College Valuations

Using data from NEBHE “Guide” to discern value of New England colleges …
The data published by Boston magazine and the New England Board of Higher Education the 2016 Guide to New England Colleges & Universities provided me with the opportunity to examine the higher education institutions (HEIs) prices, defined as tuition and plus fees, as a function of several independent factors including:

  1. Percentage of applicants accepted
  2. Percentage of accepted students who indeed enrolled
  3. Percentage of freshmen who were in top 25% of their high-school class
  4. Student-to-faculty ratio
  5. Undergraduate enrollment
  6. University versus college

I concentrated this analysis on private (or independent) HEIs in the Guide that provided details about their institutions. Which is not to say that public HEIs are not “good values,” but with their state funding, often larger enrollments and tiered in-state vs. out-of-state tuition and fee, they warrant a separate comparison.Correlation

measures the strength of the relationship between one factor and another. A higher correlation number indicates a stronger association.

Regression analysis permits one to model or generate an equation for a dependent variable, price, as a function of independent factors. Here the most powerful three: percentage acceptance, percentage of freshmen in top 25% of their high-school class and student-to-faculty ratio.

The percentage of freshmen who were in the top 25% of their high school class was the most influential variable affecting price at 0.851 correlation (1.00 is maximum possible).

The next two variables were also powerful.

The percentage of applicants accepted had a -0.758 correlation to price. The “758” indicates strength, the negative sign simply means that, as the percent applicants accepted increased (indicating less selectivity) the price decreased!

Student-to-faculty ratio had -0.709 correlation to price. Again, the “709” is strong and again the negative sign means that as student-to-faculty ratio increased (resulting in larger class-sizes), price decreased!

Percentage of accepted students who enroll (0.486 correlation), undergraduate enrollment (0.155 correlation), and university versus college (-0.139 correlation) were less impactful factors.

Pricing and regression

The pricing application of regression affects practically all our purchasing decisions. Home prices are a function of square footage, acreage, bathrooms, age, and attractiveness. Vehicle prices are a function of horsepower, seating capacity, warranty, and curb weight/safety. And salary (the price we put on our labor) is a function of experience, education, performance review and so on.

The regression model yields illuminating information.

The coefficients for each independent variable have the following interpretations:

  • For each 1% higher the percentage of freshmen in the top 25% of their class, the price in tuition plus fees rises by $147.13.
  • For each 1% higher the percentage of applicants accepted (less selective), the price declines by $34.61.
  • And for each one student higher the student-to-faculty ratio is (larger class-size), the price declines by $565.85

Please click here to download data in Microsoft Excel format to generate the correlation and regression for specific HEIs.

One substitutes the individual schools’ independent factors into the model described above to generate expected prices for each individual school. One can then compare these expected prices with actual prices to determine “value” schools.

In my state of New Hampshire, Saint Anselm is the best value school. Its actual price of $37,712 is 6.8% less than its expected price of $40,156.

In Rhode Island, Roger Williams University is an even better value. Its actual price of $31,748 is 11.2% less than its expected price of $35,764.

In Massachusetts, Simmons College’s actual price of $37,380 is 11.9% less than its expected $42,436.

In Vermont, Norwich University and Green Mountain College are “best buys” by this measure.

Bowdoin College is the best buy in Maine.

Sacred Heart University in Connecticut offers a remarkable 24% value!

Sometimes people mistakenly think this technique identifies only lower-priced schools as “good values”; that is not the case

Yale University’s actual price of $47,600 is 5.6% less than its expected $50,546.

Amherst, Harvard, Dartmouth. MIT and other expensive HEIs are also priced very appealingly because their independent quality factors justify the high prices.

Marc Rubin taught statistics to more than 16,000 students in a 38-year teaching career at both New England College and NH College Graduate School of Business. He was recognized as Teacher of the Year at both institutions. Rubin is retired from teaching now but employs these same correlation and regression techniques to counsel sports agents upon negotiating contracts for their players.

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