For the National Life Expectancies data in the book website https://instruction.bus.wisc.edu/jfrees/jfreesbooks/regression%20modeling/bookwebdec2010

1. Examining the relation between y = LIFEEXP and x = FERTILITY. 2. Fit a linear regression model of LIFEEXP using the explanatory variable x = FERTILITY. 3. The United States has a FERTILITY rate of 2.0. Determine the fitted life expectancy. 4. The island nation Dominica did not report a FERTILITY rate and thus was not included in the regression. Suppose that its FERTILITY rate is 2.0. Provide a 95% prediction interval for the life expectancy in Dominica. 5. China has a FERTILITY rate of 1.7 and a life expectancy of 72.5. Determine the residual under the model. How many multiples of s is this residual from zero? 6. Now fit a regression model on LIFEEXP using three explanatory variables, FERTILITY, PUBLICEDUCATION, and InHEALTH (the natural logarithmic transform of PRIVATEHEALTH). a. Interpret the regression coefficient associated with public education. b. Interpret the regression coefficient associated with health expenditures without using the logarithmic scale for expenditures. c. Based on the model fit, is PUBLICEDUCATION a statistically significant variable? To respond to this question, use a formal test of hypothesis. State your null and alternative hypotheses, decision-making criterion, and decision-making rule. 7. Make an overall comment for the non-statistician audience