Consider x to be the number of years after 2000. Despite the values of r^2, which model represents a real world situation?
Quadratic Model: y=0.3480x^2+2.6030x+49.7739 Cubic Model: y=-0.03125x^3+0.8125x^2+x+50 Explanation: The cubic model leads to a negative number of students after 2025, which is not a real world situation. This is why the quadratic model is more appropriate.
Practice makes perfect
Let's consider x to be the number of years after 2000 and y to be the number of students enrolled. We can rewrite the given table using our variables.
x
Number of Students Enrolled (y)
0
50
4
65
8
94
10
110
Now, in our graphing calculator we push STAT, choose Edit, and enter these values.
Once the values have been entered, we can plot them by pushing 2nd and Y= and choosing one of the plots in the list. Make sure you turn the plot ON, choose scatterplot as the type, and use L1 and L2 as XList and YList. Finally, you can pick whatever mark you want.
By pushing GRAPH the calculator will plot the data set. A standard viewing window might not show the data points, so we can change it if necessary.
By pressing STAT we can find the quadratic regression under the CALC menu. If we choose QuadReg the calculator performs a quadratic regression test. One line below in the list we can find CubicReg, which performs a cubic regression.
Let's make a plot of the regressions.
Both graphs fit the data set very well, and it is not readily apparent which is better. However, the value of r^2 in the cubic regression is 1, which implies a perfect match. But, from its graph we can see that after year 2025 the number of students enrolled will be negative, which is not a realistic model.
y=0.3480x^2+2.6030x+49.7739
In contrast, the quadratic model seems to grow over time, which seems more realistic.
