Lead is toxic, particularly for young children, and for this reason, government regulations severely restrict the amount of lead in our environment. But this was not always the case. In the early part of the 20th century, the underground water pipes in many U.S. cities contained lead, and lead from these pipes leached into drinking water. In this exercise, you will investigate the effect of these lead water pipes on infant mortality. On the ELE (assessment page), you will find the data file “lead_mortality.csv”, which contains data on infant mortality, type of water pipes (lead or nonlead), water acidity (ph), and several demographic variables for 172 U.S. cities in 1900.

a. Compute the average infant mortality rate (infrate) for cities with lead pipes and for cities with nonlead pipes. Is there a statistically significant difference in the averages?

b. The amount of lead leached from lead pipes depends on the chemistry of the water running through the pipes. The more acidic the water is (that is, the lower its ph), the more lead is leached. Run a regression of infrate on lead, ph, and the interaction term lead * ph.

i. The regression includes four coefficients (the intercept and the three coefficients multiplying the regressors). Explain what each coefficient measures.

ii. Plot the estimated regression function relating infrate to ph for Lead = 0 and for Lead = 1. Describe the differences in the regression functions, and relate these differences to the coefficients you discussed in (i).

iii. Does Lead have a statistically significant effect on infant mortality? Explain. Does the effect of Lead on infant mortality depend on ph? Is this dependence statistically significant?

iv. What is the average value of ph in the sample? At this ph level, what is the estimated effect of Lead on infant mortality? What is the standard deviation of ph? Suppose the ph level is one standard deviation lower than the average level of ph in the sample: What is the estimated effect of Lead on infant mortality? What if ph is one standard deviation higher than the average value?

c. The analysis in (b) may suffer from omitted variable bias because it neglects factors that affect infant mortality and that might potentially be correlated with lead and ph. Investigate this concern, using the other variables in the data set. What happened to the previous estimated slope coefficients after including other variables?

Answer rating: 100% (QA)

a The average infant mortality rate for cities with lead pipes is 17817 while the average infant mortality rate for cities with nonlead pipes is 13470 ... View the full answer