> To test whether intelligence mediates the observed association between family SES and children’s educational achievement, we statistically controlled for intelligence by regressing GCSE on intelligence and entering the resulting standardized residuals into the bivariate GCTA model with family SES. When controlling for variance explained by children’s intelligence, which yielded a univariate GCTA estimate of 0.38 (0.11 s.e.) (data not shown), the phenotypic correlation between family SES and children’s educational achievement was reduced from 0.50 to 0.37 (0.02 s.e.). The GCTA estimate of the genetic covariation between family SES and children’s educational achievement dropped from 0.25 (0.09 s.e.) to 0.17 (0.09 s.e.). Mirroring the mediation observed at the phenotypic level, this suggests that one-third of the SNPs tagging variation in family SES and children’s educational achievement also captured individual differences in intelligence, implying two-thirds of the SNPs linking family SES and children’s educational achievement were independent of intelligence.
The heritability of IQ and it's effect on SES is well document, but it obviously isn't the only relevant factor. I don't believe equality of outcome is feasible in this regard.