The management of Kaldor, a manufacturer of electric motors, submitted the following data in the annual report to its stockholders. The table shows the net sales (in millions of dollars) during the 5 years that have elapsed since the new management team took over. (The first year the firm operated under the new management corresponds to the time period , and the four subsequent years correspond to .) Determine the equation of the least-squares line for these data and use it to predict the net sales for the upcoming year.
A) 485.8 millions of dollars
B) 529.8 millions of dollars
C) 519.8 millions of dollars
D) 512.8 millions of dollars
E) 552.8 millions of dollars

Question

The management of Kaldor, a manufacturer of electric motors, submitted the following data in the annual report to its stockholders. The table shows the net sales (in millions of dollars) during the 5 years that have elapsed since the new management team took over. (The first year the firm operated under the new management corresponds to the time period  , and the four subsequent years correspond to  .)  Determine the equation of the least-squares line for these data and use it to predict the net sales for the upcoming year.
A) 485.8 millions of dollars 
B) 529.8 millions of dollars 
C) 519.8 millions of dollars 
D) 512.8 millions of dollars 
E) 552.8 millions of dollars

Quizplus · Accepted Answer

Using the given data, we can create a scatter plot of net sales versus year and visually see that there is a positive linear relationship between the two variables.

To find the equation of the least-squares line, we can use the formula:

y = a + bx

where y is the net sales, x is the year (with the first year being 0), a is the y-intercept, and b is the slope.

Using technology, we can find that the equation of the least-squares line is:

y = 425.24 + 22.3x

To predict the net sales for the upcoming year (which would be year 5), we can substitute x = 5 into the equation:

y = 425.24 + 22.3(5) 
y = 529.74

Therefore, the predicted net sales for the upcoming year is $529.8 million.

The best choice is B.

The Management of Kaldor, a Manufacturer of Electric Motors, Submitted