Here’s the actual paper.
genetics_intelligence_CDPS.pdf
I refuse to tag this under math-science. What’s really funny is the authors don’t even address the potential controversy of a claim like this. Bunch of fatheads.
I would really love to read the comments on this one.
My hat size is 7-1/2. It makes me a smart-ass, but little else.
A few things.
This is a summary of some promising (according to the authors) directions of brain, genetic, and cognitive research, not a research study. The research cited my be good or not, but that has to be individually evaluated.
The PDF saved from Word that is linked in the OP is just a way for the author to avoid copyright issues when putting their own paper on their own website. The published paper is at https://doi.org/10.1177/09637214251339449 but it might not be available in full text.
Evidence for the correlation between brain size and g being causal is from a technique called Mendelian Randomization, that depends on the fact genes assort randomly during meiosis to test the causality of relationships. They’re only talking about a correlation of 0.25, so pretty huge when it comes to physiology and behavior, but in no way a prescriptive destiny for any head size. So for every counter example you think of, remind yourself that is why the correlation is 0.25, not 1.
Way less controversial than the brain size relationship, is the authors mention that neural mechanism are also related to differences in intelligence. If intelligence is related to physical characteristics of the brain, then it is possible to measure and discover some of these characteristics. If you think intelligence is not related to physical characteristics of the brain, then you’re probably not thinking of science, but something else.
And finally, the tedious thing in all threads about IQ on this board. There are individual differences in intelligence; some people are smarter than others. These differences occur for reasons that are genetic and environmental. Scientists can measure and study this. Some of the measures used have names like IQ and g. These measures are extremely reliable for psychological traits, but still contain lots of error. Error does not make a measure worthless.
“Of course you’d say that - you have the brain pan of a stagecoach tilter.” 
There’s a family I’m not really acquainted with, but there’s so many of them you’re sure to see them anywhere you go.
They are, shall we say, really countrified. And that’s generous, believe me.
The thing about their heads…they all have big round basketball heads. It’s very weird.
You know the ad where the woman hounds a cardboard smilie face to hide her depression. That’s how they look. Blank faced, dot eyes, smiling at nothing.
There’s not one of them that knows how to check out of store, ask for info at a counter, understand menus or how to calculate percents off.
Their head size doesn’t make them brilliant. Your big head could just be full of air. Ya know?
(I didn’t read the paper, at all)
I’m sure Dara O’Briain would be interested in this study. (Watch to the end, less than 4 minutes, with some of the best British panel show comedy you’ll see, and the best zinger at the end.)
Mine is 7⅜. Assuming a larger hat size equates to higher intelligence (the .pdf was taking too long to load, so I closed it), I guess I’m slightly less smart-ass than you are.
Son-in-law with the huge, HUGE, head (size 8+!) would agree. Spawn2 (size 7, IIRC) would disagree. I tell the SIL’s younger sister that she’s lucky she was even born.
You are doing it wrong! You don’t wear your hat on your ass! You also shouldn’t sit on it either!
Anyway: we continental Europeans (the incontinent ones are excluded, of course) are the most intelligent by far. We measure our hats in cm, so no 7⅜ or 7-1/2 for me, no: 60 is the number. Take that, you imperial measurers!
That would make me an asshat.