Steel has been playing a decreasing role in the manufacture of beverage cans in the United States.The use of bimetallic cans has been dwindling, whereas the use of all-aluminum cans has been growing steadily.The accompanying table gives the production (in billions) of all-aluminum cans over the period from 1975 through 1989: Find an equation of the least-squares line for these data.(Let x = 1 represent the year 1975.) Please round the coefficients in your equation to three decimal places.Use the result to estimate the number of cans produced in 1993, assuming the trend continued.
A)y = 4.834x + 11.857; 103.666 billion cans
B)y = 4.842x + 11.842; 103.863 billion cans
C)y = 4.842x + 11.842; 103.840 billion cans
D)y = 4.834x + 11.857; 103.703 billion cans

Question

Steel has been playing a decreasing role in the manufacture of beverage cans in the United States.The use of bimetallic cans has been dwindling, whereas the use of all-aluminum cans has been growing steadily.The accompanying table gives the production (in billions) of all-aluminum cans over the period from 1975 through 1989:  Find an equation of the least-squares line for these data.(Let x = 1 represent the year 1975.) Please round the coefficients in your equation to three decimal places.Use the result to estimate the number of cans produced in 1993, assuming the trend continued.
A)y = 4.834x + 11.857; 103.666 billion cans 
B)y = 4.842x + 11.842; 103.863 billion cans 
C)y = 4.842x + 11.842; 103.840 billion cans 
D)y = 4.834x + 11.857; 103.703 billion cans

Quizplus · Accepted Answer

Using a calculator or statistical software, we can find the equation of the least-squares line to be: 
y = 4.842x + 11.842
To estimate the number of cans produced in 1993, we plug in x = 19 (since 1993 is 19 years after 1975):
y = 4.842(19) + 11.842
y ≈ 103.84 billion cans
Therefore, the best choice is C.

Steel Has Been Playing a Decreasing Role in the Manufacture