10-5 Nonlinear Regression 569 8. Sound Intensity The table lists intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity. Sound Intensity 316 500 750 2000 5000 Scale Value 25.0 27.0 28.75 33.0 37.0 9. Population Growth Here are the values of the world population (billions) beginning with the year 2000: 6.15 6.22 6.30 6.38 6.46 6.54 6.62 6.71 6.79 6.87 6.96 7.04 7.13 7.21 7.30 7.38 7.47 7.55 7.63 7.71 10. Deaths from Motor Vehicle Crashes Listed below are the numbers of deaths in the United States resulting from motor vehicle crashes. Use the best model to find the projected number of such deaths for the year 2025. Year 1975 1980 1985 1990 1995 2000 2005 2010 2015 Deaths 44,525 51,091 43,825 44,599 41,817 41,945 43,443 32,708 35,485 11. Richter Scale The table lists different amounts (metric tons) of the explosive TNT and the corresponding value measured on the Richter scale resulting from explosions of the TNT. TNT 2 10 15 50 100 500 Richter Scale 3.4 3.9 4.0 4.4 4.6 5.0 12. Detecting Fraud Leading digits of check amounts are often analyzed for the purpose of detecting fraud. The accompanying table lists frequencies of leading digits from checks written by the author (an honest guy). Leading Digit 1 2 3 4 5 6 7 8 9 Frequency 83 58 27 21 21 21 6 4 9 13. Stock Market Listed below in order by row are the annual high values of the Dow Jones Industrial Average for each year beginning with 2000. Find the best model and then predict the value for the last year listed. Is the predicted value close to the actual value of 26,828.4? 11723.0 11337.9 10635.3 10453.9 10854.5 10940.5 12510.6 14164.5 13058.2 10548.5 11585.4 12810.5 13610.2 16576.7 18053.7 18312.4 19974.6 24837.5 26828.4 14. Sunspot Numbers Listed below in order by row are annual sunspot numbers beginning with 1980. Is the best model a good model? Carefully examine the scatterplot and identify the pattern of the points. Which of the models fits that pattern? 154.6 140.5 115.9 66.6 45.9 17.9 13.4 29.2 100.2 157.6 142.6145.7 94.354.6 29.9 17.5 8.6 21.5 64.3 93.3 119.6123.3123.365.940.429.815.2 7.5 2.9 3.1 16.5 55.7 57.664.7 79.3 44.6 24.5 13.8 4.0 15. Earthquakes Listed below are earthquake depths (km) and magnitudes (Richter scale) of different earthquakes. Find the best model and then predict the magnitude for the last earthquake with a depth of 3.78 km. Is the predicted value close to the actual magnitude of 7.1? Depth 6.00 7.00 5.4 17.60 15.90 11.70 17.30 22.40 15.90 3.78 Magnitude 3.62 3.06 3.3 2.58 2.91 3.38 2.79 2.61 3.137.10
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