# College Cost

## Intro

We investigated trends in the college cost of Stanford and University of Texas at San Antonio. Stanford is a private university in California and UTSA is a public university in Texas. We tested linear, cubic, and exponential functions to discover what function best fits the tuition increases these schools are experiencing.

## Stanford

DATA

Real 2014-2015 actual value = \$44184.00

Real 1990-1991 actual value = \$14280.00

Linear Model = 732.355x + 31012.5

year 1990-91 = \$23688.95

Percent Error = 65.89%

year 2014-15 = \$41265.47

Percent Error = 6.60%

year 2018-19 = \$44194.89

year 2040-41 = \$60306.70

Cubic Model = 13.947x^3 - 212.154x^2 + 1559.62x + 30466.161

year 1990-91 = \$-20319.44

Percent Error = 242.29%

year 2014-15 = \$49063.31

Percent Error =11.04%

year 2018-19 = \$71297.79

year 2040-41 = \$647740.56

Exponential Model= 31111.789(1.021)^x

year 1990-91 = \$25273.63

Percent error = 76.99%

year 2014-15 = \$41618.41

Percent Error = 5.81%

year 2018-19 = \$45226.03

year 2040-41 = \$71442.20

## Which function is accurate?

The linear regression was over all the best model because the percent error was the lowest and it was the closest when to the real cost of the tuition at Stanford. However, it still had some error. Not what I expected. I thought inflation and recent economic crisis would make the growth exponential.

## The Past

64 years ago(1950) Stanford tuition = \$600

Linear regression without the value: 732.355x + 31012.5

Linear regression with the value: 623.837x + 31574.82

Small difference between linear regression shows that tuition must have increased at a somewhat steady rate

## UT San Antonio

Real 2014-2015 actual value = \$28400.00

Real 1990-1991 actual value = \$9870.00

Linear Model = 424.86x+389.927

year 1990-91 = \$11608.95

Percent Error = 14.97%

year 2014-15 = \$18765.47

Percent Error = 33.82%

year 2018-19 = \$29183.70

year 2040-41 = \$48076.30

Cubic Model = 7.52x^3+93.794x^2+147.667x+3987.82

year 1990-91 = \$-15485.81

Percent Error = 195.31%

year 2014-15 = \$49063.31

Percent Error =11.04%

year 2018-19 = \$51462.6

year 2040-41 = \$50079.56

Exponential Model= \$2056.4(1.016)^x

year 1990-91 = \$25273.63

Percent error = 16.988%

year 2014-15 = \$38556.90

Percent Error = 7.81%

year 2018-19 = \$40234.03

year 2040-41 = \$60209.40

1950-

\$367.43

2000-

\$4,056

+10%

2001-

\$4,231

+5.6%

2002-

\$4,373

+6.2%

2003-

\$4,966

+15.9%

2004-

\$5,987

+24%

2005-

\$6,056

+5.2%

2006-

\$6,736

+13.6%

2007-

\$6,846

+6.1%

2008-

\$7,249

+6.3%

2009-

\$7,527

+6%

2010-

\$8,410

+11.7%

## Graph of UTSA

Green: Exponential
Red: Cubic
Blue: Linear
x=0 where year 2000
x=year
y= cost \$

## Which Function is Accurate?

The linear function is the most accurate. The percent error was the lowest when compared to the other two. This is not what we expected. We thought because economic crisis that it would be cubic or exponential.

## The Past

64 years ago(1950) UTSA tuition = \$400

Linear regression without the value: 641.98x + 14004.95

Linear regression with the value: 494.67 + 14865.87

Small difference between linear regression shows that tuition must have increased at a somewhat steady rate

## Reflection

This project has helped us learn about the accuracy of some models and how inaccurate others are. It also showed me that college can be expensive and will only get worst. The price of college is very expensive and that the cost of the college will affect where we will apply in the future. For example the cheaper colleges such as UTSA may be more appealing to residents of Texas because of the very low price.. I think we spent too much time on this project. Calculating the errors and graphing the graph and finding how to use all these regressions in the calculator looking up video tutorials I believe we spent an accumulative time of 5-6 hours on this project. I think we worked hard on this project because of all the effort we took to learn all these calculations and function. Later having to actually calculate it and make a presentation.However at the end, I think it was worth the time because I learned more about colleges and how expensive they are; affecting my decision in applying to certain colleges. After 40 weeks I will still remember how to put all these functions into my calculator and know how to use them. After 40 months I will probably remember the same amount of functions and how to use them but I will remember how long it took to complete this project as well. I will remember the time gap given compared to the work needed to complete this assignment to remind myself that I can achieve a lot in little time. After 40 years I will remember one thing: College is expensive.