Use the data in Exercise $24$ to answer the same four questions regarding life expectancy of males. Who is more likely to benefit from adding more physicians to the population? Explain.

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 the life expectancy of females as the people$-$to$-$physician ratio decreases from $1,000$ to $500?$

d$.$ Use R$2$ to determine which of the preceding two models is more appropriate.