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Linear Regression Example Problem
A steel mill began production in 1986 of a special steel alloy, which has the following
production history (production in thousands of tons):
Year (x)
Output (y)
(x 1000 tons)
1986
9.4
1987
10.7
1988
11.0
1990
16.2
1991
22.1
1992
25.8
1993
23.0
1994
24.7
1995
27.3
1996
31.6
(Note that while the time series spans eleven years, only ten years are recorded.)
a.
By simple regression, determine the equation of the straight line which best fits all
the data.
b.
How “good” is the regression (that is, how strong is the correlation between year
index and annual output in kilotons), as measured by the correlation coefficient?
c.
How much of the variability in the annual steel output cannot be accounted for by
regression?
d.
Calculate a production forecast for 1998.
e.
The production records for 1989 were lost during a move of the corporate
headquarters.
Estimate the production for the missing year from the regression line.
f.
Suppose the peak production (capacity) of the present mill is 50,000 tons (y = 50).
When (that is, for what value of x) is capacity expected to be exceeded, if the linear
trend of the regression analysis persists?
g.
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 Fall '08
 SINGER

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