The 2018 Guide to New England Colleges & Universities data published by Boston magazine in association with the New England Board of Higher Education provided me the opportunity to examine the schools’ prices, defined as tuition plus fees, as a function of several independent factors including those listed below. (I conducted a similar study last year.)
- Percentage of freshman applicants accepted
- Percentage of freshmen who were in the top 25% of their high-school class
- Student-to-faculty ratio
- Undergraduate enrollment
- Independent (private) versus public
I conducted one analysis of independent colleges and universities listed in the 2018 Guide that provided those details for their institutions and a separate one of publics.
My analysis examined correlation, which measures the strength of the relationship between one factor and another. A higher correlation number indicates a stronger association.
Percentage of freshmen who were in the top 25% of their high school class was the most influential variable impacting price at a 0.816 correlation—quite consistent with the 0.851 correlation last year (1.00 is the maximum possible).
The next two variables were also significant.
The percentage of applicants accepted had -0.791 correlation to price, again consistent with the -0.758 correlation last year. The “791” indicates strength, the negative sign simply means that as the percent applicants accepted increased (less selective), the price decreased.
Student-to-faculty ratio had -0.586 correlation to price—weaker than the -0.709 correlation last year. Again, the “586” is strength of relationship and once more the negative sign means that as student-to-faculty ratio increased (larger class-sizes) the price decreased.
Undergraduate enrollment had a 0.305 correlation to price. Larger enrollment may be indicative of greater demand resulting in higher pricing.
Regression analysis permits one to model or generate an equation for a dependent variable, price, as a function of independent factors. The most significant were: percentage of freshman acceptance, percentage of freshmen in top 25% of their high-school class, student-to-faculty ratio and undergraduate enrollment.
This pricing application of regression affects practically all our purchasing decisions.
Home prices are a function of metrics such as square footage, acreage, bathrooms, age and attractiveness. Vehicle prices are a function of horsepower, seating capacity, warranty and curbweight/safety. Salary, the price we put on our labor, is a function of experience, education, performance review and so on.
In the case of the Guide, the regression model yields illuminating information. First, the coefficients for each independent variable have the following interpretations:
- For every 1% increase in the percentage of freshmen in the top 25% of their class, the price (tuition plus fees) rises $167.81.
- For every 1% increase in the percentage of freshmen acceptance (which means less selectivity in admissions), the price declines $92.40.
- For every additional student in the student-to-faculty ratio (which means a larger class-size on average), the price declines $15.63.
- For every additional 1,000 undergraduate students enrolled, the total price increases $58.50.
Now heading to the significant conclusion …
By applying the factors described above to each institution, one can generate an “expected” price for that institution and compare that price to its actual (quoted) price. A comparison of “expected” prices vs quoted prices at multiple institutions can then determine value based on those factors.
Simmons College has an actual price of $38,590, which is 11.5% less than its expected price of $43,583. Last year, Simmons had an actual price of $37,380, which was 11.9% less than its expected $42,436.
The University of Bridgeport, Bay Path University, Endicott College, Husson University, Unity College and Franklin Pierce University were appealingly priced–meaning their actual price compared favorably with their expected price.
Sometimes people mistakenly think this technique identifies only lower-priced institutions as “good values.” That is not the case.
Yale University’s actual price of $51,400 is 4.7% less than its expected $53,924. Last year, Yale’s actual price of $47,600 was 5.6% less than its expected $50,546. MIT and Brown University are other examples of expensive schools, which are priced very appealingly because their quality independent factors justify the high prices.
A question that might have arisen in the reader’s mind is: Just how reliable are these results?
The answer: There is a diagnostic r2, which the regression software within Excel generates, and it is a measure of the “percent of deviation in prices that is explainable by the variations in the independent factors.” In this year’s analysis the r2 comes out at a significant 0.687 (maximum is 1.00). Unfortunately that is less than the deviation (0.775) calculated in last year’s Guide data. Many institutions failed to report % freshmen in the top 25% of their high-school class and many even omitted their undergrad enrollment. To gain more insight, one would need to add other independent factors to the analysis such as: percentage of faculty with doctorates; size of campus in acreage; average SAT scores or GPAs of entering freshmen.
I conducted a separate analysis for public institutions for the correlations of factors to price that were significantly different from the correlations to their private peers.
For instance, freshman in the top 25% of their high school classes had a strong 0.816 correlation to prices of private institutions; it was only 0.556 to prices of public institutions.
The percent of freshmen acceptance had a -0.791 correlation to prices of private institutions, but -0.60 only to prices of public ones. These lower correlations yielded a less confidence-inducing r2 of 0.42. Still, the analysis yielded the following schools as ones appealingly priced: Berkshire Community College, Quinsigamond Community College, Rhode Island College, University of Southern Maine and Nashua Community College.
Marc Rubin taught statistics to more than 16,000 students in a 38-year teaching career at both New England College and Southern New Hampshire University. He was recognized as Teacher of the Year at both institutions. Rubin is retired from teaching now but has an exciting consulting business employing these same correlation and regression techniques to counsel sports agents upon negotiating contracts for their players, including $100 million deals for Colin Kaepernick and Russell Wilson in football and Brian McCann, Pablo Sandoval and Kyle Seager in baseball.