and outright superfluousness are built into the capitalist division of labor, the capitalist system of education, and the habitus of the working class. The deskilled underclass and the immobile unskilled worker are not the products of low IQ but the capitalist division of labor. The full development of the social individual can only proceed after the destruction of class society. This is one of Marx's most brilliant insights.
best, rakesh