Chapter 5.6, Problem 1E

A Dubious Model of Oil Prices The following table shows the prices of oil in U.S. dollars per barrel, $t$ years since 1990,

One analysis (involving additional data) used a cubic equation to model this data.

$t$ Years since 1990	$0$	$2$	$5$	$7$	$10$	$12$	$15$	$17$	$20$	$21$
$P$ Price, dollars per barrel	$18.91$	$16.22$	$16.63$	$18.20$	$27.04$	$23.47$	$49.63$	$69.04$	$77.46$	$106.92$

a. Use cubic regression to model these data. Round the regression parameters to four decimal places.

b. Plot the data along with the cubic model.

c. In the analysis mentioned above, the graph is expanded through 2020. Expand the viewing window to show the model from 1990 to 2020.

d. What estimate does the model give for oil prices in 2015?

e. The actual price of oil in December of 2015 was about $\$35$ per barrel. What basic principle in the use of models would be violated in relying on the estimate in part (d)?