College Cost Project
By Natalie Lopez, Meredith Munro & Alex Rouke
Data Table
Texas State University
location: San Marcos, Texas
Public, in state
Brigham Young University
Private, out of state
Linear, Cubic & Exponential Models - Texas State
linear: y= 986.909x + 5795.273
cubic: y=-11.729x^3 + 207.065x^2 + 4.692x + 6684.503
exponential: y= 6404.173 x 1.099^xLinear, Cubic & Exponential Models - BYU
linear: y=320.909x + 5493.636
cubic: y= -1.068x^3 + 33.671x^2 + 83.341x + 5796.783
exponential: y=5612.441 x 1.045^x
Part B - Mathematical Analysis
Texas State
1990-91
linear: y= 986.909(-10)+5795.273= $-4,073.82
cubic: y= -11.729(-10)^3+207.065(-10)^2+4.692(-10)+6684.503= $39,073.08
exponential: y= 6404.173 X 1.099^(-10)= $2,491.64
2014-15
linear: y= 986.909(14)+5795.273= $19,612.00
cubic: y= -11.729(14)^3+207.065(14)^2+4.692(14)+6684.503= $15,150.56
exponential: y= 6404.173 X 1.099^(14)= $24,012.13
2018-19
linear: y= 986.909(18)+5795.273= $23,559.64
cubic: y= -11.729(18)^3+207.065(18)^2+4.692(18)+6684.503= $5,454.49
exponential: y= 6404.173 X 1.099^(18)= $35,028.50
2040-41
linear: y= 986.909(40)+5795.273= $45,271.63
cubic: y= -11.729(40)^3+207.065(40)^2+4.692(40)+6684.503= $-412,479.82
exponential: y= 6404.173 X 1.099^(40)= $279,492.88
Actual Tuition
1990-91: $2,382
2014-15: $16,660
Percent Error
1990-91:
Linear: 271.03%
Cubic: 1540.36%
Exponential: 46.03%
2014-15:
Linear: 17.72%
Cubic: 9.06%
Exponential: 44.13%
BYU
1990-91
linear: y=320.909(-10)+5493.636= $2,284.55
cubic: y= -1.068(-10)^3+33.671(-10)^2+83.341(-10)+5796.783= $9,398.47
exponential: y=5612.441 X 1.045^(-10)= $3,614.01
2014-15
linear: y=320.909(14)+5493.636= $9,986.36
cubic: y= -1.068(14)^3+33.671(14)^2+83.341(14)+5796.783= $10,632.48
exponential: y=5612.441 X 1.045^(14)= $10,393.93
2018-19
linear: y=320.909(18)+5493.636= $11,297.00
cubic: y= -1.068(18)^3+33.671(18)^2+83.341(18)+5796.783= $11,977.75
exponential: y=5612.441 X 1.045^(18)= $12,394.96
2040-41
linear: y=320.909(40)+5493.636= $18,330.00
cubic: y= -1.068(40)^3+33.671(40)^2+83.341(40)+5796.783= $-5347.98
exponential: y=5612.441 X 1.045^(40)= $32,644.00
Actual Tuition
1990-91: $1,800
2014-2015: $10,000
Percent Error
1990-91:
Linear: 26.92%
Cubic: 422.14%
Exponential: 100.77%
2014-2015:
Linear: -.13%
Cubic: 6.32%
Exponential: 3.94%
#6
#7
#8
Texas State
Linear: 216.801x+9785.833
Cubic: 0.272x^3+25.47x^2+707.142x+6227.668
Exponential: 7774.036 x 1.056^x
Linear:
Tuition 1990-91:$-1054.22
Tuition 2014-2015: $12, 821.05
Cubic:
Tuition 1990-91:$545.57
Tuition 2014-15: $21,866.14
Exponential:
Tuition 1990-91: $4508.24
Tuition 2014-15: $17,253.10
BYU
Linear: 130.782x+6478.841
Cubic: .253x^3+13.681x^2+160.669x+5746.493
Exponential: 5305.999 x 1.057^x
Linear:
Tuition 1990-91: $-60.25
Tuition 2014-15: $8309.79
Cubic:
Tuition 1990-91: $327.01
Tuition 2014-15:$11,370.88
Exponential:
Tuition 1990-91: $3038.97
Tuition 2014-15: $11,577.77
By adding the new value at 1964, the cubic regression model seems to become the more precise equation to use. The exponential regression model's tuition from 1990-91 became much higher and less exact. The linear regression model is not the right choice either because it would allow you negative money, which is not possible.