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Solved: You Explain It! CO2 and Energy ProductionThe
Chapter 3, Problem 16AYU(choose chapter or problem)
The least-squares regression equation \(\hat{y}\) = 0.7676 x – 52.6841 relates the carbon dioxide emissions (in hundred thousands of tons), y, and energy produced (hundred thousands of megawatts), x, for all countries in the world in 2010. Source: CARMA (www.carma.org)
(a) Interpret the slope.
(b) Is the y-intercept of the model reasonable? Why? What would you expect the y-intercept of the model to equal? Why?
(c) For 2010, the lowest energy-producing country was Rwanda, which produced 0.094 hundred thousand megawatts of energy. The highest energy-producing country was the United States, which produced 4190 hundred thousand megawatts of energy in 2010. Would it be reasonable to use this model to predict the \(CO_2\) emissions of a country if it produced 6394 hundred thousand megawatts of energy in 2010? Why or why not?
(d) In 2010, China produced 3260 hundred thousand megawatts of energy and emitted 3120 hundred thousand tons of carbon dioxide. What is the residual for China? How would you interpret this residual?
Questions & Answers
QUESTION:
The least-squares regression equation \(\hat{y}\) = 0.7676 x – 52.6841 relates the carbon dioxide emissions (in hundred thousands of tons), y, and energy produced (hundred thousands of megawatts), x, for all countries in the world in 2010. Source: CARMA (www.carma.org)
(a) Interpret the slope.
(b) Is the y-intercept of the model reasonable? Why? What would you expect the y-intercept of the model to equal? Why?
(c) For 2010, the lowest energy-producing country was Rwanda, which produced 0.094 hundred thousand megawatts of energy. The highest energy-producing country was the United States, which produced 4190 hundred thousand megawatts of energy in 2010. Would it be reasonable to use this model to predict the \(CO_2\) emissions of a country if it produced 6394 hundred thousand megawatts of energy in 2010? Why or why not?
(d) In 2010, China produced 3260 hundred thousand megawatts of energy and emitted 3120 hundred thousand tons of carbon dioxide. What is the residual for China? How would you interpret this residual?
ANSWER:
Step 1 of 5
The least squares regression equation is
\(\hat{\mathrm{y}} = 0.7676x - 52.6841\)
Its represents the linear relation between carbon dioxide emissions (in hundred thousands of tons), (y), and energy produced (hundred thousands of megawatts), (x).