Look at the graphs of the models to see which one fits the data better. If you cannot decide, look at the values of r^2 obtained in each regression.
Cubic Model: y=0.92x^3 - 1.46x^2 + 7.98x + 4.68 Quartic Model: y=-0.33x^4 + 1.67x^3 + 0.33x^2 + 5.33x + 3 Better fit: The quartic model fits the data better, because r^2=1.
Practice makes perfect
Let's begin by plotting the values using our graphing calculator.
x
-2
-1
0
2
3
y
-25
-4
3
23
40
Now, 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 dataset. A standard viewing window might not show the data points, so we can change it if necessary.
Next, we perform the cubic and quartic regressions.
Performing Regressions
By pressing STAT we can find the cubic regression under the CALC menu. If we choose CubicReg the calculator performs a cubic regression test. One line below in the list, we can find QuartReg, which performs a quartic regression.
To determine which model is best, we will plot the results we got and examine how they fit the data.
Both graphs fit the data set very well but we can see that the quartic model fits better. Additionally, if we compare the r^2 obtained in each regression, the one obtained in the quartic model was equal to , which implies a perfect match.
