John Hinrichs

John Hinrichs is a Certified Financial Planner in Bellaire, TX with 25 years experience in estate planning.

I. Introduction

Americans now owe more on student loans than on credit cards. The total surpasses $1 trillion dollars with nearly 40% of those between the ages of 20 and 40 have student debt (Wessel, par. 3). Gordon and Hedlund (p. 2) note that from 1987 to 2010, tuition and fees ballooned from $6,600 to $14,500 in 2010 dollars. More people are going to college, prices are up, and government programs make it easy to borrow. The graph below provided by the Federal Reserve Bank of New York displays the striking positive trend line between years and total debt.

Student Loans vs auto and credit cards

Federal Reserve data on student loans, auto loans and credit cards

Why does the price keep rising? Weissmann states the real link between college costs and aid [grants, loans, and employment] is complicated, but loans could be the primary cause of skyrocketing tuition. Researchers ponder that if student loans-with few questions asked-were not readily available, tuition and fees might not have gone up so much in the first place.

Student loans enable colleges to raise tuition because they are confident that loans will cushion the increases (Bennett, par. 3). Gillen studies other causes: changes in state funding, faculty compensation, and college-funded financial aid (Abstract, 1). And Bowen’s Rule refers to the tendency of colleges to raise and spend all the money they can in the pursuit of excellence (Gillen, Inside Higher Ed, par. 6). Regression results support the Bennett Hypothesis.

II. Analysis of Regression Results

 Note: The total Excel output is in the Appendix.

Regression Statistics

Multiple R


R Square


Adjusted R Square


Standard Error










The student loans1 are total federal and nonfederal loans in 2014 dollars from 1994-95 to 2014-15 (College Board.2015b, figure 5); and tuition costs and required fees for the same years are in 2014-15 dollars (NCES, Table 330.10). The “Loans Line Fit Plot” shows a high degree of relatedness (correlation) between the two variables. The trend line depicts a linear relationship with a direction of upward and to the right so as student loans are increasing the tuition costs are increasing. The statistic r is the Pearson product-moment correlation coefficient; and this simple regression results in an r of 0.9582 which is a strong positive correlation where an r value of +1 denotes a perfect positive relationship. This high correlation indicates that this model has potential for predicting tuition costs. However, just because there is a relationship between the two variables does not mean that it is a cause and effect relationship. In other words, colleges may not raise tuition costs just by recognizing upward trending student loans. Often a third variable affects the relationship between the other two variables, and the third variable is not included in the regression model. There is also an assumption that error terms are normally distributed in the model. This line of best fit expressed by the equation ( = b0 + b1x) drawn through the data displays six outliers out of twenty-one observations. However, only one observation constitutes an outlier which at 1504.365 has a larger residual (2014-15, 106.1, 11487) than the other five so overall the outliers do not overly influence the predictive value of this bivariate regression. Clearly, 71% of the residuals are small.

Excel uses a least squares analysis-a process whereby a regression model is developed by producing the minimum sum of the squared error values. In this sample the slope (b1) is 51.913 and the y-intercept (b0) is 4474.718. The x-values are actually in $1 billion dollar denominations: the slope is actually $51.913 billion dollars. The slope determines how increases in student loans (x-axis) cause tuition costs (y-axis) to go up. The positive sign of the slope indicates a positive relationship between the two variables. In this analysis the y-intercept indicates that even if no student loans were outstanding the tuition costs are $4,475. This regression predicts a value of by substitution, for example, say x = 140 (billion dollars), then $4,475 + (51.913 x 140) = $11,743 in tuition costs and required fees.

Excel calculates an r (0.9583, high), the correlation coefficient which tells how strong the linear relationship is; and r2 – also called coefficient of determination-which equals the proportion of the variability of y (tuition costs) associated for by x (student loans). The higher the r2 the better the model. In this model the r2 is high at 0.918 on a range of 0 to 1. This means that 8.20% of the variance in tuition costs (y) is unaccounted for by x (student loans) or unexplained by this model. The adjusted r2 is somewhat less at 0.914 because the sample size is small with only 21 cases. The standard error (se) measures the precision of the regression coefficient, and if the coefficient is large compared to the standard error then the coefficient is probably different than zero. In this model the coefficient is not large compared to the standard error. The se is the standard deviation of error of the model. The tuition costs range from $6,364 to $11,487. The model yields a se of $480.487 so that 68% of the error terms will be within plus or minus $480.487 if the error terms are normally distributed about the given values of x. Also, since the P-value (8.775E-12) is substantially less than the significance level of (0.05); the model rejects the null hypothesis, and there are significant regression effects in the model.1

III. Conclusion

Tuition and debt levels are highly correlated suggesting that students respond to higher tuition by borrowing (Ley and Keppo, Abstract, 1). The data for the twenty-one year period presents loans in 1994-95 at $36 billion dollars, and in 2014-15, $106.1 billion dollars, an increase of 295%, while tuition costs increase 180%. This regression results in an r of 0.9582 which is a strong positive correlation. There are significant regression effects in the model. The more students can borrow, the more colleges can charge. Economists from the Federal Reserve Bank of New York publish research that implies that “increasing federal aid results in colleges raising tuition, which in turn offsets the benefit to students.”1 Multiple regression analyses indicate that loans do drive tuition increases over the years.2 This model with an r2 of 0.918 strongly supports the Bennett Hypothesis.


1 Bary writes about a government program that forgives federal loans for graduates who take on public-sector jobs and pay 10% of their discretionary income toward the loan balance for a decade.

2  The loans are broken down into categories as follows: nonfederal, Perkins, Grad PLUS, Parent PLUS, federal unsubsidized, and federal subsidized.

3  I reviewed my notes taken in Dr. Ken Black’s class at University of Houston-Clear Lake, and reread Chapter 12 entitled “Simple Regression Analysis and Correlation” from his textbook.

4 See Staff Report No. 733 by Lucca, Nadauld, and Shen. Federal loans are a large component of aid.

5 Gordon and Hedlund report that demand-side shocks by themselves cause tuition to jump by 102%. With all the other changes except the demand-side shocks, tuition only increases by 16% (3).

Works Cited

 Bary, Emily. “The Cost of Forgiveness.” Barron’s 10 Oct. 2016.

Bennett, William J. “Our Greedy Colleges.” The New York Times 18 February 1987: par. 3.

Black, Ken. Business Statistics for Contemporary Decision Making. 7th ed. Hoboken, NJ: Wiley, 2012: 470-521.

College Board. 2015b. “Trends in Student Aid: 2015.” (Figure 5) Trends in Higher Education.

Gillen, Andrew. “Why Does Tuition Keep Increasing?” (September 20, 2015). Available at SSRN: or

---. “Gillen essay updating Bill Bennett hypothesis on college prices.” Inside Higher Ed ( 20 February 2012: par. 6.

Gordon, Grey and Aaron Hedlund. “Accounting for the Rise in College Tuition.” 1-60 (Sept. 2015) (CAEPR Working Paper #2015-015), available at (on file with Department of Economics at Indiana University Bloomington).

Ley, Katharina and Jussi Keppo. “The credits that count: How credit growth and financial aid affect college tuition and fees.” (November 16, 2011) Available at SSRN:

Lucca, David O, Taylor Nadauld, and Karen Shen. “Credit Supply and the Rise in College Tuition: Evidence from the Expansion in Federal Student Aid Programs.” Federal Reserve Bank of New York Staff Reports (Staff Report No. 733). July 2015, revised October 2016.

National Center for Education Statistics (NCES). 2015. Digest of Education Statistics: 2015. Washington: U.S. Department of Education ( Table 330.10.

Weissmann, Jordan. “Is Financial Aid Really Making College More Expensive?” The Atlantic 16 Feb. 2012 (Business): par. 1.

 Wessel, David. “Student Loans: Don’t Call It a Crisis.” Wall Street Journal 12 Oct. 2016.  

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