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Question: Suppose you are interested in studying the effect of clean water on school attendance in developing countries. You find a program that installed water filtration systems in 25 Kenyan villages. You collect data on the 25 villages that receive water filtration and 25 villages that do not receive the water filtration. Your data includes 10 years of village school attendance, the year that water filtration was installed, and whether filtration was ever installed. (You can assume water filtration systems were all installed in the same year.)
(a) Write out an estimating equation to determine the effect of clean water on school attendance. (Be sure to have the proper subscripts.)
(b) Carefully describe the interpretation of each coefficient (including the constant) in your proposed regression.
(c) After presenting your research a skeptic tells you that the villages that received water filtration systems started with worse school attendance before the filtration system was added. Is this a problem? Why or why not? Explain a scenario that could bias our results.
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