Chapter B.5, Problem 107E

Infant Mortality Rates. In the article “Children's Environmental Index," the ZPG Reporter (September. 1997) provided data for 219 U.S. cities or 20 variables that measure aspects of the quality of life for children. In this exercise, we consider the relationship between infant mortality rate (1990-1994) and the following 11 predictor variables.

  1. Density (population per square mile)

  2. Birth rate per 1000 population (1988)

  3. Percentage of births to teens (1994)

  4. Physicians per 1000 population (1995)

  5. Student-to-teacher ratio in schools (1993–1994)

  6. Student drop-out rate (1990)

  7. Unemployment rate (1995)

  8. Percentage of children in poverty (1989)

  9. Violent crimes per 1000 population (1995)

  10. Percentage of juvenile arrests (1995)

  11. Pounds of toxic releases per 1000 population (1994)

  We will use the data in the table on pages B-145–B-147, obtained from the article, for 50 cities chosen randomly from the 219 cities considered. Use the technology of your choice to do the following.

1. a. Use the forward selection method to obtain a regression equation for the data. (Take t_enter = 2.00, α_enter = 0.05.)
2. b. Use the backward elimination method to obtain a regression equation for the data. (Take t_remove = 2.00, α_remove = 0.05.)
3. c. Use stepwise regression to obtain a regression equation for the data. (Take t_enter = t_remove = 2.00, α_enter = α_remove = 0.05.)
4. d. Are the regression equations obtained in parts (a), (b), and (c) the same?
5. e. For the regression equation selected by stepwise regression in part (c) obtain plots of residuals versus fitted values, residuals versus the included predictor variables, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.