# College Cost Project

### By Natalie Lopez, Meredith Munro & Alex Rouke

## Data Table

## 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^x## Linear, 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

__Predictions__

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

__Predictions__

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.