It would have been helpful to model the effect of legacy status while accounting for academic indices.
Maybe for Harvard, but I'm not sure a legacy for some random private liberal arts school nobody has ever heard of (or $STATE University) will be any more academically gifted than someone whose parents both went to college anyway.
Maybe we need to differentiate between "legacy of a school" and "legacy of a school with a historically high academic quality"
They also tend to be smarter because smarter people have smarter kids.
Most people applying to an Ivy are already self-selecting as pretty exceptional applicants (putting aside the delusional) and the legacy admits had same/worse SATs, etc.
edit: just looked it up, Harvard is at ~34% legacy admit rate versus regular 6% admit rate..
“Among the admitted legacies, grades and test scores were indistinguishable from non-legacy students. Both groups had an average SAT score that surpassed 1430.”
At Harvard, my understanding is that the legacy admits have slightly higher test scores than non-legacy admits.