Consider x to be the number of years after 1900. If the two graphs fit the data set very well, look at the value of r^2 in each regression.
Quadratic Model: y=-1.25*10^(-4)x^2-0.003x+2.804 Cubic Model: y=-8.33*10^(-6)x^3 + 0.002x^2 - 0.19x + 8.142 Better Fit: The cubic model fits the data set better.
Practice makes perfect
To know which models to use to approximate the data, we will begin by plotting the values using our graphic calculator. Let's consider x to be the number of years after 1900 and y to be the Average Growth Rate.
x
Average Growth Rate (y)
72
1.96
82
1.73
92
1.5
102
1.22
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 data set. A standard viewing window might not show the data points, so we can change it if necessary.
Let's try to approximate the average annual growth rate of the world population either by using a quadratic or a cubic regression.
Performing Regressions
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.
Which Model is Best?
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, and it is not readily apparent which is better. To determine which one is best, let's look at the r^2 value. The closer r^2 is to 1, the better the fit. Therefore, we will choose the cubic model as the one that best represents the data set.
