13-14 For each scatter plot, decide what type of function you might choose as a model for the data. Explain your choices. 13. (a) 14. (a) (b) y 15. The table shows (lifetime) peptic ulcer rates (per 100 popu- lation) for various family incomes as reported by the 1989 National Health Interview Survey. Temperature (°F) Chirping rate (chirps/min) 50 20 55 46 60 79 65 91 70 113 75 140 80 173 85 198 90 211 (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Use the linear model in part (b) to estimate the chirping rate at 100 °F. 17. The table gives the winning heights for the Olympic pole vault competitions in the 20th century. Year Height (ft) Year Height (ft) 1900 10.83 1956 14.96 1904 11.48 1960 15.42 1908 12.17 1964 16.73 1912 12.96 1968 17.71 1920 13.42 1972 18.04 1924 12.96 1976 18.04 1928 13.77 1980 18.96 1932 14.15 1984 18.85 1936 14.27 1988 19.77 1948 14.10 1992 19.02 1952 14.92 1996 19.42 Ulcer rate Income (per 100 population) $4,000 14.1 $6,000 13.0 $8,000 13.4 $12,000 12.5 $16,000 12.0 $20,000 12.4 $30,000 10.5 $45,000 9.4 $60,000 8.2 (a) Make a scatter plot of these data and decide whether a linear model is appropriate. (b) Find and graph a linear model using the first and last data points. (a) Make a scatter plot and decide whether a linear model is appropriate. (b) Find and graph the regression line. (c) Use the linear model to predict the height of the win- ning pole vault at the 2000 Olympics and compare with the winning height of 19.36 feet. (d) Is it reasonable to use the model to predict the winning height at the 2100 Olympics? 18. A study by the U.S. Office of Science and Technology in 1972 estimated the cost (in 1972 dollars) to reduce auto- mobile emissions by certain percentages: (c) Find and graph the least squares regression line. (d) Use the linear model in part (c) to estimate the ulcer rate for an income of $25,000. (e) According to the model, how likely is someone with an income of $80,000 to suffer from peptic ulcers? (f) Do you think it would be reasonable to apply the model to someone with an income of $200,000? 16. Biologists have observed that the chirping rate of crickets of a certain species appears to be related to temperature. The table shows the chirping rates for various temperatures. Reduction in emissions (%) Cost per car (in $) Reduction in emissions (%) Cost per car (in $) 50 45 75 90 55 55 80 100 60 62 85 200 65 70 90 375 70 80 95 600 Find a model that captures the "diminishing returns" trend of these data.