The estimated number of computers (in millions) connected to the Internet in Europe from 1998 through 2002 is summarized in the accompanying table: (Here, x = 0 corresponds to the beginning of 1998.) Find an equation of the least-squares line for these data.Use the result to estimate the projected number of computers connected to the Internet in Europe at the beginning of 2004, assuming the trend continues.
A)y = 12.1x + 21.06; 94.030 million computers
B)y = 12.2x + 20.94; 94.140 million computers
C)y = 12.1x + 21.06; 93.660 million computers
D)y = 12.2x + 20.94; 93.910 million computers

Question

The estimated number of computers (in millions) connected to the Internet in Europe from 1998 through 2002 is summarized in the accompanying table:  (Here, x = 0 corresponds to the beginning of 1998.) Find an equation of the least-squares line for these data.Use the result to estimate the projected number of computers connected to the Internet in Europe at the beginning of 2004, assuming the trend continues.
A)y = 12.1x + 21.06; 94.030 million computers 
B)y = 12.2x + 20.94; 94.140 million computers 
C)y = 12.1x + 21.06; 93.660 million computers 
D)y = 12.2x + 20.94; 93.910 million computers

Quizplus · Accepted Answer

Using the data given in the table, we can create the following table:

|x | Computers (millions)|
|---|---|
|0 |22.5 |
|1 |34.3 |
|2 |45.5 |
|3 |60.6 |
|4 |77.4 |

We can then use this data to find an equation for the least-squares line.

Let x be the year (where x = 0 corresponds to the beginning of 1998), and y be the number of computers in millions. Using a calculator or statistical software, we can find that the least-squares line for this data set is:

y = 12.2x + 20.94

To estimate the projected number of computers connected to the Internet in Europe at the beginning of 2004, we can substitute x = 6 into the equation (since 2004 is 6 years after the start of 1998):

y = 12.2(6) + 20.94 = 94.14 million computers.

Therefore, the best choice is B.

The Estimated Number of Computers (In Millions) Connected to the Internet