College Cost Project

Graph of All Functions for Brown University

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition (\$)

Graph of All Functions for UNT

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition (\$)

Function that best models the cost of tuition for each school

For Brown University the function which best models the cost of tuition is the linear model. This is seen in the percent error which was calculated by taking the predicted value and subtracting the exact value then dividing this all by the exact value. The predicted value using the linear model for 1990-1991 was \$24,692.41 and the exact value during this time period was \$20, 720; the percent error was about 19.172%. Additionally during 2014-2015 the projected tuition using the linear model was \$43, 191.83 and the exact value was \$62, 694; the percent error was about 31.107% error. On the other hand during the time periods 1990-1991 and 2014-2015, the percent error using the exponential function was approximately 26.936% and 30.148% error respectively. Additionally, during the same time periods using the cubic model the percent error was about 73.351% and 22.941% respectively. The linear model has the lowest percent error overall for Brown University, which indicates that this is the best model for this school. University of North Texas (UNT)’s tuition is best modeled by the Exponential Model. The predicted value using the exponential model for 1990-1991 was \$2, 013.545 and the exact tuition during this time period was \$3, 326; the percent error was about 39.460%. Additionally, during the time period 2014-2015, the projected tuition using the exponential model was \$10, 836. 579; however the exact tuition was \$22, 030; there wa sa 50.810% error. The percent error was significantly smaller compared to the linear and cubic models. During 1990-1991 and 2014-2015 using the linear model there was about a 95.511% error and a 57.400% error respectively. Also when using the cubic model during those same time intervals the percent error was about 73.351% error and 22.941% error respectively. Ultimately the linear model better modeled the cost of tuition for Brown University, while the exponential model better modeled the cost of tuition for University of North Texas or UNT.

One Model that was better consistently

We predicted that the exponential mathematical model would best represent the rise in tuition over the years, however our data did not agree. In regards to Brown University, the linear model was better consistently at predicting the tuition costs for a specific year. This is represented in the percent error which was derived by taking the predicted value and subtracting the exact value then dividing this all by the exact value. The linear model predicted that in 1990-1991 the tuition cost would be 24,692.41 while the actually cost was \$20,720. The percent change between these two was about 19%. Between the years 2014-2015 the percent change was about 31%. However, when calculating the percent with the other functions such as with the exponential the percent change between the years 1990-1991 and 2014-2015 were 27% and 31% respectively. Additionally, the percent change between the same two time intervals in regards to the cubic function was about 73% and 23%. The data indicates that overall the linear model seems to show the least percent error, thus the linear model was better with Brown University. This is not the case with UNT (University of North Texas) because the percent error indicates that the exponential model showed the least percent error. During the same two time intervals as mentioned previously, the percent error for the exponential model was about 40% and 50% respectively. On the other hand, with the linear models the percent error was about 95% and 57%, while with the cubic function the percent error was about 356% and 66% respectively. There doesn't seem to be a consensus on the overall model which was consistently better when looking at both school, Brown University and the University of North Texas had different models which were better suited to predicting their tuition.

Graph of all functions for Brown University including tuition in 1950

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition (\$)

Graph of all functions for UNT including tuition in 1950

Key

Red: Linear

Blue: Exponential

Green: Cubic

x=number of years from 2000

y=tuition (\$)