Greenwood press

LINEAR FUNCTIONS
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tion, the absolute value of r is equal to 0.88, indicating that the line is a pretty
good model for the data.
The linear equation acts as an approximate prediction of the relationship
between time and year. This predicted pattern is much more reliable within the
range of data, so the variables may not have the same relationship for future
Olympics. After all, the line should eventually level off, because the runners will
never be able to run a time equal to zero! Therefore, this line is most useful to
make predictions between 1900 and 2000, such as estimating the winning times
when the Olympics did not occur or when participation was reduced (often due
to world conflicts). For example, there is no time for 1944 because the Olympics
were suspended during World War II. The time that might have been achieved in
the 1944 Olympics could be estimated using the linear model Predicted Time =
–0.01119Year + 32.185 by substituting 1944 for Year. That gives a predicted win-
ning time of 10.43 seconds. Linear relationships are also common with winning
times and championship performances in many other Olympic events.
Forensic scientists use linear functions to predict the height of a person based
on the length of his arm or leg bones. This information can be useful in identify-
ing missing people and tracing evolutionary patterns in human growth over time.
When a complete skeleton cannot be found, then the height of the deceased per-
son can be predicted by identifying the person’s sex and finding the length of his
or her femur, tibia, humerus, or radius. For example, the height 
h in centimeters
of a male can be estimated by the linear equation 
h = 69.089 + 2.238f , where
f is the length of the femur bone in centimeters. In addition, the linear equation
s = –0.06(a − 30) or s = –0.06a + 1.80 is the amount of shrinkage s for indi-
viduals of age 
a greater than 30 that needs to be accounted for in the height of a
deceased person. For example, if the person had an estimated age of 
60 at death,
then –
0.06(60) + 1.80 = –1.80 cm would be included in the height prediction.
Ever feel cold in an airplane? The outside temperature decreases linearly with
an increase in altitude. The equation 
t = –0.0066a + 15 has been described as a
linear model that compares the temperature 
t (°C) with the altitude a (meters)
when the ground temperature is 15°. Recognizing this relationship helps engi-
neers design heating and cooling systems on the airplanes so that metal alloys
can adapt to the changes in temperature and passengers obtain reasonable air