SOLUTION: The least-squares regression line (line-of-best-fit) for volume (in millions of shares) of a company's stock as a function of time is given by S(t) = 18-0.46t, t months after the b

Question 985838: The least-squares regression line (line-of-best-fit) for volume (in millions of shares) of a company's stock as a function of time is given by S(t) = 18-0.46t, t months after the beginning of the year. The linear correlation coefficient relating stock and time is -0.88.
a) Is the linear relationship between the two variables strong or weak?
b) Is the linear relationship positive or negative?
c) What does the model predict the volume of the stock will be at the end of the year?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

The linear correlation is fairly strong since -0.88 is somewhat close to -1. The closer you get to +1 or -1, the stronger the linear correlation is.

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b)

This linear correlation is negative because r is negative. Over time, the volume of shares traded is decreasing.

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c)

At the end of the year is t = 12 months. Plug this value into the regression line function

S(t) = 18 - 0.46t
S(12) = 18 - 0.46*12
S(12) = 12.48

The predicted volume at the end of the year is approximately 12.48 million shares.
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