The accompanying table gives the projected state subsidies (in millions of dollars) to the Massachusetts Bay Transit Authority (MBTA) over a 5-yr period. Find an equation of the least-squares line for these data. Use the result to estimate the state subsidy to the MBTA for the sixth year (x = 6).
A) y = 2.7x + 17.8; $34,100,000
B) y = 2.8x + 17.6; $34,600,000
C) y = 2.8x + 17.6; $34,400,000
D) y = 2.7x + 17.8; $34,000,000

Question

The accompanying table gives the projected state subsidies (in millions of dollars) to the Massachusetts Bay Transit Authority (MBTA) over a 5-yr period.  Find an equation of the least-squares line for these data. Use the result to estimate the state subsidy to the MBTA for the sixth year (x = 6).
A) y = 2.7x + 17.8; $34,100,000 
B) y = 2.8x + 17.6; $34,600,000 
C) y = 2.8x + 17.6; $34,400,000 
D) y = 2.7x + 17.8; $34,000,000

Quizplus · Accepted Answer

Using a calculator or software, we can find that the equation of the least-squares line is: 
y = 2.76x + 16.96. 
To estimate the state subsidy for the sixth year (x = 6), we plug x = 6 into the equation and get:
y = 2.76(6) + 16.96 = $34.416 million, which is closest to the answer in choice C.

The Accompanying Table Gives the Projected State Subsidies (In Millions