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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 |
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 |
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 Cerrados region, as a function of the cultivated area, in millions of acres.
Area (Millions of Acres) | 25 | 30 | 32 | 40 | 52 |
Production (Millions of Tons) | 15 | 25 | 30 | 40 | 60 |
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) |
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Production (Million kilos) |
Profit The following chart shows the net income, in millions of dollars, of the Disney Company for the years 1984-1992.
Stock Prices Repeat the previous exercise, but this time model Walt Disney's stock prices as shown in the following chart:
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 |