Finite mathematics exercises: linear and exponential regression |

In Exercises 1–4 calculate the value of SSE for the given points and line.

The use of technology to compute regression lines is recommended in the applications exercises below.

** Pollution Control ** According to surveys, the percentage of new plant and equipment expenditures by US manufacturing companies allocated to pollution control in the period 1975–1987 was as shown:*

1975 | 1980 | 1981 | 1984 | 1987 |

9.3 | 4.8 | 4.3 | 3.3 | 4.3 |

*Source:

Obtain a linear regression model of the form y = mx + b where x is time in years since 1975, and use it to estimate the figure for 1985. (Round your regression coefficients to four decimal places, and the predicted value for 1985 to one decimal place.)

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

1975 | 1980 | 1981 | 1984 | 1987 |

**Figures are approximate (partially randomized). Source:

Obtain a linear regression model of the form y = mx + b where x is time in years since 1970, and use it to estimate the figure for 1988. (Round your regression coefficients to four decimal places, and the predicted value for 1988 to one decimal place.)

** Soybean Production: Brazil** The following table shows soybean production, in millions of tons, in Brazil's

Area(Millions of Acres) | 25 | 30 | 32 | 40 | 52 |

Production(Millions of Tons) | 15 | 25 | 30 | 40 | 60 |

*Source: Brazil Agriculture Ministry/

** Soybean Production: Mars** The following table shows soybean production, in millions of kilos, in the recently cultivated foothills of Olympus Mons, as a function of the cultivated area, in thousands of square meters.

Area(Thousand sq. meters) |
|||||

Production(Million kilos) |

*Source: Mars Imperial Ministry of Food/

** Profit **The following chart shows the net income, in millions of dollars, of the Disney Company for the years 1984-1992.

Profits estimated to the nearest $5 million.

Source: Company Reports/

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

Source: Company Reports/

** Power Usage **Here are some data and a graph showing monthly electricity use versus the size of a home:

Size (thousand sq. ft) \pmb{x} | 1.29 | 1.35 | 1.47 | 1.60 | 1.71 | 1.84 | 1.98 | 2.23 | 2.40 | 2.93 |

Usage (kw-hrs) \pmb{y} | 1180 | 1170 | 1260 | 1490 | 1570 | 1710 | 1800 | 1840 | 1960 | 1950 |

** Housing Costs: Mars **
The cost of housing in Utarek, Mars, goes up rapidly with size, due to the extreme limitations of space. The following table shows the cost of housing in zonars () for various size dwellings.

Size x (hundred sq. m) |
||||||

Price y ( million) |

** 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.

** Beer **The following chart shows approximate after-tax profits, in millions of dollars, of South African Breweries for the years 1991 through 1997.

*Last Updated: January 2008
Copyright © 2008 Stefan Waner*