Life expectancy at birth is the average number of years that a person is expected to live. There is huge variation in life expectancies between countries with highest being in japan, and the lowest in some African countries. An important factor for such variability is the availability of suitable health care. Once measure of a person's access to health care is the people-to-physician ration. We expect life expectancy to be lower for countries where this ratio is high. The accompanying table lists a portion of life expectancy of males and females in 40 countries and their corresponding people-to-physician ratio; the complete data, labeled Life Expectancy, are available on the text website.

a. Construct a scatterplot of female life expectancy against the people-to-physician ratio. Superimpose a linear trend and a logarithmic trend to determine the appropriate model.

b. Estimate a simple linear regression model with life expectancy of females as the response variable and the people-to-physician ratio as the explanatory variable. What happens to life expectancy of females as the people-to-physician ratio decreases from 1,000 to 500?

c. Estimate a logarithmic regression model with the natural log of the people-to-physician ratio as the explanatory variable. What happens to life expectancy of females as the people-to-physician ratio decreases from 1,000 to 500?

d. Use the data in Exercise 19 to answer the same four question regarding life expectancy of males. Who is more likely to benefit from adding more physicians to the population? Explain.