Exercises for

Calculus Applied to the Real World

This Topic: Regression: Fitting Functions to Data


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Finite Mathematics Applied to the Real World

Calculus Applied to the Real World

Finite Mathematics & Calculus Applied to the Real World

Find the regression line associated with each of the sets of points in Exercises 1-4. Graph the data and the best fit line.

The use of technology will be helpful in Exercises 5-24.

5. Pollution Control According to recent surveys, the percentage of new plant and equipment expenditures by US manufacturing companies on pollution control is as shown:*

19751980198119841987
9.34.84.33.34.3

Use a linear regression model to estimate the figure for 1985. (Round your answer to one decimal place.)

*Source: Survey of Current Business 58, 62, 66, 68

6. Pollution Control The percentage of new plant and equipment expenditures by US public utility companies on pollution control is as shown:**

19751980198119841987
8.48.17.36.85.1

Use a linear regression model to estimate the figure for 1985. (Round answer to one decimal place.)

**Source: Survey of Current Business 58, 62, 66, 68

7. Oil Recovery In 1978, Congress conducted a study of the amount of additional oil that can be extracted from existing oil wells by "enhanced recovery techniques" (such as injecting solvents or steam into an oil well to lower the density of the oil). As the price of oil increases, the amount of oil that can be recovered economically in this manner also increases. The following table gives the study's estimates of recoverable oil based on the price per barrel:*

Price per Barrel$12$14$22$30
Recovery (billions of barrels)21.229.441.649.2

Use a best fit line to estimate the additional amount of oil that can be economically recovered if the price of oil were to drop to $10 per barrel. (Round your answer to one decimal place.)

*Source: U.S. Congress, Office of Technology Assessment, Enhanced Oil Recovery Potential in the U.S. (Washington, CD: OTA, 1978): 7. The recovery figures are based on a 10% minimum rate of return, and the prices are in constant 1976 dollars and rounded to the nearest $1.

9. Profit The following chart shows the net income of the Walt Disney Company for the years 1984-1992.**

Find a least squares fit linear model for this data. (Find profit p as a function of the year t, with t = 0 corresponding to 1980.) Use your model it to estimate Disney's profit (to the nearest million dollars) in 1993.

Answer for 9

**Profits estimated to the nearest $5 million. Source: Company Reports/The New York Times, December, 1992, p. D1.

10. Stock Prices Repeat the previous exercise, but this time model Walt Disney's stock prices as shown in the following chart#

#Stock prices are rough approximations. Source: Company Reports/The New York Times, December, 1992, p. D1.

Find the regression exponential curve associated with each of the sets of points in Exercises 11-14. Graph the data and the regression curve.

15. Big Brother In 1995, the FBI was seeking the ability to monitor 74,250 phone lines at once. The following chart shows the number of phone lines monitored from 1987 through 1993.

Source: Electronic Privacy Information Center, Justice Department, Administrative Office of the United States Courts/The New York Times, November 2, 1995, p. D5.

Use an exponential model of this data to project the number of phone lines tapped by the FBI in 1999. (Round your answer to the nearest 100 phone lines.)

16. Beer The following table shows after-tax profits of South African Breweries for the years 1991 through 1997.

Year199119921993194199519961997
Profit ($ million)330340360400500580600

Data are rounded. Source: Comapny reports/Bloomberg Financial Markets/The New York Times, August 27, 1997.

Use an exponential regression of the data to predict SAB's profit in 2000.


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Finite Mathematics Applied to the Real World

Calculus Applied to the Real World

Finite Mathematics & Calculus Applied to the Real World

Last Updated:February, 1998
Copyright © 1998 StefanWaner and Steven R. Costenoble