Exercise 34 Page 337

Let x be the number of years after 1950 and y be the gross domestic product (GDP) in billions of dollars. From the given table, we can now write a new table with our variables.

Next, we plot all these points using a graphing calculator. To do so, 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.

Now, let's perform a cubic and quartic regression to approximate the data.

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 regressions seem to fit the data set very well. However, we need to look at the context to decide which one is better over the years.

Deciding Which Model Is Better

Let's summarize some properties of the two regressions we just made.

Due to the end behavior, as the years pass at some point both models will start to decrease and reach negative values, which is not realistic. However, we can see that the quartic model will reach these negative values more rapidly than the cubic model.

Therefore, we conclude the cubic model seems most likely to model the gross domestic product over the years, at least in the near future.