Question

Carbon dioxide is produced by burning fossil fuels such as oil and natural gas, and has been connected to global warming. The following table presents the average amounts (in metric tons) of emissions for certain years per person in the United States and per person in the rest of the world
Year Non-U.S. U.S.
1990 3.6 19.2
1994 3.3 19.8
1997 3.4 20
1999 3.2 19.6
2000 3.3 20
2001 3.3 19.6
2002 3.3 19.6
2003 3.5 19.4
2004 3.7 19.6
2006 3.7 19


The regression line equation is 23.3860 - 1.1096x

(b) If the non-U.S. emissions differ by 0.2 from one year to the next, by how much would you predict the U.S. emissions to differ? Round your answer to four decimal places.

Answer 1

(c) Predict the U.S. emissions for a year when the non-U.S. emissions level is 3.4.
Round the answer to two decimal places.

Answer 2

The regression line equation given is:

\[ y = 23.3860 - 1.1096x \]

In this equation, \( y \) represents the U.S. emissions, and \( x \) represents the non-U.S. emissions. The coefficient of \( x \) (which is -1.1096) indicates the expected change in U.S. emissions for a one-unit change in non-U.S. emissions.

If the non-U.S. emissions differ by \( 0.2 \) metric tons, we can calculate the corresponding change in U.S. emissions as follows:

\[
\text{Change in U.S. emissions} = \text{change in non-U.S. emissions} \times \text{coefficient} = 0.2 \times (-1.1096)
\]

Calculating this:

\[
\text{Change in U.S. emissions} = 0.2 \times (-1.1096) = -0.22192
\]

Thus, if non-U.S. emissions differ by 0.2 metric tons from one year to the next, we would predict the U.S. emissions to differ by approximately

\[
\boxed{-0.2219}
\]

(rounded to four decimal places).

Answer 3

To predict the U.S. emissions when the non-U.S. emissions level is \( x = 3.4 \), we can use the regression line equation:

\[
y = 23.3860 - 1.1096x
\]

Substituting \( x = 3.4 \) into the equation:

\[
y = 23.3860 - 1.1096 \times 3.4
\]

Calculating the multiplication first:

\[
1.1096 \times 3.4 = 3.77064
\]

Now substituting this back into the equation:

\[
y = 23.3860 - 3.77064 = 19.61536
\]

Rounding this to two decimal places, we get:

\[
\boxed{19.62}
\]

Thus, the predicted U.S. emissions when the non-U.S. emissions level is 3.4 metric tons is **19.62** metric tons.