Hai Lin '10 Researching Regression towards the Mean, Preferential Recruiting

Hai Lin '10
Hai Lin '10
Although school is out for the summer, Hai Lin '10 is still keeping busy on campus. The rising junior is working on two separate projects in the math department, one with Professor of Mathematics Larry Knop studying regression towards the mean, and another investigating preferential recruiting with Associate Professors of Mathematics Sally Cockburn and Timothy Kelly.

"Regression towards the mean" refers to the idea that when measuring one variable in a certain population, members who have show an extreme value on the first observation will likely exhibit a less extreme value on the second observation. For example, if a student scores a grade on a test that is far above average, it is likely that the student's grade on a second, similar test would drop somewhat. Unless there was no element of chance or guesswork involved, the student would be unlikely to repeat the first exceptional result. Similarly, a score far below the mean would likely be followed by a somewhat higher result on a second attempt.

The theory was first investigated by the English polymath Francis Galton, who studied relative heights of families and found that taller-than-average parents generally had children who were shorter than they, while shorter-than-average parents often had slightly taller offspring than they were. However, Lin and Professor Knop believe that the theory may be misapplied, since it assumes an absolute independent variable. For example, the fathers of exceptionally short or tall children are also supposed to show regression towards the mean, which leads to inconsistency (if sons are shorter than their fathers but still above average height, then taking the situation in reverse shows that the tall population of sons has a still taller group of fathers). Lin says that by using the minimum distance between the two groups, instead of assuming one or the other to be the independent variable, the problem can be solved.

For his work with Professors Cockburn and Kelly, Lin researched the effect of preferential recruiting, where students are admitted to college not based solely on their academics, such as their performances on the SAT, but also due to other factors like athletic recruiting, legacies, or diversity. Some information was impossible to obtain and had to be estimated, such as how many schools students applied to or how many overlaps occurred. Lin says, though, that the general trend was a drop in SAT scores for schools that practiced preferential recruiting. The top college (from the list published by USNews.com) exhibited the greatest drop, and the effects lessened going down the list. Based on the 25 top-ranked liberal arts colleges in the U.S., the effect disappears around the 13th-ranked institution.

This is Lin's first experience with summer research. As a math major, he wanted to find a research opportunity in the department: "I asked around," he says, "and fortunately there was a project available for me." Lin notes that this experience is particularly beneficial since he is interested in an academic career. His projects this summer give him an idea of the work professors do when they aren't teaching.

Lin's work is supported by the Monica Odening Student Internship and Research Fund in Mathematics, established by Life Trustee William M. Bristol, III '43 in honor of his granddaughter, Monica Hastings Lee Odening, Class of 2005. The fund provides support for directed student internships in mathematics and student-faculty collaborative research in mathematics. 

-- by Laura Bramley

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