Greenwood press
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book-20600
LINEAR FUNCTIONS
51 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 Download 1.81 Mb. Do'stlaringiz bilan baham: |
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