College Cost
Matthew Whiting and Dan Josef
Intro
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 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
Table
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
Red: Cubic
Blue: Linear
x=0 where year 2000
x=year
y= cost $
Which Function is Accurate?
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