Question

The amount of methane emissions, in millions of metric tons, from 2002 to 2008 is shown.

A 2-column table with 7 rows. The first column is labeled year with entries 2002, 2003, 2004, 2005, 2006, 2007, 2008. The second column is labeled methane (millions of metric tons) with entries 673.3, 660.6, 661.6, 669.2, 678.5, 690.9, 724.2.
Find a regression model that best models the data.

The function that best models the data is
.



Use the model to complete the statements.

The amount of methane emissions in 2000 was about
million metric tons.

The amount of methane emissions in the years immediately following 2008 would most likely
.

Answer 1

A quadratic fits these data best. Using t = year − 2005, the least-squares quadratic is

y = 3.4476 t^2 + 8.2214 t + 665.9667, where y is methane (millions of metric tons).

(Equivalently y ≈ 3.4476( year − 2005 )^2 + 8.2214( year − 2005 ) + 665.9667.)

Using this model, for the year 2000 (t = −5):

y(2000) ≈ 711.1 million metric tons.

For the years immediately following 2008 the model predicts the emissions would most likely continue to increase (and the rate of increase would accelerate, since the quadratic opens upward).