Estimate the conditional average treatment effect (CATE) for below-median water users.

Questions on Ferraro and Price
In the Ferraro-Price data set, the variable percent_report reports the household’s percentile for water use the year before the experiment was conducted (2006). Let’s define “below median” as any household with percent_report<50 and “above median” as any household with percent_report>=50. We have thus defined two subgroups: (1) treated and control households who were below the median; and (2) treated and control households who were at or above the median. Within each subgroup, you can estimate an average treatment effect, known as a conditional average treatment effect (CATE) because it’s an ATE conditional on some characteristic of the experimental units.
1a. Estimate the conditional average treatment effect (CATE) for below-median water users. You can estimate this CATE by either calculating a simple difference-in-means in summer 2007 water use  between treated and control groups or by regressing summer 2007 water use on treat3, water_2006, and apr_may07 . For calculating standard errors, you can either use formula 3.6 in your textbook (like in HW1) or the output that Excel reports from the regression .
1b. Estimate the standard error of the estimated CATE for below-median water users.
1c. What is the 95% confidence interval of the estimated CATE for below-median water users?

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